Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Hauptseminar zur Geldtheorie und –politik im WS 2012/13
Hinweis:
Die nachfolgenden Übungsaufgaben entstanden mit der Hilfe von EViews6 (Student
Edition) und beziehen sich auf die Orginaldaten der EZB (ecb.int) für die Jahre 1999-2012
(Monatsdaten aus den Monatsberichten der EZB).
Welche Fragen sind bei den einzelnen Aufgaben zu
beantworten:
a. Was zeigen die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten eine gewisse Relevanz besitzen?
Einführung: Das EViews und dessen Anwendungsmöglichkeiten
Beispiel a
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
4,000
5,000
6,000
7,000
8,000
9,000
10,000
1,998 2,000 2,002 2,004 2,006 2,008 2,010 2,012 2,014
ZEIT
M3
8.4
8.5
8.6
8.7
8.8
8.9
9.0
9.1
9.2
9.3
1,998 2,000 2,002 2,004 2,006 2,008 2,010 2,012 2,014
ZEIT
LOG
(M3)
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
-2
0
2
4
6
8
10
12
1,998 2,000 2,002 2,004 2,006 2,008 2,010 2,012 2,014
ZEIT
DM
3
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Aufgabe b
a. Was zeigt die nachfolgende Darstellung?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
-.008
-.004
.000
.004
.008
.012
.016
.020
1,998 2,000 2,002 2,004 2,006 2,008 2,010 2,012 2,014
ZEIT
DLO
G(M
3)
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Aufgabe c
a. Was zeigt die nachfolgende Darstellung?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
0
2
4
6
8
10
12
14
16
1,998 2,000 2,002 2,004 2,006 2,008 2,010 2,012 2,014
ZEIT
DM
1
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
0
5
10
15
20
25
5000 6000 7000 8000 9000 10000
Series: M3Sample 1 162Observations 162
Mean 7223.951Median 6986.500Maximum 9927.000Minimum 4481.000Std. Dev. 1844.050Skewness 0.068402Kurtosis 1.473829
Jarque-Bera 15.84841Probability 0.000362
0
4
8
12
16
20
8.500 8.625 8.750 8.875 9.000 9.125
Series: LOG(M3)Sample 1 162Observations 162
Mean 8.851511Median 8.851735Maximum 9.203014Minimum 8.407602Std. Dev. 0.262777Skewness -0.132001Kurtosis 1.563622
Jarque-Bera 14.39692Probability 0.000748
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
0
2
4
6
8
10
12
14
16
0 2 4 6 8 10 12
Series: DM3Sample 1 162Observations 162
Mean 6.048148Median 6.450000Maximum 11.70000Minimum -0.400000Std. Dev. 2.955450Skewness -0.405147Kurtosis 2.495132
Jarque-Bera 6.152409Probability 0.046134
0
4
8
12
16
20
24
-0.005 0.000 0.005 0.010 0.015 0.020
Series: DLOG(M3)Sample 1 162Observations 161
Mean 0.004928Median 0.004799Maximum 0.019389Minimum -0.007200Std. Dev. 0.005108Skewness 0.239434Kurtosis 3.094435
Jarque-Bera 1.598146Probability 0.449746
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Aufgabe d
a. Was zeigt die nachfolgende Darstellung?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Null Hypothesis: M3 has a unit root Exogenous: Constant Lag Length: 3 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -0.452860 0.8958
Test critical values: 1% level -3.471987 5% level -2.879727 10% level -2.576546
*MacKinnon (1996) one-sided p-values.
Null Hypothesis: LOG(M3) has a unit root
0
5
10
15
20
25
30
35
40
-0.02 0.00 0.02 0.04 0.06
Series: DLOG(M1)Sample 1 162Observations 161
Mean 0.006229Median 0.005374Maximum 0.065993Minimum -0.033987Std. Dev. 0.012792Skewness 0.646423Kurtosis 6.034488
Jarque-Bera 72.98376Probability 0.000000
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -2.082703 0.2520
Test critical values: 1% level -3.471454 5% level -2.879494 10% level -2.576422
*MacKinnon (1996) one-sided p-values.
Null Hypothesis: DM3 has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -0.888714 0.7898
Test critical values: 1% level -3.471192 5% level -2.879380 10% level -2.576361
*MacKinnon (1996) one-sided p-values.
Null Hypothesis: DLOG(M3) has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -9.829006 0.0000
Test critical values: 1% level -3.471454 5% level -2.879494 10% level -2.576422
*MacKinnon (1996) one-sided p-values. Null Hypothesis: DLOG(M1) has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -14.37861 0.0000
Test critical values: 1% level -3.471454 5% level -2.879494 10% level -2.576422
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
*MacKinnon (1996) one-sided p-values.
Aufgabe e
a. Was zeigt die nachfolgende Darstellung?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Aufgabe f
a. Was zeigt die nachfolgende Darstellung?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
-.015
-.010
-.005
.000
.005
.010
.015
8.2
8.4
8.6
8.8
9.0
9.2
9.4
25 50 75 100 125 150
LOG(M3) Trend Cycle
Hodrick-Prescott Filter (lambda=100)
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Date: 08/18/12 Time: 09:20 Sample (adjusted): 6 159 Included observations: 154 after adjustments Trend assumption: Linear deterministic trend Series: LOG(M3) LOG(BIPNOM) Lags interval (in first differences): 1 to 4
Unrestricted Cointegration Rank Test (Trace) Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.** None * 0.104189 20.12161 15.49471 0.0093
At most 1 0.020422 3.177619 3.841466 0.0746 Trace test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Pairwise Granger Causality Tests Date: 08/18/12 Time: 09:22 Sample: 1 162 Lags: 2
Null Hypothesis: Obs F-Statistic Prob. LOG(BIPNOM) does not Granger Cause LOG(M3) 157 13.0782 6.E-06
LOG(M3) does not Granger Cause LOG(BIPNOM) 7.24216 0.0010
Aufgabe g
a. Was zeigt die nachfolgende Darstellung?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Pairwise Granger Causality Tests Date: 04/05/12 Time: 11:42 Sample: 1 158 Lags: 2
Null Hypothesis: Obs F-Statistic Prob.
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
LOG(BIPNOM) does not Granger Cause LOG(M2) 154 11.7973 2.E-05 LOG(M2) does not Granger Cause LOG(BIPNOM) 6.72610 0.0016
Thema 1: Die Geldnachfrage, empirische Analysen und
theoretische Grundlagen
Aufgabe 1-a
a. Was zeigt die nachfolgenden
Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten
relevant sein?
System: UNTITLED Estimation Method: Least Squares Date: 08/17/12 Time: 22:03 Sample: 2 159 Included observations: 158 Total system (balanced) observations 158
Coefficient Std. Error t-Statistic Prob. C(1) 0.616271 0.032235 19.11797 0.0000
C(4) 0.158640 0.024430 6.493647 0.0000 C(5) 0.442508 0.063903 6.924729 0.0000 C(6) -0.164082 0.013375 -12.26772 0.0000
Determinant residual covariance 8.18E-05
Equation: LOG(M1) = C(1)*LOG(M1(-1)) + C(4)*LOG(BIPREAL) + C(5) *LOG(PREISNIVEAU) + C(6)*VMEINS Observations: 158 R-squared 0.999210 Mean dependent var 8.032599 Adjusted R-squared 0.999194 S.D. dependent var 0.322778 S.E. of regression 0.009162 Sum squared resid 0.012928 Durbin-Watson stat 1.784182
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
System: UNTITLED Estimation Method: Least Squares Date: 08/17/12 Time: 22:23 Sample: 1 159 Included observations: 159 Total system (balanced) observations 159
Coefficient Std. Error t-Statistic Prob. C(4) 0.286191 0.042915 6.668776 0.0000
C(5) 1.374744 0.075329 18.24976 0.0000 C(6) -0.407853 0.007344 -55.53712 0.0000
Determinant residual covariance 0.000275
Equation: LOG(M1) = C(4)*LOG(BIPREAL) + C(5)*LOG(PREISNIVEAU) + C(6)*VMEINS Observations: 159 R-squared 0.997377 Mean dependent var 8.029204 Adjusted R-squared 0.997343 S.D. dependent var 0.324591 S.E. of regression 0.016730 Sum squared resid 0.043663 Durbin-Watson stat 0.662022
Aufgabe 1-b
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
System: UNTITLED Estimation Method: Least Squares Date: 09/01/10 Time: 16:20 Sample: 2 138 Included observations: 137 Total system (balanced) observations 137
Coefficient Std. Error t-Statistic Prob. C(1) 0.846890 0.032640 25.94626 0.0000
C(3) 2.297894 0.481042 4.776908 0.0000 C(4) -0.380303 0.089447 -4.251711 0.0000
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Determinant residual covariance 0.921969
Equation: DM1 = C(1)*DM1(-1) + C(3) + C(4)*ZINS1TAG Observations: 137 R-squared 0.914254 Mean dependent var 8.235766 Adjusted R-squared 0.912975 S.D. dependent var 3.291114 S.E. of regression 0.970881 Sum squared resid 126.3098 Durbin-Watson stat 2.108940
System: UNTITLED Estimation Method: Least Squares Date: 09/01/10 Time: 16:21 Sample: 1 138 Included observations: 138 Total system (balanced) observations 138
Coefficient Std. Error t-Statistic Prob. C(4) 2.190073 0.163256 13.41494 0.0000 Determinant residual covariance 34.41398
Equation: DM1 = C(4)*ZINS1TAG Observations: 138 R-squared -2.130266 Mean dependent var 8.284058 Adjusted R-squared -2.130266 S.D. dependent var 3.327792 S.E. of regression 5.887714 Sum squared resid 4749.129 Durbin-Watson stat 0.042822
System: UNTITLED Estimation Method: Least Squares Date: 09/01/10 Time: 16:34 Sample: 4 138 Included observations: 135 Total system (balanced) observations 135
Coefficient Std. Error t-Statistic Prob. C(2) -0.188738 0.085026 -2.219756 0.0281
C(3) 0.014008 0.003007 4.658211 0.0000 C(4) -0.001972 0.000930 -2.119696 0.0359
Determinant residual covariance 0.000165
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Equation: DLOG(M1) = C(2)*DLOG(M1(-2)) + C(3) + C(4)*ZINS1TAG Observations: 135 R-squared 0.057016 Mean dependent var 0.007124 Adjusted R-squared 0.042729 S.D. dependent var 0.013286 S.E. of regression 0.012999 Sum squared resid 0.022306 Durbin-Watson stat 2.374492
System: UNTITLED Estimation Method: Least Squares Date: 09/01/10 Time: 16:35 Sample: 2 138 Included observations: 137 Total system (balanced) observations 137
Coefficient Std. Error t-Statistic Prob. C(1) 0.817725 0.034261 23.86749 0.0000
C(3) 2.870851 0.529761 5.419144 0.0000 C(4) -0.464364 0.093957 -4.942282 0.0000
Determinant residual covariance 0.885021
Equation: DM1 = C(1)*DM1(-1) + C(3) + C(4)*ZINS3MT Observations: 137 R-squared 0.917691 Mean dependent var 8.235766 Adjusted R-squared 0.916462 S.D. dependent var 3.291114 S.E. of regression 0.951228 Sum squared resid 121.2478 Durbin-Watson stat 2.137275
System: UNTITLED Estimation Method: Least Squares Date: 08/18/12 Time: 10:09 Sample: 2 158 Included observations: 157 Total system (balanced) observations 157
Coefficient Std. Error t-Statistic Prob. C(1) 0.962964 0.017061 56.44333 0.0000
C(4) 0.072329 0.035570 2.033453 0.0437 Determinant residual covariance 0.256223
Equation: DM3 = C(1)*DM3(-1) + C(4)*ZINS1J(4) Observations: 157
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
R-squared 0.970602 Mean dependent var 6.127389 Adjusted R-squared 0.970413 S.D. dependent var 2.961692 S.E. of regression 0.509440 Sum squared resid 40.22698 Durbin-Watson stat 1.874277
Aufgabe 1-c
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Dependent Variable: VMEINS Method: ML - ARCH (Marquardt) - Normal distribution Date: 09/01/10 Time: 16:45 Sample (adjusted): 2 135 Included observations: 134 after adjustments Convergence achieved after 50 iterations Presample variance: backcast (parameter = 0.7) VMEINS=C(1)*VMEINS(-1)+C(2)*ZINS5J(-1) GARCH = C(3) + C(4)*RESID(-1)^2 + C(5)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob. C(1) 0.974897 0.000116 8376.893 0.0000
C(2) 0.014747 0.000308 47.92105 0.0000 Variance Equation C 1.14E-05 9.33E-06 1.221279 0.2220
RESID(-1)^2 -0.051199 0.010430 -4.909009 0.0000 GARCH(-1) 1.041782 0.008010 130.0634 0.0000
R-squared 0.988607 Mean dependent var 2.684851
Adjusted R-squared 0.988520 S.D. dependent var 0.444547 S.E. of regression 0.047630 Akaike info criterion -3.590419 Sum squared resid 0.299463 Schwarz criterion -3.482290 Log likelihood 245.5580 Hannan-Quinn criter. -3.546479 Durbin-Watson stat 2.381734
Aufgabe 1-d
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
System: UNTITLED Estimation Method: Least Squares Date: 09/01/10 Time: 16:49 Sample: 2 136 Included observations: 135 Total system (balanced) observations 135
Coefficient Std. Error t-Statistic Prob. C(1) 0.919391 0.014998 61.29954 0.0000
C(3) -0.579991 0.113220 -5.122669 0.0000 C(4) 0.144821 0.027231 5.318223 0.0000
Determinant residual covariance 2.08E-05
Equation: LOG(M3) = C(1)*LOG(M3(-1)) + C(3) + C(4)*LOG(BIPNOM(-1)) Observations: 135 R-squared 0.999638 Mean dependent var 8.792656 Adjusted R-squared 0.999633 S.D. dependent var 0.240358 S.E. of regression 0.004607 Sum squared resid 0.002802 Durbin-Watson stat 1.650142
Aufgabe 1-e
a. Was zeigt die nachfolgende Darstellung?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
System: UNTITLED Estimation Method: Least Squares Date: 08/18/12 Time: 10:20 Sample: 14 158 Included observations: 145 Total system (balanced) observations 145
Coefficient Std. Error t-Statistic Prob. C(1) 0.265201 0.074576 3.556115 0.0005
C(2) -0.064257 0.065892 -0.975176 0.3314 C(3) 2.054688 0.620160 3.313156 0.0012 C(4) -0.008088 0.012407 -0.651834 0.5157 C(5) 0.072619 0.026842 2.705477 0.0078 C(6) -0.050409 0.041412 -1.217263 0.2258 C(7) -1.530651 0.395254 -3.872581 0.0002 C(8) -0.019889 0.027352 -0.727168 0.4685 C(9) 0.712680 0.061188 11.64737 0.0000
C(10) 0.004268 0.006904 0.618142 0.5376 C(11) -0.014854 0.002980 -4.983994 0.0000 C(12) 0.070994 0.082576 0.859740 0.3916 C(13) -0.783042 0.311873 -2.510776 0.0133 C(14) 0.197866 0.333262 0.593726 0.5538 C(15) 1.445864 0.436140 3.315138 0.0012 C(16) -1.084843 0.292992 -3.702630 0.0003 C(17) -0.069607 0.369142 -0.188564 0.8507 C(18) 0.833740 0.181407 4.595963 0.0000 C(19) -0.380178 0.131628 -2.888273 0.0046 C(20) -0.204460 0.080182 -2.549961 0.0120
Determinant residual covariance 0.092605
Equation: DM3 = C(1)*DM3(-1) + C(2)*DM3(-2) + C(3) + C(4) *DARBEITSLOSE + C(5)*DBIPNOM + C(6)*DBIPREAL + C(7) *EURUSD(-1) + C(8)*DKREDMFI + C(9)*DM2 + C(10)*DMINDRES + C(11)*DROHSTOFFE(-1) + C(12)*INFLATIONSRATE(1) + C(13)
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
*MINDBIET(2) + C(14)*ZINS1TAG(2) + C(15)*ZINS1MT(2) + C(16) *ZINS3MT(2) + C(17)*ZINS6MT(2) + C(18)*ZINS1J(4) + C(19) *ZINS2J(4) + C(20)*ZMIND Observations: 145 R-squared 0.990156 Mean dependent var 6.166207 Adjusted R-squared 0.988660 S.D. dependent var 3.077815 S.E. of regression 0.327752 Sum squared resid 13.42768 Durbin-Watson stat 1.428978
System: UNTITLED Dependent Variable: DM3 Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/18/12 Time: 10:33 Sample (adjusted): 2 159 Included observations: 158 after adjustments Convergence achieved after 25 iterations Presample variance: backcast (parameter = 0.7) DM3 = C(1)*DM3(-1) + C(5)*DBIPNOM + C(9)*DM2 + C(20)*ZMIND GARCH = C(21) + C(22)*RESID(-1)^2 + C(23)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob. C(1) 0.673177 0.045688 14.73409 0.0000
C(5) 0.114713 0.013447 8.530909 0.0000 C(9) 0.309688 0.047072 6.579016 0.0000
C(20) -0.159888 0.029139 -5.487000 0.0000 Variance Equation C 0.033284 0.075272 0.442190 0.6584
RESID(-1)^2 0.053793 0.085690 0.627763 0.5302 GARCH(-1) 0.740177 0.523781 1.413143 0.1576
R-squared 0.981271 Mean dependent var 6.108861
Adjusted R-squared 0.980906 S.D. dependent var 2.961416 S.E. of regression 0.409214 Akaike info criterion 1.106080 Sum squared resid 25.78823 Schwarz criterion 1.241765 Log likelihood -80.38036 Hannan-Quinn criter. 1.161184 Durbin-Watson stat 1.794855
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
System: UNTITLED Estimation Method: ARCH Maximum Likelihood (Marquardt) Covariance specification: Diagonal VECH Date: 08/18/12 Time: 10:59 Sample: 4 160 Included observations: 157 Total system (balanced) observations 157 Presample covariance: backcast (parameter =0.7) Convergence achieved after 26 iterations
Coefficient Std. Error z-Statistic Prob. C(1) 0.978307 0.007347 133.1592 0.0000
C(4) -8.387092 3.296767 -2.544035 0.0110 C(9) 25.78744 5.844801 4.412030 0.0000
C(11) 1.067216 0.301089 3.544518 0.0004 Variance Equation Coefficients C(12) 0.103543 0.040122 2.580733 0.0099
C(13) 0.406978 0.170635 2.385082 0.0171 C(14) 0.172251 0.170946 1.007639 0.3136
Log likelihood -98.61258 Schwarz criterion 1.481649
Avg. log likelihood -0.628106 Hannan-Quinn criter. 1.400726 Akaike info criterion 1.345383
Equation: DM3 = C(1)*DM3(-1) + C(4)*DLOG(ARBEITSLOSE(-2)) + C(9) *DLOG(M2) + C(11)*DLOG(ZINS1TAG(2)) R-squared 0.975627 Mean dependent var 6.096178 Adjusted R-squared 0.975149 S.D. dependent var 2.982833 S.E. of regression 0.470215 Sum squared resid 33.82864 Durbin-Watson stat 2.081043
Thema 2: Das Geldangebot, empirische Analysen und
theoretische Grundlagen
Aufgabe 2-a
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
xM1=Geldschöpfungsmultiplikator M1 und Kreditschöpfungsmultiplikator
Aufgabe 2-b
a. Was zeigt die nachfolgenden
Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten
relevant sein?
System: UNTITLED
Dependent Variable: XM1 Method: Least Squares Date: 08/19/12 Time: 09:55 Sample (adjusted): 12 156 Included observations: 145 after adjustments XM1=C(1)*XM1(-1)+C(5)*DEZBKREDITE(2)+C(12)*ZINS5J(6)
Coefficient Std. Error t-Statistic Prob.
2
4
6
8
10
12
14
1,998 2,000 2,002 2,004 2,006 2,008 2,010 2,012 2,014
ZEIT
XM
1
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
C(1) 0.967062 0.015357 62.97073 0.0000 C(5) -0.005318 0.001622 -3.279398 0.0013
C(12) 0.094779 0.038084 2.488689 0.0140 R-squared 0.944985 Mean dependent var 8.643724
Adjusted R-squared 0.944210 S.D. dependent var 1.693629 S.E. of regression 0.400032 Akaike info criterion 1.025927 Sum squared resid 22.72361 Schwarz criterion 1.087514 Log likelihood -71.37970 Hannan-Quinn criter. 1.050952 Durbin-Watson stat 2.061513
Dependent Variable: XM1 Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/19/12 Time: 09:59 Sample (adjusted): 12 156 Included observations: 145 after adjustments Convergence achieved after 40 iterations Presample variance: backcast (parameter = 0.7) XM1=C(1)*XM1(-1)+C(5)*DEZBKREDITE(2)+C(12)*ZINS5J(6) GARCH = C(13) + C(14)*RESID(-1)^2 + C(15)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob. C(1) 0.961613 0.012999 73.97609 0.0000
C(5) -0.005183 0.001759 -2.946548 0.0032 C(12) 0.105044 0.033409 3.144164 0.0017
Variance Equation C 0.212637 0.091559 2.322401 0.0202
RESID(-1)^2 -0.067698 0.043513 -1.555839 0.1197 GARCH(-1) -0.269448 0.593705 -0.453842 0.6499
R-squared 0.944907 Mean dependent var 8.643724
Adjusted R-squared 0.944131 S.D. dependent var 1.693629 S.E. of regression 0.400316 Akaike info criterion 1.056343 Sum squared resid 22.75591 Schwarz criterion 1.179518 Log likelihood -70.58484 Hannan-Quinn criter. 1.106393 Durbin-Watson stat 2.048039
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Aufgabe 2-c
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Dependent Variable: LOG(KREDITEMFI) Method: Least Squares Date: 08/19/12 Time: 14:14 Sample (adjusted): 2 162 Included observations: 161 after adjustments LOG(KREDITEMFI) = C(1)*LOG(KREDITEMFI(-1)) + C(3) + C(4)*LOG(M3) + C(5)*ARBEITSLOSE
Coefficient Std. Error t-Statistic Prob. C(1) 0.919503 0.022831 40.27379 0.0000
C(3) 0.149203 0.029996 4.974168 0.0000 C(4) 0.068405 0.020585 3.323097 0.0011 C(5) -0.001837 0.000392 -4.692143 0.0000
R-squared 0.999584 Mean dependent var 9.123465
Adjusted R-squared 0.999576 S.D. dependent var 0.233896 S.E. of regression 0.004817 Akaike info criterion -7.808893 Sum squared resid 0.003643 Schwarz criterion -7.732336 Log likelihood 632.6159 Hannan-Quinn criter. -7.777808 F-statistic 125704.5 Durbin-Watson stat 1.780173 Prob(F-statistic) 0.000000
Aufgabe 2-d
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Pairwise Granger Causality Tests Date: 09/22/11 Time: 22:18 Sample: 1 152 Lags: 2
Null Hypothesis: Obs F-Statistic Prob.
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
LOG(EZBKREDITE) does not Granger Cause LOG(KREDITEMFI) 148 1.27920 0.2814 LOG(KREDITEMFI) does not Granger Cause LOG(EZBKREDITE) 3.22025 0.0429
Pairwise Granger Causality Tests Date: 08/19/12 Time: 14:17 Sample: 1 162 Lags: 2
Null Hypothesis: Obs F-Statistic Prob. LOG(EZBKREDITE) does not Granger Cause LOG(KREDITEMFI) 159 2.04960 0.1323
LOG(KREDITEMFI) does not Granger Cause LOG(EZBKREDITE) 1.19601 0.3052
Aufgabe 2-e
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
System: UNTITLED Estimation Method: Least Squares Date: 08/19/12 Time: 14:58 Sample: 9 159 Included observations: 151 Total system (balanced) observations 151
Coefficient Std. Error t-Statistic Prob. C(1) -0.028535 0.083575 -0.341423 0.7333
C(2) -0.005546 0.085650 -0.064750 0.9485 C(3) 0.002930 0.007180 0.408060 0.6839 C(4) 0.005401 0.008851 0.610235 0.5428 C(5) 0.000829 0.000881 0.940438 0.3487 C(6) -0.039367 0.015710 -2.505921 0.0134 C(7) 0.121060 0.082662 1.464517 0.1454 C(8) -0.043710 0.073191 -0.597201 0.5514 C(9) -0.013490 0.008374 -1.610931 0.1096
C(10) 0.183358 0.088724 2.066599 0.0407 C(11) -0.002567 0.003220 -0.797018 0.4269 C(12) -0.004976 0.004979 -0.999464 0.3194 C(13) 0.010839 0.005423 1.998817 0.0477 C(14) -0.013148 0.020796 -0.632243 0.5283 C(15) 0.012229 0.006648 1.839570 0.0681 C(16) -0.007602 0.004489 -1.693481 0.0927 C(17) 0.004888 0.003689 1.324938 0.1875 C(18) 0.000360 0.006377 0.056387 0.9551 C(19) -0.000715 0.021440 -0.033367 0.9734 C(20) -0.002948 0.020706 -0.142361 0.8870
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Determinant residual covariance 1.82E-05
Equation: DLOG(KREDITEMFI) = C(1)*DLOG(KREDITEMFI(-1)) + C(2) *DLOG(KREDITEMFI(-2)) + C(3) + C(4)*DLOG(AKTIENINDEX) + C(5) *ARBEITSLOSE + C(6)*DLOG(BARGELD) + C(7)*DLOG(BIPNOM) + C(8)*DLOG(BIPREAL) + C(9)*DLOG(EZBKREDITE) + C(10)*DLOG(M3) + C(11)*MINDBIET + C(12)*ZINS1TAG + C(13)*ZINS1MT + C(14) *ZINS3MT + C(15)*ZINS6MT + C(16)*ZINS1J + C(17)*ZINS2J + C(18) *ZINS5J + C(19)*ZINS10J + C(20)*ZMIND Observations: 151 R-squared 0.370513 Mean dependent var 0.004593 Adjusted R-squared 0.279213 S.D. dependent var 0.005393 S.E. of regression 0.004579 Sum squared resid 0.002747 Durbin-Watson stat 2.071524
System: UNTITLED Estimation Method: ARCH Maximum Likelihood (Marquardt) Covariance specification: Diagonal VECH Date: 08/19/12 Time: 14:59 Sample: 9 159 Included observations: 151 Total system (balanced) observations 151 Presample covariance: backcast (parameter =0.7) Convergence achieved after 32 iterations
Coefficient Std. Error z-Statistic Prob. C(1) 0.001640 0.064163 0.025558 0.9796
C(2) -0.020169 0.098564 -0.204625 0.8379 C(3) 0.001657 0.005986 0.276788 0.7819 C(4) 0.003623 0.010694 0.338759 0.7348 C(5) 0.000759 0.000831 0.913601 0.3609 C(6) -0.029800 0.013310 -2.238952 0.0252 C(7) 0.115281 0.066877 1.723788 0.0847 C(8) -0.038434 0.061805 -0.621858 0.5340 C(9) -0.011066 0.007826 -1.413951 0.1574
C(10) 0.188518 0.089956 2.095678 0.0361 C(11) -0.003719 0.002916 -1.275177 0.2022 C(12) -0.004887 0.004439 -1.100961 0.2709 C(13) 0.010836 0.004676 2.317583 0.0205 C(14) -0.011833 0.007729 -1.530880 0.1258 C(15) 0.012564 0.005976 2.102346 0.0355 C(16) -0.007750 0.004566 -1.697360 0.0896 C(17) 0.004874 0.003743 1.302197 0.1928 C(18) 6.12E-07 0.006585 9.30E-05 0.9999 C(19) -0.000524 0.008273 -0.063320 0.9495 C(20) -0.002281 0.006895 -0.330880 0.7407
Variance Equation Coefficients C(21) 4.39E-07 4.43E-07 0.992279 0.3211
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Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
C(22) -0.060152 0.014227 -4.228048 0.0000 C(23) 1.040732 0.029193 35.65014 0.0000
Log likelihood 620.4999 Schwarz criterion -7.454320
Avg. log likelihood 4.109271 Hannan-Quinn criter. -7.727198 Akaike info criterion -7.913905
Equation: DLOG(KREDITEMFI) = C(1)*DLOG(KREDITEMFI(-1)) + C(2) *DLOG(KREDITEMFI(-2)) + C(3) + C(4)*DLOG(AKTIENINDEX) + C(5) *ARBEITSLOSE + C(6)*DLOG(BARGELD) + C(7)*DLOG(BIPNOM) + C(8)*DLOG(BIPREAL) + C(9)*DLOG(EZBKREDITE) + C(10)*DLOG(M3) + C(11)*MINDBIET + C(12)*ZINS1TAG + C(13)*ZINS1MT + C(14) *ZINS3MT + C(15)*ZINS6MT + C(16)*ZINS1J + C(17)*ZINS2J + C(18) *ZINS5J + C(19)*ZINS10J + C(20)*ZMIND R-squared 0.361266 Mean dependent var 0.004593 Adjusted R-squared 0.268626 S.D. dependent var 0.005393 S.E. of regression 0.004612 Sum squared resid 0.002787 Durbin-Watson stat 2.141457
Dependent Variable: DLOG(KREDITEMFI) Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/19/12 Time: 15:08 Sample (adjusted): 2 162 Included observations: 161 after adjustments Convergence achieved after 33 iterations Presample variance: backcast (parameter = 0.7) DLOG(KREDITEMFI) =C(10)*DLOG(M3) + C(17)*ZINS2J GARCH = C(18) + C(19)*RESID(-1)^2 + C(20)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob. C(10) 0.237190 0.050149 4.729685 0.0000
C(17) 0.001241 9.20E-05 13.49594 0.0000 Variance Equation C 3.94E-07 4.42E-07 0.892286 0.3722
RESID(-1)^2 -0.053183 0.008777 -6.059484 0.0000 GARCH(-1) 1.050391 0.025208 41.66946 0.0000
R-squared 0.197692 Mean dependent var 0.004556
Adjusted R-squared 0.192646 S.D. dependent var 0.005348 S.E. of regression 0.004805 Akaike info criterion -7.953519 Sum squared resid 0.003671 Schwarz criterion -7.857823 Log likelihood 645.2583 Hannan-Quinn criter. -7.914663 Durbin-Watson stat 1.926023
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Dependent Variable: DLOG(KREDITEMFI) Method: Least Squares Date: 08/20/12 Time: 14:24 Sample (adjusted): 2 162 Included observations: 161 after adjustments DLOG(KREDITEMFI) = C(6)*DLOG(BARGELD) +C(10)*DLOG(M3)+C(17) *ZINS2J
Coefficient Std. Error t-Statistic Prob. C(6) -0.042163 0.014974 -2.815716 0.0055
C(10) 0.270463 0.076668 3.527713 0.0005 C(17) 0.001227 0.000173 7.074039 0.0000
R-squared 0.236381 Mean dependent var 0.004556
Adjusted R-squared 0.226715 S.D. dependent var 0.005348 S.E. of regression 0.004703 Akaike info criterion -7.862912 Sum squared resid 0.003494 Schwarz criterion -7.805495 Log likelihood 635.9644 Hannan-Quinn criter. -7.839598 Durbin-Watson stat 1.932552
Aufgabe 2-f
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
System: UNTITLED Estimation Method: Least Squares Date: 09/01/10 Time: 17:35 Sample: 12 138 Included observations: 127 Total system (balanced) observations 127
Coefficient Std. Error t-Statistic Prob. C(1) 0.896494 0.029962 29.92055 0.0000
C(3) 1.465408 0.366108 4.002661 0.0001 C(4) -0.102859 0.028285 -3.636539 0.0004
Determinant residual covariance 0.926077
Equation: DM1 = C(1)*DM1(-1) + C(3) + C(4)*DKREDMFI Observations: 127
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Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
R-squared 0.907549 Mean dependent var 7.900787 Adjusted R-squared 0.906058 S.D. dependent var 3.177488 S.E. of regression 0.973900 Sum squared resid 117.6117 Durbin-Watson stat 2.132678
Aufgabe 2-f
Pairwise Granger Causality Tests Date: 09/22/11 Time: 22:20 Sample: 1 152 Lags: 2
Null Hypothesis: Obs F-Statistic Prob. LOG(M1) does not Granger Cause LOG(EZBKREDITE) 148 5.44962 0.0052
LOG(EZBKREDITE) does not Granger Cause LOG(M1) 0.72780 0.4847
Thema 3: Die Geldmärkte, empirische Analysen der
Tageszinsen und theoretische Grundlagen
Aufgabe 3-a
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Dependent Variable: ZINS1TAG Method: Least Squares Date: 08/19/12 Time: 17:38 Sample (adjusted): 12 155 Included observations: 144 after adjustments ZINS1TAG=C(1)*ZINS1TAG(-1)+C(2)*ZINS1TAG(-2)+C(3)+C(4) *DLOG(AKTIENINDEX(-3))+C(5)*ARBEITSLOSE(6)+C(6) *DLOG(BARGELD(1))+C(7)*DLOG(BIPNOM)+C(8)*DLOG(BIPREAL(3)) +C(9)*DERDOL+C(10)*DLOG(M2(2))+C(11)*DLOG(M3(2))+C(12) *DROHSTOFFE+C(13)*DLOG(PREISNIVEAU)+C(14)*LOHN(4)+C(15) *MINDBIET+C(16)*ZINS1MT+C(17)*ZINS3MT+C(18)*ZINS6MT+C(19) *ZINS1J+C(20)*ZINS2J+C(21)*ZINS5J+C(22)*ZINS10J+C(23) *ZMIND(4)
Coefficient Std. Error t-Statistic Prob. C(1) 0.245432 0.076440 3.210765 0.0017
C(2) 0.018616 0.048074 0.387235 0.6993 C(3) -0.034121 0.143759 -0.237350 0.8128 C(4) -0.027604 0.141791 -0.194679 0.8460 C(5) 0.007633 0.019161 0.398347 0.6911 C(6) 0.171363 0.249464 0.686923 0.4934 C(7) 0.201720 1.122493 0.179707 0.8577 C(8) 1.874521 0.996692 1.880742 0.0624 C(9) -0.000491 0.000246 -1.994038 0.0484
C(10) 3.747154 1.656984 2.261430 0.0255 C(11) -0.941009 2.100156 -0.448066 0.6549 C(12) 0.000620 0.000515 1.203740 0.2310 C(13) 2.658581 1.987083 1.337932 0.1834 C(14) 0.001640 0.019288 0.085049 0.9324 C(15) 0.340300 0.044576 7.634175 0.0000 C(16) 0.579644 0.076001 7.626814 0.0000 C(17) 0.005664 0.059721 0.094843 0.9246 C(18) -0.295104 0.112333 -2.627049 0.0097 C(19) -0.040566 0.083374 -0.486550 0.6275 C(20) 0.260150 0.071228 3.652384 0.0004 C(21) -0.109403 0.110767 -0.987688 0.3253 C(22) 0.001949 0.075487 0.025816 0.9794 C(23) -0.026183 0.020494 -1.277555 0.2039
R-squared 0.997613 Mean dependent var 2.586875
Adjusted R-squared 0.997179 S.D. dependent var 1.364032 S.E. of regression 0.072450 Akaike info criterion -2.266407 Sum squared resid 0.635137 Schwarz criterion -1.792062 Log likelihood 186.1813 Hannan-Quinn criter. -2.073660 F-statistic 2298.491 Durbin-Watson stat 2.193900 Prob(F-statistic) 0.000000
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Dependent Variable: ZINS1TAG Method: Least Squares Date: 08/19/12 Time: 17:57 Sample (adjusted): 9 155 Included observations: 147 after adjustments ZINS1TAG=C(1)*ZINS1TAG(-1)+C(5)*ARBEITSLOSE(6)+C(8) *DLOG(BIPREAL(3))+C(10)*DLOG(M2(2))+C(14)*LOHN(4)+C(15) *MINDBIET+C(16)*ZINS1MT+C(20)*ZINS2J
Coefficient Std. Error t-Statistic Prob. C(1) 0.418076 0.039792 10.50652 0.0000
C(5) -0.035259 0.003656 -9.645125 0.0000 C(8) 2.762911 1.130232 2.444552 0.0158
C(10) 3.207252 1.354666 2.367559 0.0193 C(14) 0.053256 0.020049 2.656334 0.0088 C(15) 0.357470 0.046200 7.737509 0.0000 C(16) 0.139000 0.050070 2.776120 0.0063 C(20) 0.117247 0.016257 7.212058 0.0000
R-squared 0.995602 Mean dependent var 2.587619
Adjusted R-squared 0.995380 S.D. dependent var 1.350343 S.E. of regression 0.091779 Akaike info criterion -1.885988 Sum squared resid 1.170843 Schwarz criterion -1.723243 Log likelihood 146.6201 Hannan-Quinn criter. -1.819863 Durbin-Watson stat 1.457888
System: UNTITLED Estimation Method: ARCH Maximum Likelihood (Marquardt) Covariance specification: Diagonal VECH Date: 08/19/12 Time: 21:16 Sample: 17 156 Included observations: 140 Total system (balanced) observations 140 Presample covariance: backcast (parameter =0.7) Convergence achieved after 19 iterations
Coefficient Std. Error z-Statistic Prob. C(1) 0.074895 0.090689 0.825850 0.4089
C(2) 0.185822 0.072926 2.548076 0.0108 C(3) -0.194787 0.001795 -108.5148 0.0000 C(4) 0.385408 0.083930 4.592013 0.0000 C(5) 0.016235 0.001157 14.03594 0.0000 C(6) 0.895713 0.829714 1.079544 0.2803 C(7) 2.351308 0.842378 2.791274 0.0053 C(8) 0.000307 8.90E-05 3.454804 0.0006 C(9) 0.333092 0.205701 1.619304 0.1054
C(10) -0.031279 0.098015 -0.319121 0.7496 C(11) 0.798102 0.713176 1.119082 0.2631 C(12) 2.868421 1.021897 2.806956 0.0050 C(13) 1.704774 0.471698 3.614125 0.0003 C(14) 4.659370 1.751956 2.659525 0.0078 C(15) 0.000972 0.004388 0.221480 0.8247
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Variance Equation Coefficients C(16) -3.15E-06 2.84E-05 -0.110730 0.9118
C(17) -0.040965 0.019996 -2.048630 0.0405 C(18) 1.077903 0.022958 46.95106 0.0000
Log likelihood 188.6634 Schwarz criterion -2.059837
Avg. log likelihood 1.347595 Hannan-Quinn criter. -2.284354 Akaike info criterion -2.438048
Equation: DLOG(ZINS1TAG) = C(1)*DLOG(ZINS1TAG(-1)) + C(2) *DLOG(ZINS1TAG(-2)) + C(3) + C(4)*DLOG(AKTIENINDEX(-4)) + C(5) *ARBEITSLOSE(2) + C(6)*DLOG(BIPNOM(3)) + C(7)*DLOG(BIPREAL(3 )) + C(8)*DERDOL(-5) + C(9)*DLOG(EURUSD) + C(10) *DLOG(EZBKREDITE) + C(11)*DLOG(KREDITEMFI) + C(12) *DLOG(M3(-2)) + C(13)*DLOG(MINDRES(1)) + C(14) *DLOG(PREISNIVEAU) + C(15)*LOHN R-squared 0.332583 Mean dependent var -0.012626 Adjusted R-squared 0.257832 S.D. dependent var 0.112558 S.E. of regression 0.096967 Sum squared resid 1.175336 Durbin-Watson stat 2.045543
Dependent Variable: DLOG(ZINS1TAG) Method: Least Squares Date: 08/19/12 Time: 21:24 Sample (adjusted): 6 156 Included observations: 151 after adjustments DLOG(ZINS1TAG) = C(2)*DLOG(ZINS1TAG(-2)) +C(4)*DLOG(AKTIENINDE X(-4)) +C(7)*DLOG(BIPREAL(3))
Coefficient Std. Error t-Statistic Prob. C(2) 0.135903 0.073923 1.838450 0.0680
C(4) 0.717431 0.158439 4.528123 0.0000 C(7) 4.277284 1.164156 3.674151 0.0003
R-squared 0.229007 Mean dependent var -0.009259
Adjusted R-squared 0.218588 S.D. dependent var 0.109894 S.E. of regression 0.097143 Akaike info criterion -1.805593 Sum squared resid 1.396647 Schwarz criterion -1.745647 Log likelihood 139.3223 Hannan-Quinn criter. -1.781240 Durbin-Watson stat 1.866807
Dependent Variable: DLOG(ZINS1TAG) Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/19/12 Time: 21:25 Sample (adjusted): 6 156 Included observations: 151 after adjustments Convergence achieved after 21 iterations Presample variance: backcast (parameter = 0.7) DLOG(ZINS1TAG) = C(2)*DLOG(ZINS1TAG(-2)) +C(4)*DLOG(AKTIENINDE
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Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
X(-4)) +C(7)*DLOG(BIPREAL(3)) GARCH = C(8) + C(9)*RESID(-1)^2 + C(10)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob. C(2) 0.236524 0.062849 3.763365 0.0002
C(4) 0.264622 0.079046 3.347679 0.0008 C(7) 1.055457 0.382727 2.757730 0.0058
Variance Equation C 6.68E-05 3.47E-05 1.928511 0.0538
RESID(-1)^2 0.298418 0.069701 4.281389 0.0000 GARCH(-1) 0.783881 0.033580 23.34336 0.0000
R-squared 0.124152 Mean dependent var -0.009259
Adjusted R-squared 0.112316 S.D. dependent var 0.109894 S.E. of regression 0.103538 Akaike info criterion -2.563821 Sum squared resid 1.586591 Schwarz criterion -2.443929 Log likelihood 199.5685 Hannan-Quinn criter. -2.515115 Durbin-Watson stat 1.818868
Dependent Variable: DLOG(ZINS1TAG) Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/19/12 Time: 21:37 Sample (adjusted): 10 162 Included observations: 153 after adjustments Convergence achieved after 11 iterations Presample variance: backcast (parameter = 0.7) DLOG(ZINS1TAG) = C(4)*DLOG(AKTIENINDEX(-4)) + C(16) *DLOG(ZINS1MT) GARCH = C(17) + C(18)*RESID(-1)^2 + C(19)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob. C(4) 0.114037 0.044059 2.588256 0.0096
C(16) 0.864698 0.032680 26.45937 0.0000 Variance Equation C 0.000178 6.17E-05 2.883443 0.0039
RESID(-1)^2 0.662885 0.142472 4.652746 0.0000 GARCH(-1) 0.466504 0.080896 5.766729 0.0000
R-squared 0.566414 Mean dependent var -0.013049
Adjusted R-squared 0.563542 S.D. dependent var 0.116320 S.E. of regression 0.076847 Akaike info criterion -3.112521 Sum squared resid 0.891726 Schwarz criterion -3.013487 Log likelihood 243.1079 Hannan-Quinn criter. -3.072292 Durbin-Watson stat 2.207373
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Aufgabe 3-b
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Null Hypothesis: ZINS1TAG has a unit root Exogenous: Constant Lag Length: 2 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -1.625077 0.4674
Test critical values: 1% level -3.471719 5% level -2.879610 10% level -2.576484 *MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(ZINS1TAG) Method: Least Squares Date: 08/19/12 Time: 21:38 Sample (adjusted): 4 162 Included observations: 159 after adjustments
Null Hypothesis: DLOG(ZINS1TAG) has a unit root Exogenous: Constant Lag Length: 2 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -4.009285 0.0018
Test critical values: 1% level -3.471987 5% level -2.879727 10% level -2.576546 *MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLOG(ZINS1TAG)) Method: Least Squares Date: 08/19/12 Time: 21:40 Sample (adjusted): 5 162
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Included observations: 158 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DLOG(ZINS1TAG(-1)) -0.404266 0.100833 -4.009285 0.0001
D(DLOG(ZINS1TAG(-1))) -0.380976 0.093106 -4.091874 0.0001 D(DLOG(ZINS1TAG(-2))) -0.362426 0.074988 -4.833123 0.0000
C -0.005174 0.008277 -0.625114 0.5328 R-squared 0.448592 Mean dependent var 0.000305
Adjusted R-squared 0.437850 S.D. dependent var 0.136813 S.E. of regression 0.102577 Akaike info criterion -1.691406 Sum squared resid 1.620410 Schwarz criterion -1.613872 Log likelihood 137.6211 Hannan-Quinn criter. -1.659918 F-statistic 41.76159 Durbin-Watson stat 1.967395 Prob(F-statistic) 0.000000
Aufgabe 3-c
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
0
5
10
15
20
25
30
1 2 3 4 5
Series: ZINS1TAGSample 1 162Observations 162
Mean 2.500679Median 2.535000Maximum 5.060000Minimum 0.330000Std. Dev. 1.363879Skewness -0.127468Kurtosis 1.947707
Jarque-Bera 7.913114Probability 0.019129
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Aufgabe 3-d
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Pairwise Granger Causality Tests Date: 08/19/12 Time: 21:46 Sample: 1 162 Lags: 5
Null Hypothesis: Obs F-Statistic Prob. ZINS1TAG does not Granger Cause INFLATIONSRATE 157 1.86108 0.1047
INFLATIONSRATE does not Granger Cause ZINS1TAG 3.04868 0.0120
System: UNTITLED Estimation Method: ARCH Maximum Likelihood (Marquardt) Covariance specification: Diagonal VECH Date: 08/19/12 Time: 21:50
0
10
20
30
40
50
60
70
-0.6 -0.4 -0.2 -0.0 0.2 0.4
Series: DLOG(ZINS1TAG)Sample 1 162Observations 161
Mean -0.013993Median -0.002466Maximum 0.441833Minimum -0.664976Std. Dev. 0.113640Skewness -1.250842Kurtosis 13.67589
Jarque-Bera 806.5634Probability 0.000000
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Sample: 3 154 Included observations: 152 Total system (balanced) observations 152 Presample covariance: backcast (parameter =0.7) Convergence achieved after 20 iterations
Coefficient Std. Error z-Statistic Prob. C(1) 1.405847 0.095327 14.74757 0.0000
C(2) -0.422704 0.094071 -4.493433 0.0000 C(4) 0.021976 0.007110 3.090704 0.0020
Variance Equation Coefficients C(5) 0.002830 0.001162 2.435037 0.0149
C(6) 0.249826 0.104117 2.399471 0.0164 C(7) 0.634730 0.098767 6.426519 0.0000
Log likelihood 87.90556 Schwarz criterion -0.958341
Avg. log likelihood 0.578326 Hannan-Quinn criter. -1.029215 Akaike info criterion -1.077705
Equation: ZINS1TAG = C(1)*ZINS1TAG(-1) + C(2)*ZINS1TAG(-2) + C(4) *INFLATIONSRATE(8) R-squared 0.987355 Mean dependent var 2.600658 Adjusted R-squared 0.987186 S.D. dependent var 1.320054 S.E. of regression 0.149431 Sum squared resid 3.327120 Durbin-Watson stat 2.238986
Covariance specification: Diagonal VECH
System: UNTITLED Estimation Method: ARCH Maximum Likelihood (Marquardt) Covariance specification: Diagonal VECH Date: 08/19/12 Time: 21:51 System: UNTITLED Estimation Method: ARCH Maximum Likelihood (Marquardt) Covariance specification: Diagonal VECH Date: 08/19/12 Time: 21:53 Sample: 3 162 Included observations: 160 Total system (balanced) observations 160 Presample covariance: backcast (parameter =0.7) Convergence achieved after 45 iterations
Coefficient Std. Error z-Statistic Prob. C(1) 0.548355 0.063721 8.605515 0.0000
C(2) -0.159465 0.050840 -3.136585 0.0017 C(5) 0.627491 0.032437 19.34493 0.0000
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Variance Equation Coefficients C(6) 5.16E-05 9.19E-05 0.560749 0.5750
C(7) 0.223279 0.053747 4.154218 0.0000 C(8) 0.824973 0.021769 37.89659 0.0000
Log likelihood 128.9111 Schwarz criterion -1.421069
Avg. log likelihood 0.805694 Hannan-Quinn criter. -1.489561 Akaike info criterion -1.536388
Equation: ZINS1TAG = C(1)*ZINS1TAG(-1) + C(2)*ZINS1TAG(-2) + C(5) *MINDBIET R-squared 0.980724 Mean dependent var 2.492813 Adjusted R-squared 0.980478 S.D. dependent var 1.370591 S.E. of regression 0.191500 Sum squared resid 5.757551 Durbin-Watson stat 0.357713
Thema 4: Die Kapitalmarktzinsen, empirische Analysen der
10-Jahreszinsen und theoretische Grundlagen
Aufgabe 4-a
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Null Hypothesis: ZINS10J has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -0.662846 0.8517
Test critical values: 1% level -3.471192
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
1,998 2,000 2,002 2,004 2,006 2,008 2,010 2,012 2,014
ZEIT
ZIN
S10
J
0
2
4
6
8
10
12
14
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
Series: ZINS10JSample 1 162Observations 162
Mean 4.099506Median 4.065000Maximum 5.660000Minimum 1.890000Std. Dev. 0.799218Skewness -0.117354Kurtosis 2.590338
Jarque-Bera 1.504652Probability 0.471269
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
5% level -2.879380 10% level -2.576361 *MacKinnon (1996) one-sided p-values.
Null Hypothesis: DLOG(ZINS10J) has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -12.29032 0.0000
Test critical values: 1% level -3.471454 5% level -2.879494 10% level -2.576422 *MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLOG(ZINS10J)) Method: Least Squares Date: 08/19/12 Time: 23:15 Sample (adjusted): 3 162 Included observations: 160 after adjustments
0
5
10
15
20
25
30
35
-0.2 -0.1 -0.0 0.1 0.2
Series: DLOG(ZINS10J)Sample 1 162Observations 161
Mean -0.003097Median -0.003766Maximum 0.204990Minimum -0.267641Std. Dev. 0.055122Skewness -0.656811Kurtosis 7.203442
Jarque-Bera 130.1049Probability 0.000000
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Aufgabe 4-b
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Dependent Variable: DLOG(ZINS10J) Method: Least Squares Date: 08/20/12 Time: 08:37 Sample (adjusted): 9 158 Included observations: 150 after adjustments DLOG(ZINS10J) = C(1)*DLOG(ZINS10J(-1)) + C(2)*DLOG(ZINS10J(-2)) + C(3) + C(4)*DLOG(AKTIENINDEX(-1))+C(5)*ARBEITSLOSE(3)+C(6) *DLOG(BIPNOM(-7))+C(7)*DLOG(BIPREAL(-2))+C(8) *DLOG(KREDITEMFI(-1))+C(9)*DLOG(M2)+C(10)*DLOG(PREISNIVEA U(-1))+C(11)*DLOG(MINDBIET(4))+C(12)*DLOG(ZINS1TAG(4))+C(13) *DLOG(ZINS1MT(4))+C(14)*DLOG(ZINS3MT(4))+C(15) *DLOG(ZINS6MT(4))+C(16)*DLOG(ZINS1J(2))+C(17)*DLOG(ZINS2J(3) )+C(18)*DLOG(ZINS5J(2))+C(19)*DLOG(ZINSUS10J)
Coefficient Std. Error t-Statistic Prob. C(1) -0.130709 0.069026 -1.893606 0.0605
C(2) -0.120160 0.063533 -1.891314 0.0608 C(3) 0.062087 0.036850 1.684881 0.0944 C(4) 0.213770 0.066957 3.192652 0.0018 C(5) -0.007448 0.003883 -1.918006 0.0573 C(6) -0.147172 0.505965 -0.290873 0.7716 C(7) 0.584686 0.479559 1.219215 0.2250 C(8) 0.855214 0.667392 1.281428 0.2023 C(9) -1.372979 0.583718 -2.352125 0.0202
C(10) 1.602062 0.995048 1.610036 0.1098 C(11) 0.117976 0.060807 1.940186 0.0545 C(12) 0.036020 0.044016 0.818336 0.4147 C(13) -0.196264 0.079783 -2.459977 0.0152 C(14) 0.107402 0.112248 0.956826 0.3404 C(15) 0.018237 0.130590 0.139653 0.8891 C(16) -0.005585 0.061573 -0.090697 0.9279 C(17) 0.056382 0.026117 2.158870 0.0327 C(18) -0.156158 0.055677 -2.804714 0.0058 C(19) 0.303896 0.049483 6.141415 0.0000
R-squared 0.514421 Mean dependent var -0.004465
Adjusted R-squared 0.447700 S.D. dependent var 0.048433 S.E. of regression 0.035994 Akaike info criterion -3.693045 Sum squared resid 0.169718 Schwarz criterion -3.311697 Log likelihood 295.9783 Hannan-Quinn criter. -3.538115 F-statistic 7.710043 Durbin-Watson stat 2.030636 Prob(F-statistic) 0.000000
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Dependent Variable: DLOG(ZINS10J) Method: Least Squares Date: 08/20/12 Time: 08:44 Sample (adjusted): 3 162 Included observations: 160 after adjustments DLOG(ZINS10J) =C(19)*DLOG(ZINSUS10J)
Coefficient Std. Error t-Statistic Prob. C(19) 0.450142 0.052962 8.499276 0.0000 R-squared 0.309810 Mean dependent var -0.003373
Adjusted R-squared 0.309810 S.D. dependent var 0.055183 S.E. of regression 0.045845 Akaike info criterion -3.320874 Sum squared resid 0.334179 Schwarz criterion -3.301654 Log likelihood 266.6699 Hannan-Quinn criter. -3.313070 Durbin-Watson stat 2.327931
Dependent Variable: DLOG(ZINS10J) Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/20/12 Time: 08:43 Sample (adjusted): 3 162 Included observations: 160 after adjustments Convergence achieved after 16 iterations Presample variance: backcast (parameter = 0.7) DLOG(ZINS10J) =C(19)*DLOG(ZINSUS10J) GARCH = C(20) + C(21)*RESID(-1)^2 + C(22)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob. C(19) 0.470636 0.037175 12.66003 0.0000 Variance Equation C 4.21E-05 3.78E-05 1.113695 0.2654
RESID(-1)^2 0.347200 0.099135 3.502309 0.0005 GARCH(-1) 0.719329 0.060435 11.90246 0.0000
R-squared 0.309160 Mean dependent var -0.003373
Adjusted R-squared 0.309160 S.D. dependent var 0.055183 S.E. of regression 0.045867 Akaike info criterion -3.600626 Sum squared resid 0.334494 Schwarz criterion -3.523747 Log likelihood 292.0501 Hannan-Quinn criter. -3.569408 Durbin-Watson stat 2.338424
Dependent Variable: DLOG(ZINS10J) Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/20/12 Time: 08:45
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Sample (adjusted): 3 162 Included observations: 160 after adjustments Convergence achieved after 29 iterations Presample variance: backcast (parameter = 0.7) DLOG(ZINS10J) =C(19)*DLOG(ZINSUS10J) LOG(GARCH) = C(20) + C(21)*ABS(RESID(-1)/@SQRT(GARCH(-1))) + C(22)*RESID(-1)/@SQRT(GARCH(-1)) + C(23)*LOG(GARCH(-1))
Variable Coefficient Std. Error z-Statistic Prob. C(19) 0.513655 0.031772 16.16692 0.0000 Variance Equation C(20) -0.941366 0.279147 -3.372299 0.0007
C(21) 0.700301 0.130103 5.382650 0.0000 C(22) -0.038182 0.082752 -0.461407 0.6445 C(23) 0.933604 0.040136 23.26085 0.0000
R-squared 0.303568 Mean dependent var -0.003373
Adjusted R-squared 0.303568 S.D. dependent var 0.055183 S.E. of regression 0.046052 Akaike info criterion -3.575230 Sum squared resid 0.337202 Schwarz criterion -3.479131 Log likelihood 291.0184 Hannan-Quinn criter. -3.536207 Durbin-Watson stat 2.356075
Aufgabe 4-c
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Pairwise Granger Causality Tests Date: 08/20/12 Time: 08:48 Sample: 1 162 Lags: 1
Null Hypothesis: Obs F-Statistic Prob. DLOG(ZINS10J) does not Granger Cause DLOG(PREISNIVEAU) 159 2.91174 0.0899
DLOG(PREISNIVEAU) does not Granger Cause DLOG(ZINS10J) 8.44556 0.0042
Dependent Variable: DLOG(ZINS10J) Method: Least Squares Date: 08/20/12 Time: 08:54 Sample (adjusted): 3 162 Included observations: 160 after adjustments
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
DLOG(ZINS10J)=C(3)+C(4)*DLOG(PREISNIVEAU(-1)) Coefficient Std. Error t-Statistic Prob. C(3) -0.009206 0.004832 -1.905346 0.0586
C(4) 3.249491 1.243869 2.612407 0.0099 R-squared 0.041406 Mean dependent var -0.003373
Adjusted R-squared 0.035339 S.D. dependent var 0.055183 S.E. of regression 0.054199 Akaike info criterion -2.979873 Sum squared resid 0.464137 Schwarz criterion -2.941433 Log likelihood 240.3898 Hannan-Quinn criter. -2.964264 F-statistic 6.824672 Durbin-Watson stat 1.951651 Prob(F-statistic) 0.009858
Dependent Variable: DLOG(ZINS10J) Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/20/12 Time: 08:54 Sample (adjusted): 3 162 Included observations: 160 after adjustments Convergence achieved after 50 iterations Presample variance: backcast (parameter = 0.7) DLOG(ZINS10J)=C(3)+C(4)*DLOG(PREISNIVEAU(-1)) GARCH = C(5) + C(6)*RESID(-1)^2 + C(7)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob. C(3) -0.006053 0.004105 -1.474656 0.1403
C(4) 2.926818 1.326418 2.206558 0.0273 Variance Equation C -2.99E-05 4.64E-05 -0.644947 0.5190
RESID(-1)^2 0.098309 0.051785 1.898413 0.0576 GARCH(-1) 0.941310 0.052589 17.89952 0.0000
R-squared 0.038809 Mean dependent var -0.003373
Adjusted R-squared 0.032725 S.D. dependent var 0.055183 S.E. of regression 0.054273 Akaike info criterion -3.235221 Sum squared resid 0.465394 Schwarz criterion -3.139122 Log likelihood 263.8177 Hannan-Quinn criter. -3.196198 F-statistic 1.594844 Durbin-Watson stat 1.947049 Prob(F-statistic) 0.178290
Dependent Variable: DLOG(ZINS10J) Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/20/12 Time: 08:53
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Sample (adjusted): 3 162 Included observations: 160 after adjustments Convergence achieved after 16 iterations Presample variance: backcast (parameter = 0.7) DLOG(ZINS10J)=C(3)+C(4)*DLOG(PREISNIVEAU(-1)) LOG(GARCH) = C(5) + C(6)*ABS(RESID(-1)/@SQRT(GARCH(-1))) + C(7) *RESID(-1)/@SQRT(GARCH(-1)) + C(8)*LOG(GARCH(-1))
Variable Coefficient Std. Error z-Statistic Prob. C(3) -0.015180 0.000595 -25.52995 0.0000
C(4) 3.080838 0.323488 9.523813 0.0000 Variance Equation C(5) 0.146586 1.71E-05 8561.296 0.0000
C(6) -0.012294 2.60E-05 -473.2906 0.0000 C(7) -0.173901 0.000160 -1083.691 0.0000 C(8) 1.016190 8.43E-06 120546.3 0.0000
R-squared 0.028276 Mean dependent var -0.003373
Adjusted R-squared 0.022126 S.D. dependent var 0.055183 S.E. of regression 0.054569 Akaike info criterion -3.377363 Sum squared resid 0.470494 Schwarz criterion -3.262044 Log likelihood 276.1891 Hannan-Quinn criter. -3.330536 F-statistic 0.919539 Durbin-Watson stat 1.925410 Prob(F-statistic) 0.469934
Aufgabe 4-d
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Pairwise Granger Causality Tests Date: 08/20/12 Time: 08:56 Sample: 1 162 Lags: 2
Null Hypothesis: Obs F-Statistic Prob. DLOG(BIPREAL) does not Granger Cause DLOG(ZINS10J) 156 2.52442 0.0835
DLOG(ZINS10J) does not Granger Cause DLOG(BIPREAL) 0.27884 0.7570
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Dependent Variable: DLOG(ZINS10J) Method: Least Squares Date: 08/20/12 Time: 09:12 Sample (adjusted): 3 160 Included observations: 158 after adjustments DLOG(ZINS10J)=C(4)*DLOG(BIPREAL(-1))
Coefficient Std. Error t-Statistic Prob. C(4) -1.234722 0.565881 -2.181944 0.0306 R-squared 0.025662 Mean dependent var -0.003019
Adjusted R-squared 0.025662 S.D. dependent var 0.048606 S.E. of regression 0.047978 Akaike info criterion -3.229848 Sum squared resid 0.361394 Schwarz criterion -3.210464 Log likelihood 256.1580 Hannan-Quinn criter. -3.221976 Durbin-Watson stat 1.805805
Thema 5: Die älteren Zinsstrukturtheorien (I): Empirische
Analysen und theoretische Grundlagen
(1) Stellen Sie die mathematischen Grundlagen der (anschließend) durchgeführten,
beliebig ausgewählten oder selbst durchgeführten Analysen dar.
(2) Zeigen und erläutern Sie Ihre Analysen.
(3) Ziehen Sie ggf. Schlüsse auf theoretische Grundlagen.
Aufgabe 5-a
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Laufzeit Standard Zins Standard% 1 1,363 2,535 0,537
30 1,389 2,620 0,530 90 1,308 2,746 0,476
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
180 1,269 2,879 0,440 360 1,209 3,026 0,420 720 1,300 2,834 0,458
1800 1,029 3,452 0,298 3600 0,799 4,099 0,194
Dependent Variable: ZINS Method: Least Squares Date: 08/20/12 Time: 10:55 Sample: 1 8 Included observations: 8 ZINS=C(1)+C(2)*LAUFZEIT
Coefficient Std. Error t-Statistic Prob. C(1) 2.685983 0.057599 46.63256 0.0000
C(2) 0.000399 3.96E-05 10.05592 0.0001 R-squared 0.943989 Mean dependent var 3.023875
Adjusted R-squared 0.934654 S.D. dependent var 0.517626 S.E. of regression 0.132320 Akaike info criterion -0.994863 Sum squared resid 0.105052 Schwarz criterion -0.975003 Log likelihood 5.979453 Hannan-Quinn criter. -1.128814 F-statistic 101.1216 Durbin-Watson stat 1.747682 Prob(F-statistic) 0.000056
2.4
2.8
3.2
3.6
4.0
4.4
0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000
LAUFZEIT
ZIN
S
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Dependent Variable: ZINS Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/20/12 Time: 10:56 Sample: 1 8 Included observations: 8 Failure to improve Likelihood after 32 iterations Presample variance: backcast (parameter = 0.7) ZINS=C(1)+C(2)*LAUFZEIT GARCH = C(3) + C(4)*RESID(-1)^2 + C(5)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob. C(1) 2.697890 0.056364 47.86573 0.0000
C(2) 0.000410 3.18E-05 12.88275 0.0000 Variance Equation C 0.005326 0.123702 0.043051 0.9657
RESID(-1)^2 -0.809957 2.251241 -0.359783 0.7190 GARCH(-1) 1.468011 7.787274 0.188514 0.8505
R-squared 0.941197 Mean dependent var 3.023875
-.2
-.1
.0
.1
.2
2.4
2.8
3.2
3.6
4.0
4.4
1 2 3 4 5 6 7 8
Residual Actual Fitted
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Adjusted R-squared 0.931397 S.D. dependent var 0.517626 S.E. of regression 0.135578 Akaike info criterion -0.703343 Sum squared resid 0.110288 Schwarz criterion -0.653692 Log likelihood 7.813370 Hannan-Quinn criter. -1.038218 F-statistic 24.00912 Durbin-Watson stat 1.673310 Prob(F-statistic) 0.000777
Dependent Variable: ZINS Method: Least Squares Date: 08/20/12 Time: 10:57 Sample: 1 8 Included observations: 8 ZINS=C(1)+C(2)*STANDARD_
Coefficient Std. Error t-Statistic Prob. C(1) 4.854710 0.098431 49.32091 0.0000
C(2) -4.368231 0.227162 -19.22961 0.0000 R-squared 0.984033 Mean dependent var 3.023875
Adjusted R-squared 0.981372 S.D. dependent var 0.517626 S.E. of regression 0.070648 Akaike info criterion -2.249897 Sum squared resid 0.029947 Schwarz criterion -2.230036 Log likelihood 10.99959 Hannan-Quinn criter. -2.383847 F-statistic 369.7779 Durbin-Watson stat 2.121758 Prob(F-statistic) 0.000001
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
-.08
-.04
.00
.04
.082.4
2.8
3.2
3.6
4.0
4.4
1 2 3 4 5 6 7 8
Residual Actual Fitted
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Thema 6: Die affine Zinsstrukturtheorie (II): Empirische
Analysen und theoretische Grundlagen
Aufgabe 6-a
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Drift
-.2
-.1
.0
.1
.2
2.4
2.8
3.2
3.6
4.0
4.4
1 2 3 4 5 6 7 8
Residual Actual Fitted
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Aufgabe 6-b
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Brownsche Bewegung (stochastischer Prozess)
System: UNTITLED Estimation Method: ARCH Maximum Likelihood (Marquardt) Covariance specification: Diagonal VECH Date: 08/20/12 Time: 11:28 Sample: 1 162 Included observations: 162 Total system (balanced) observations 162 Presample covariance: backcast (parameter =0.7) Failure to improve Likelihood after 22 iterations WARNING: Singular covariance - coefficients are not unique
Coefficient Std. Error z-Statistic Prob.
-2
-1
0
1
2
3
0
1
2
3
4
5
6
25 50 75 100 125 150
ZINS1TAG Trend Cycle
Hodrick-Prescott Filter (lambda=100000000)
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
C(4) 0.001042 NA NA NA Variance Equation Coefficients C(5) 0.009233 NA NA NA
C(6) 1.244982 NA NA NA C(7) -0.106435 NA NA NA
Log likelihood -185.9324 Schwarz criterion 2.421081
Avg. log likelihood -1.147731 Hannan-Quinn criter. 2.375798 Akaike info criterion 2.344844
Equation: ZINS1TAG =C(4)*ZEIT R-squared -0.095250 Mean dependent var 2.500679 Adjusted R-squared -0.095250 S.D. dependent var 1.363879 S.E. of regression 1.427356 Sum squared resid 328.0128 Durbin-Watson stat 0.014696
System: UNTITLED Estimation Method: ARCH Maximum Likelihood (Marquardt) Covariance specification: Diagonal VECH Date: 08/20/12 Time: 11:31 Sample: 2 162 Included observations: 161 Total system (balanced) observations 161
0
1
2
3
4
5
6
25 50 75 100 125 150
ZINS1TAG
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Presample covariance: backcast (parameter =0.7) Convergence achieved after 7 iterations
Coefficient Std. Error z-Statistic Prob. C(4) 3.08E-06 1.64E-06 1.876405 0.0606 Variance Equation Coefficients C(5) 0.000137 3.59E-05 3.818099 0.0001
C(6) 0.278842 0.047991 5.810351 0.0000 C(7) 0.772163 0.023408 32.98653 0.0000
Log likelihood 193.4199 Schwarz criterion -2.276486
Avg. log likelihood 1.201366 Hannan-Quinn criter. -2.321958 Akaike info criterion -2.353043
Equation: DLOG(ZINS1TAG) =C(4)*ZEIT R-squared -0.031698 Mean dependent var -0.013993 Adjusted R-squared -0.031698 S.D. dependent var 0.113640 S.E. of regression 0.115427 Sum squared resid 2.131760 Durbin-Watson stat 1.380130
Aufgabe 6-c Mean Reversion
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
(Ko varianz: dlog(zins1tag) zu dlog(Preisniveau) Dependent Variable: DLOG(ZINS1TAG) Method: Least Squares Date: 08/20/12 Time: 11:44 Sample (adjusted): 3 161 Included observations: 159 after adjustments DLOG(ZINS1TAG)=C(1)*DLOG(ZINS1TAG(-1))+C(3)+C(4) *DLOG(PREISNIVEAU)
Coefficient Std. Error t-Statistic Prob. C(1) 0.297461 0.073769 4.032353 0.0001
C(3) -0.025384 0.009501 -2.671785 0.0083 C(4) 8.695867 2.434096 3.572524 0.0005
R-squared 0.152258 Mean dependent var -0.013941
Adjusted R-squared 0.141390 S.D. dependent var 0.114349 S.E. of regression 0.105957 Akaike info criterion -1.632878 Sum squared resid 1.751395 Schwarz criterion -1.574975 Log likelihood 132.8138 Hannan-Quinn criter. -1.609364 F-statistic 14.00913 Durbin-Watson stat 2.091280 Prob(F-statistic) 0.000003
-.8
-.6
-.4
-.2
.0
.2
.4
.6
-.8
-.6
-.4
-.2
.0
.2
.4
.6
25 50 75 100 125 150
Residual Actual Fitted
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Dependent Variable: DLOG(ZINS1TAG) Method: ML - ARCH (Marquardt) - Normal distribution Date: 09/23/11 Time: 15:16 Sample (adjusted): 3 146 Included observations: 144 after adjustments Convergence achieved after 35 iterations Presample variance: backcast (parameter = 0.7) DLOG(ZINS1TAG)=C(1)*DLOG(ZINS1TAG(-1))+C(2)*DLOG(PREISNIVEAU( 5)) LOG(GARCH) = C(3) + C(4)*ABS(RESID(-1)/@SQRT(GARCH(-1))) + C(5) *RESID(-1)/@SQRT(GARCH(-1)) + C(6)*LOG(GARCH(-1))
Variable Coefficient Std. Error z-Statistic Prob. C(1) 0.334652 0.055946 5.981731 0.0000
C(2) 2.401094 0.812758 2.954255 0.0031 Variance Equation C(3) -6.853982 0.385897 -17.76116 0.0000
C(4) 1.352600 0.205431 6.584193 0.0000 C(5) 0.208250 0.090774 2.294165 0.0218 C(6) -0.122465 0.091205 -1.342738 0.1794
-.6
-.4
-.2
.0
.2
.4
.6
-.8
-.6
-.4
-.2
.0
.2
.4
.6
25 50 75 100 125 150
Residual Actual Fitted
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
R-squared 0.078455 Mean dependent var -0.010280
Adjusted R-squared 0.071965 S.D. dependent var 0.103591 S.E. of regression 0.099794 Akaike info criterion -2.415159 Sum squared resid 1.414142 Schwarz criterion -2.291417 Log likelihood 179.8915 Hannan-Quinn criter. -2.364877 Durbin-Watson stat 2.136016
Thema 7: Der Kreditmarkt im Eurowährungsgebiet,
empirische Analysen und theoretische Grundlagen
Aufgabe 7-a
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
8.6
8.7
8.8
8.9
9.0
9.1
9.2
9.3
9.4
9.5
1,998 2,000 2,002 2,004 2,006 2,008 2,010 2,012 2,014
ZEIT
LOG
(KR
ED
ITE
MF
I)
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Null Hypothesis: LOG(KREDITEMFI) has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -2.756711 0.0669
Test critical values: 1% level -3.471454 5% level -2.879494 10% level -2.576422 *MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(LOG(KREDITEMFI)) Method: Least Squares Date: 08/20/12 Time: 11:55 Sample (adjusted): 3 162 Included observations: 160 after adjustments
0
4
8
12
16
20
24
6000 7000 8000 9000 10000 11000 12000
Series: KREDITEMFISample 1 162Observations 162
Mean 9394.901Median 8927.000Maximum 12430.00Minimum 5942.000Std. Dev. 2160.794Skewness 0.064284Kurtosis 1.503534
Jarque-Bera 15.22760Probability 0.000494
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Null Hypothesis: DKREDMFI has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -0.988098 0.7567
Test critical values: 1% level -3.474265 5% level -2.880722 10% level -2.577077 *MacKinnon (1996) one-sided p-values.
-2
0
2
4
6
8
10
12
14
1,998 2,000 2,002 2,004 2,006 2,008 2,010 2,012 2,014
ZEIT
DK
RE
DM
FI
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12
Series: DKREDMFISample 1 162Observations 151
Mean 5.797285Median 5.800000Maximum 12.90000Minimum -1.000000Std. Dev. 3.532377Skewness -0.078412Kurtosis 2.067656
Jarque-Bera 5.623866Probability 0.060089
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Augmented Dickey-Fuller Test Equation Dependent Variable: D(DKREDMFI) Method: Least Squares Date: 08/20/12 Time: 11:56 Sample (adjusted): 13 162 Included observations: 150 after adjustments
-.03
-.02
-.01
.00
.01
.02
.03
1,998 2,000 2,002 2,004 2,006 2,008 2,010 2,012 2,014
ZEIT
DLO
G(K
RE
DIT
EM
FI)
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Null Hypothesis: DLOG(KREDITEMFI) has a unit root Exogenous: Constant Lag Length: 2 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -4.692441 0.0001
Test critical values: 1% level -3.471987 5% level -2.879727 10% level -2.576546 *MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLOG(KREDITEMFI)) Method: Least Squares Date: 08/20/12 Time: 13:57 Sample (adjusted): 5 162 Included observations: 158 after adjustments
Aufgabe 7-b (Wiederholung zu Kapitel 2)
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
0
10
20
30
40
-0.02 -0.01 -0.00 0.01 0.02
Series: DLOG(KREDITEMFI)Sample 1 162Observations 161
Mean 0.004556Median 0.004395Maximum 0.021059Minimum -0.023494Std. Dev. 0.005348Skewness -0.565565Kurtosis 7.404850
Jarque-Bera 138.7429Probability 0.000000
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
System: UNTITLED Estimation Method: Least Squares Date: 08/19/12 Time: 14:58 Sample: 9 159 Included observations: 151 Total system (balanced) observations 151
Coefficient Std. Error t-Statistic Prob. C(1) -0.028535 0.083575 -0.341423 0.7333
C(2) -0.005546 0.085650 -0.064750 0.9485 C(3) 0.002930 0.007180 0.408060 0.6839 C(4) 0.005401 0.008851 0.610235 0.5428 C(5) 0.000829 0.000881 0.940438 0.3487 C(6) -0.039367 0.015710 -2.505921 0.0134 C(7) 0.121060 0.082662 1.464517 0.1454 C(8) -0.043710 0.073191 -0.597201 0.5514 C(9) -0.013490 0.008374 -1.610931 0.1096
C(10) 0.183358 0.088724 2.066599 0.0407 C(11) -0.002567 0.003220 -0.797018 0.4269 C(12) -0.004976 0.004979 -0.999464 0.3194 C(13) 0.010839 0.005423 1.998817 0.0477 C(14) -0.013148 0.020796 -0.632243 0.5283 C(15) 0.012229 0.006648 1.839570 0.0681 C(16) -0.007602 0.004489 -1.693481 0.0927 C(17) 0.004888 0.003689 1.324938 0.1875 C(18) 0.000360 0.006377 0.056387 0.9551 C(19) -0.000715 0.021440 -0.033367 0.9734 C(20) -0.002948 0.020706 -0.142361 0.8870
Determinant residual covariance 1.82E-05
Equation: DLOG(KREDITEMFI) = C(1)*DLOG(KREDITEMFI(-1)) + C(2) *DLOG(KREDITEMFI(-2)) + C(3) + C(4)*DLOG(AKTIENINDEX) + C(5) *ARBEITSLOSE + C(6)*DLOG(BARGELD) + C(7)*DLOG(BIPNOM) + C(8)*DLOG(BIPREAL) + C(9)*DLOG(EZBKREDITE) + C(10)*DLOG(M3) + C(11)*MINDBIET + C(12)*ZINS1TAG + C(13)*ZINS1MT + C(14) *ZINS3MT + C(15)*ZINS6MT + C(16)*ZINS1J + C(17)*ZINS2J + C(18) *ZINS5J + C(19)*ZINS10J + C(20)*ZMIND Observations: 151 R-squared 0.370513 Mean dependent var 0.004593 Adjusted R-squared 0.279213 S.D. dependent var 0.005393 S.E. of regression 0.004579 Sum squared resid 0.002747 Durbin-Watson stat 2.071524
System: UNTITLED Estimation Method: ARCH Maximum Likelihood (Marquardt) Covariance specification: Diagonal VECH Date: 08/19/12 Time: 14:59 Sample: 9 159 Included observations: 151 Total system (balanced) observations 151
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Presample covariance: backcast (parameter =0.7) Convergence achieved after 32 iterations
Coefficient Std. Error z-Statistic Prob. C(1) 0.001640 0.064163 0.025558 0.9796
C(2) -0.020169 0.098564 -0.204625 0.8379 C(3) 0.001657 0.005986 0.276788 0.7819 C(4) 0.003623 0.010694 0.338759 0.7348 C(5) 0.000759 0.000831 0.913601 0.3609 C(6) -0.029800 0.013310 -2.238952 0.0252 C(7) 0.115281 0.066877 1.723788 0.0847 C(8) -0.038434 0.061805 -0.621858 0.5340 C(9) -0.011066 0.007826 -1.413951 0.1574
C(10) 0.188518 0.089956 2.095678 0.0361 C(11) -0.003719 0.002916 -1.275177 0.2022 C(12) -0.004887 0.004439 -1.100961 0.2709 C(13) 0.010836 0.004676 2.317583 0.0205 C(14) -0.011833 0.007729 -1.530880 0.1258 C(15) 0.012564 0.005976 2.102346 0.0355 C(16) -0.007750 0.004566 -1.697360 0.0896 C(17) 0.004874 0.003743 1.302197 0.1928 C(18) 6.12E-07 0.006585 9.30E-05 0.9999 C(19) -0.000524 0.008273 -0.063320 0.9495 C(20) -0.002281 0.006895 -0.330880 0.7407
Variance Equation Coefficients C(21) 4.39E-07 4.43E-07 0.992279 0.3211
C(22) -0.060152 0.014227 -4.228048 0.0000 C(23) 1.040732 0.029193 35.65014 0.0000
Log likelihood 620.4999 Schwarz criterion -7.454320
Avg. log likelihood 4.109271 Hannan-Quinn criter. -7.727198 Akaike info criterion -7.913905
Equation: DLOG(KREDITEMFI) = C(1)*DLOG(KREDITEMFI(-1)) + C(2) *DLOG(KREDITEMFI(-2)) + C(3) + C(4)*DLOG(AKTIENINDEX) + C(5) *ARBEITSLOSE + C(6)*DLOG(BARGELD) + C(7)*DLOG(BIPNOM) + C(8)*DLOG(BIPREAL) + C(9)*DLOG(EZBKREDITE) + C(10)*DLOG(M3) + C(11)*MINDBIET + C(12)*ZINS1TAG + C(13)*ZINS1MT + C(14) *ZINS3MT + C(15)*ZINS6MT + C(16)*ZINS1J + C(17)*ZINS2J + C(18) *ZINS5J + C(19)*ZINS10J + C(20)*ZMIND R-squared 0.361266 Mean dependent var 0.004593 Adjusted R-squared 0.268626 S.D. dependent var 0.005393 S.E. of regression 0.004612 Sum squared resid 0.002787 Durbin-Watson stat 2.141457
Dependent Variable: DLOG(KREDITEMFI) Method: Least Squares Date: 08/20/12 Time: 14:24 Sample (adjusted): 2 162 Included observations: 161 after adjustments
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
DLOG(KREDITEMFI) = C(6)*DLOG(BARGELD) +C(10)*DLOG(M3)+C(17) *ZINS2J
Coefficient Std. Error t-Statistic Prob. C(6) -0.042163 0.014974 -2.815716 0.0055
C(10) 0.270463 0.076668 3.527713 0.0005 C(17) 0.001227 0.000173 7.074039 0.0000
R-squared 0.236381 Mean dependent var 0.004556
Adjusted R-squared 0.226715 S.D. dependent var 0.005348 S.E. of regression 0.004703 Akaike info criterion -7.862912 Sum squared resid 0.003494 Schwarz criterion -7.805495 Log likelihood 635.9644 Hannan-Quinn criter. -7.839598 Durbin-Watson stat 1.932552
Dependent Variable: DLOG(KREDITEMFI) Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/20/12 Time: 14:27 Sample (adjusted): 2 162 Included observations: 161 after adjustments Convergence achieved after 16 iterations Presample variance: backcast (parameter = 0.7) DLOG(KREDITEMFI) = C(6)*DLOG(BARGELD) +C(10)*DLOG(M3)+C(17) *ZINS2J GARCH = C(18) + C(19)*RESID(-1)^2 + C(20)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob. C(6) -0.021983 0.009630 -2.282738 0.0224
C(10) 0.298484 0.050218 5.943796 0.0000 C(17) 0.001168 0.000103 11.34344 0.0000
Variance Equation C 4.44E-07 4.72E-07 0.941722 0.3463
RESID(-1)^2 -0.053920 0.009868 -5.464007 0.0000 GARCH(-1) 1.049041 0.026085 40.21564 0.0000
R-squared 0.226113 Mean dependent var 0.004556
Adjusted R-squared 0.216317 S.D. dependent var 0.005348 S.E. of regression 0.004734 Akaike info criterion -7.951528 Sum squared resid 0.003541 Schwarz criterion -7.836693 Log likelihood 646.0980 Hannan-Quinn criter. -7.904901 Durbin-Watson stat 1.952904
Dependent Variable: DLOG(KREDITEMFI) Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/20/12 Time: 14:27
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Sample (adjusted): 2 162 Included observations: 161 after adjustments Convergence achieved after 23 iterations Presample variance: backcast (parameter = 0.7) DLOG(KREDITEMFI) = C(6)*DLOG(BARGELD) +C(10)*DLOG(M3)+C(17) *ZINS2J LOG(GARCH) = C(18) + C(19)*ABS(RESID(-1)/@SQRT(GARCH(-1))) + C(20)*RESID(-1)/@SQRT(GARCH(-1)) + C(21)*LOG(GARCH(-1))
Variable Coefficient Std. Error z-Statistic Prob. C(6) -0.027927 0.008742 -3.194744 0.0014
C(10) 0.223616 0.053713 4.163170 0.0000 C(17) 0.001229 0.000148 8.299492 0.0000
Variance Equation C(18) -19.86819 0.560163 -35.46856 0.0000
C(19) 0.428774 0.096687 4.434634 0.0000 C(20) 0.161870 0.051421 3.147945 0.0016 C(21) -0.810516 0.057703 -14.04630 0.0000
R-squared 0.229883 Mean dependent var 0.004556
Adjusted R-squared 0.220134 S.D. dependent var 0.005348 S.E. of regression 0.004723 Akaike info criterion -7.935637 Sum squared resid 0.003524 Schwarz criterion -7.801663 Log likelihood 645.8188 Hannan-Quinn criter. -7.881238 Durbin-Watson stat 1.910619
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Thema 8: Die Aktienmärkte, empirische Analysen und
theoretische Grundlagen
Aufgabe 8-a
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
-.03
-.02
-.01
.00
.01
.02
-.03
-.02
-.01
.00
.01
.02
.03
25 50 75 100 125 150
Residual Actual Fitted
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
150
200
250
300
350
400
450
500
1,998 2,000 2,002 2,004 2,006 2,008 2,010 2,012 2,014
ZEIT
AK
TIE
NIN
DE
X
-60
-40
-20
0
20
40
60
1,998 2,000 2,002 2,004 2,006 2,008 2,010 2,012 2,014
ZEIT
DA
KT
IEN
IND
EX
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Null Hypothesis: DAKTIENINDEX has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -2.699454 0.0765
Test critical values: 1% level -3.474874 5% level -2.880987 10% level -2.577219 *MacKinnon (1996) one-sided p-values.
0
2
4
6
8
10
12
14
16
-37.5 -25.0 -12.5 0.0 12.5 25.0 37.5 50.0
Series: DAKTIENINDEXSample 1 162Observations 150
Mean 0.728667Median 5.600000Maximum 48.20000Minimum -47.10000Std. Dev. 23.57974Skewness -0.153936Kurtosis 2.096250
Jarque-Bera 5.697186Probability 0.057926
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Null Hypothesis: DLOG(AKTIENINDEX) has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=13)
-.25
-.20
-.15
-.10
-.05
.00
.05
.10
.15
1,998 2,000 2,002 2,004 2,006 2,008 2,010 2,012 2,014
ZEIT
DLO
G(A
KT
IEN
IND
EX
)
0
5
10
15
20
25
30
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10
Series: DLOG(AKTIENINDEX)Sample 1 162Observations 161
Mean -0.002163Median 0.011050Maximum 0.127398Minimum -0.222313Std. Dev. 0.050783Skewness -0.995626Kurtosis 5.520405
Jarque-Bera 69.21341Probability 0.000000
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -9.215511 0.0000
Test critical values: 1% level -3.471454 5% level -2.879494 10% level -2.576422 *MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLOG(AKTIENINDEX)) Method: Least Squares Date: 08/20/12 Time: 14:56 Sample (adjusted): 3 162 Included observations: 160 after adjustments
Aufgabe 8-b
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Dependent Variable: DLOG(AKTIENINDEX) Method: Least Squares Date: 08/20/12 Time: 17:27 Sample (adjusted): 14 152 Included observations: 139 after adjustments DLOG(AKTIENINDEX)=C(1)*DLOG(AKTIENINDEX(-1))+C(2) *DLOG(AKTIENINDEX(-2))+C(3)+C(4)*DLOG(ARBEITSLOSE)+C(5) *DLOG(BARGELD(2))+C(6)*DLOG(BIPNOM(7))+C(7) *DLOG(BIPREAL(7))+C(8)*DERDOL+C(9)*DLOG(EURUSD(1))+C(10) *DLOG(EZBKREDITE(4))+C(11)*DLOG(KREDITEMFI(2))+C(12) *DLOG(M1(3))+C(13)*DLOG(MINDRES(6))+C(14)*DROHSTOFFE(4) +C(15)*DLOG(MINDBIET(-4))+C(16)*DLOG(ZINS1TAG(-2))+C(17) *DLOG(ZINS1MT(-4))+C(18)*DLOG(ZINS3MT(-5))+C(19) *DLOG(ZINS6MT(-5))
Coefficient Std. Error t-Statistic Prob. C(1) 0.259849 0.086067 3.019136 0.0031
C(2) -0.082551 0.084800 -0.973487 0.3323 C(3) -0.013598 0.006470 -2.101827 0.0377 C(4) 0.073902 0.405268 0.182352 0.8556 C(5) -0.194106 0.154077 -1.259796 0.2102 C(6) 1.014437 0.818177 1.239875 0.2174 C(7) 0.530554 0.715554 0.741460 0.4599 C(8) 7.91E-05 0.000147 0.539157 0.5908 C(9) 0.169798 0.157167 1.080366 0.2821
C(10) -0.070257 0.082550 -0.851084 0.3964
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
C(11) 1.742362 0.788690 2.209186 0.0291 C(12) -0.849244 0.331779 -2.559669 0.0117 C(13) 0.176610 0.071299 2.477038 0.0146 C(14) 0.000316 0.000285 1.110080 0.2692 C(15) -0.070563 0.089246 -0.790660 0.4307 C(16) -0.059206 0.041911 -1.412665 0.1603 C(17) -0.033447 0.065159 -0.513313 0.6087 C(18) 0.107207 0.122325 0.876414 0.3826 C(19) -0.198013 0.151539 -1.306679 0.1938
R-squared 0.345903 Mean dependent var -0.004478
Adjusted R-squared 0.247789 S.D. dependent var 0.050876 S.E. of regression 0.044125 Akaike info criterion -3.277183 Sum squared resid 0.233641 Schwarz criterion -2.876068 Log likelihood 246.7642 Hannan-Quinn criter. -3.114181 F-statistic 3.525503 Durbin-Watson stat 2.064762 Prob(F-statistic) 0.000017
Dependent Variable: DLOG(AKTIENINDEX) Method: Least Squares Date: 08/20/12 Time: 17:38 Sample (adjusted): 3 156 Included observations: 154 after adjustments DLOG(AKTIENINDEX)=C(1)*DLOG(AKTIENINDEX(-1))+C(13) *DLOG(MINDRES(6))
Coefficient Std. Error t-Statistic Prob. C(1) 0.283334 0.074386 3.808956 0.0002
C(13) 0.250963 0.068034 3.688773 0.0003 R-squared 0.158206 Mean dependent var -0.001998
Adjusted R-squared 0.152668 S.D. dependent var 0.051040 S.E. of regression 0.046983 Akaike info criterion -3.265167 Sum squared resid 0.335523 Schwarz criterion -3.225726 Log likelihood 253.4178 Hannan-Quinn criter. -3.249146 Durbin-Watson stat 1.982421
System: UNTITLED Estimation Method: ARCH Maximum Likelihood (Marquardt) Covariance specification: Diagonal VECH Date: 08/20/12 Time: 17:52 Sample: 14 162 Included observations: 149 Total system (balanced) observations 149 Presample covariance: backcast (parameter =0.7) Convergence achieved after 16 iterations
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Coefficient Std. Error z-Statistic Prob. C(1) 0.295211 0.097526 3.026980 0.0025
C(5) -0.090431 0.044317 -2.040543 0.0413 Variance Equation Coefficients C(6) 0.000189 0.000186 1.016161 0.3096
C(7) 0.088896 0.048765 1.822969 0.0683 C(8) 0.839489 0.118220 7.101095 0.0000
Log likelihood 243.4132 Schwarz criterion -3.099374
Avg. log likelihood 1.633646 Hannan-Quinn criter. -3.159223 Akaike info criterion -3.200178
Equation: DLOG(AKTIENINDEX) = C(1)*DLOG(AKTIENINDEX(-1)) + C(5) *DLOG(ZINS1MT(-4)) R-squared 0.090705 Mean dependent var -0.004511 Adjusted R-squared 0.084520 S.D. dependent var 0.050731 S.E. of regression 0.048540 Sum squared resid 0.346355 Durbin-Watson stat 2.005068
Aufgabe 8-c
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
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Var(DLOG(AKTIENINDEX))
Conditional Covariance
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Conditional standard deviation
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Aufgabe 8-d
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Dependent Variable: DAKTIENINDEX Method: Least Squares Date: 08/20/12 Time: 20:10 Sample (adjusted): 20 155 Included observations: 136 after adjustments DAKTIENINDEX=C(1)*DAKTIENINDEX(-1)+C(2)*DAKTIENINDEX(-2)+C(3) +C(4)*ARBEITSLOSE(-4)+BARGELD(-3)+C(6)*DBIPREAL(4)+C(7) *DERDOL(5)+C(8)*DEZBKREDITE(-6)+C(9)*DKREDMFI(-3)+C(10) *DM1+C(11)*DROHSTOFFE(-4)+C(12)*INFLATIONSRATE+C(13) *LOHN(-1)+C(14)*MINDBIET(-2)+C(15)*ZINS1TAG(-1)+C(16) *ZINS1MT(-2)+C(17)*ZINS3MT(-2)+C(18)*ZINS6MT(-2)+C(19)*ZINS1J( -2)+C(20)*ZINS2J(-7)+C(21)*ZINS5J(-6)+C(22)*ZMIND+C(23) *ZINSUS10J(-10)
Coefficient Std. Error t-Statistic Prob. C(1) -0.761540 0.676524 -1.125665 0.2627
C(2) 0.066997 0.600980 0.111480 0.9114 C(3) -1539.768 136.2044 -11.30483 0.0000 C(4) 21.39731 13.06777 1.637411 0.1043 C(6) 17.66789 4.555939 3.877991 0.0002 C(7) -0.299136 0.197736 -1.512804 0.1331 C(8) 0.457286 0.381320 1.199218 0.2329 C(9) -5.038877 3.847816 -1.309542 0.1930
C(10) 23.15339 2.384318 9.710697 0.0000 C(11) 0.131511 0.412422 0.318875 0.7504 C(12) 47.85844 13.10400 3.652202 0.0004 C(13) 19.87810 17.87153 1.112278 0.2684 C(14) -139.4818 33.28774 -4.190184 0.0001 C(15) 163.2688 27.26425 5.988383 0.0000 C(16) 182.4239 39.29842 4.642016 0.0000 C(17) 112.7489 41.21487 2.735637 0.0072 C(18) -395.7353 71.33150 -5.547834 0.0000 C(19) 170.8325 50.79007 3.363502 0.0010 C(20) -16.04645 23.27310 -0.689485 0.4919 C(21) 57.57842 22.53822 2.554702 0.0119 C(22) 86.55519 13.17048 6.571909 0.0000 C(23) 7.752970 12.33372 0.628599 0.5309
R-squared -2.071340 Mean dependent var -0.288971
Adjusted R-squared -2.637113 S.D. dependent var 22.83430 S.E. of regression 43.54778 Akaike info criterion 10.53267 Sum squared resid 216190.7 Schwarz criterion 11.00383 Log likelihood -694.2214 Hannan-Quinn criter. 10.72414
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Durbin-Watson stat 1.128483
Dependent Variable: DAKTIENINDEX Method: Least Squares Date: 08/20/12 Time: 20:17 Sample (adjusted): 20 155 Included observations: 136 after adjustments DAKTIENINDEX=C(1)*DAKTIENINDEX(-1)+C(3)+C(6)*DBIPREAL(4)+C(8) *DEZBKREDITE(-6)+C(11)*DROHSTOFFE(-4)+C(23)*ZINSUS10J(-10)
Coefficient Std. Error t-Statistic Prob. C(1) 0.737547 0.036496 20.20893 0.0000
C(3) 12.30614 3.123369 3.940022 0.0001 C(6) 2.397413 0.381512 6.283973 0.0000 C(8) 0.185728 0.034231 5.425780 0.0000
C(11) -0.110307 0.031280 -3.526490 0.0006 C(23) -3.668955 0.678112 -5.410548 0.0000
R-squared 0.937431 Mean dependent var -0.288971
Adjusted R-squared 0.935025 S.D. dependent var 22.83430 S.E. of regression 5.820510 Akaike info criterion 6.403768 Sum squared resid 4404.184 Schwarz criterion 6.532267 Log likelihood -429.4562 Hannan-Quinn criter. 6.455987 F-statistic 389.5439 Durbin-Watson stat 1.866822 Prob(F-statistic) 0.000000
Dependent Variable: DAKTIENINDEX Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/20/12 Time: 20:18 Sample (adjusted): 20 155 Included observations: 136 after adjustments Convergence achieved after 49 iterations Presample variance: backcast (parameter = 0.7) DAKTIENINDEX=C(1)*DAKTIENINDEX(-1)+C(3)+C(6)*DBIPREAL(4)+C(8) *DEZBKREDITE(-6)+C(11)*DROHSTOFFE(-4)+C(23)*ZINSUS10J(-10) GARCH = C(24) + C(25)*RESID(-1)^2 + C(26)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob. C(1) 0.707848 0.035301 20.05165 0.0000
C(3) 14.79331 3.070053 4.818585 0.0000 C(6) 2.552149 0.361526 7.059372 0.0000 C(8) 0.193704 0.031110 6.226441 0.0000
C(11) -0.120790 0.030976 -3.899454 0.0001 C(23) -4.322899 0.728303 -5.935575 0.0000
Variance Equation C 11.54721 14.09920 0.818997 0.4128
RESID(-1)^2 0.083685 0.080364 1.041327 0.2977
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
GARCH(-1) 0.539801 0.477018 1.131614 0.2578 R-squared 0.936535 Mean dependent var -0.288971
Adjusted R-squared 0.934094 S.D. dependent var 22.83430 S.E. of regression 5.862079 Akaike info criterion 6.418300 Sum squared resid 4467.316 Schwarz criterion 6.611049 Log likelihood -427.4444 Hannan-Quinn criter. 6.496628 F-statistic 239.7947 Durbin-Watson stat 1.788607 Prob(F-statistic) 0.000000
Dependent Variable: DAKTIENINDEX Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/20/12 Time: 20:18 Sample (adjusted): 20 155 Included observations: 136 after adjustments Convergence achieved after 23 iterations Presample variance: backcast (parameter = 0.7) DAKTIENINDEX=C(1)*DAKTIENINDEX(-1)+C(3)+C(6)*DBIPREAL(4)+C(8) *DEZBKREDITE(-6)+C(11)*DROHSTOFFE(-4)+C(23)*ZINSUS10J(-10) LOG(GARCH) = C(24) + C(25)*ABS(RESID(-1)/@SQRT(GARCH(-1))) + C(26)*RESID(-1)/@SQRT(GARCH(-1)) + C(27)*LOG(GARCH(-1))
Variable Coefficient Std. Error z-Statistic Prob. C(1) 0.692854 0.032973 21.01258 0.0000
C(3) 12.64994 2.338094 5.410366 0.0000 C(6) 2.710965 0.346966 7.813335 0.0000 C(8) 0.207000 0.024993 8.282462 0.0000
C(11) -0.164025 0.027295 -6.009272 0.0000 C(23) -3.885305 0.559861 -6.939769 0.0000
Variance Equation C(24) 1.600306 0.792409 2.019546 0.0434
C(25) 0.895075 0.273846 3.268537 0.0011 C(26) 0.035854 0.154467 0.232113 0.8165 C(27) 0.320587 0.226454 1.415684 0.1569
R-squared 0.934095 Mean dependent var -0.288971
Adjusted R-squared 0.931560 S.D. dependent var 22.83430 S.E. of regression 5.973694 Akaike info criterion 6.400424 Sum squared resid 4639.053 Schwarz criterion 6.614590 Log likelihood -425.2289 Hannan-Quinn criter. 6.487456 F-statistic 204.7253 Durbin-Watson stat 1.714992 Prob(F-statistic) 0.000000
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Aufgabe 8-e
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Dependent Variable: AKTIENINDEX Method: Least Squares Date: 08/20/12 Time: 18:04 Sample (adjusted): 2 162 Included observations: 161 after adjustments AKTIENINDEX=C(1)*AKTIENINDEX(-1)
Coefficient Std. Error t-Statistic Prob. C(1) 0.997342 0.003752 265.7828 0.0000 R-squared 0.955520 Mean dependent var 300.6236
Adjusted R-squared 0.955520 S.D. dependent var 69.76831 S.E. of regression 14.71433 Akaike info criterion 8.221712
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Residual Actual Fitted
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Sum squared resid 34641.83 Schwarz criterion 8.240851 Log likelihood -660.8478 Hannan-Quinn criter. 8.229484 Durbin-Watson stat 1.394010
Dependent Variable: DAKTIENINDEX Method: Least Squares Date: 08/20/12 Time: 18:05 Sample (adjusted): 14 162 Included observations: 149 after adjustments DAKTIENINDEX=C(1)*DAKTIENINDEX(-1)
Coefficient Std. Error t-Statistic Prob. C(1) 0.946104 0.024999 37.84592 0.0000 R-squared 0.906309 Mean dependent var 0.477181
Adjusted R-squared 0.906309 S.D. dependent var 23.45656 S.E. of regression 7.179826 Akaike info criterion 6.787116 Sum squared resid 7629.386 Schwarz criterion 6.807277 Log likelihood -504.6402 Hannan-Quinn criter. 6.795307 Durbin-Watson stat 1.538076
Dependent Variable: DLOG(AKTIENINDEX) Method: Least Squares Date: 08/20/12 Time: 18:09 Sample (adjusted): 3 162 Included observations: 160 after adjustments DLOG(AKTIENINDEX)=C(1)*DLOG(AKTIENINDEX(-1))
Coefficient Std. Error t-Statistic Prob. C(1) 0.301603 0.075648 3.986947 0.0001 R-squared 0.089340 Mean dependent var -0.002095
Adjusted R-squared 0.089340 S.D. dependent var 0.050935 S.E. of regression 0.048607 Akaike info criterion -3.203882 Sum squared resid 0.375655 Schwarz criterion -3.184662 Log likelihood 257.3106 Hannan-Quinn criter. -3.196078 Durbin-Watson stat 1.972750
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
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AKTIENINDEX Trend Cycle
Hodrick-Prescott Filter (lambda=10)
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
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AKTIENINDEX Trend Cycle
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Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
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Residual Actual Fitted
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Thema 9: Die Devisenmärkte, empirische Analyse der Devisenkurse (EUR-USD) und theoretische Grundlagen
Aufgabe 9-a
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
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Conditional standard deviation
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
0.8
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Series: EURUSDSample 1 162Observations 162
Mean 1.193488Median 1.250000Maximum 1.570000Minimum 0.844000Std. Dev. 0.203990Skewness -0.293365Kurtosis 1.889269
Jarque-Bera 10.65134Probability 0.004865
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Null Hypothesis: EURUSD has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -1.474207 0.5443
Test critical values: 1% level -3.471454 5% level -2.879494 10% level -2.576422 *MacKinnon (1996) one-sided p-values.
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Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Null Hypothesis: DEURUSD has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -3.215709 0.0210
Test critical values: 1% level -3.474874 5% level -2.880987 10% level -2.577219 *MacKinnon (1996) one-sided p-values.
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Series: DEURUSDSample 1 162Observations 150
Mean 3.504600Median 4.425000Maximum 26.28000Minimum -16.60000Std. Dev. 9.962871Skewness 0.024245Kurtosis 2.256246
Jarque-Bera 3.472010Probability 0.176223
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Null Hypothesis: DLOG(EURUSD) has a unit root
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DLOG(EURUSD)
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Series: DLOG(EURUSD)Sample 1 162Observations 161
Mean 0.001263Median 0.000000Maximum 0.066036Minimum -0.072496Std. Dev. 0.024113Skewness 0.032389Kurtosis 3.370864
Jarque-Bera 0.950816Probability 0.621631
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -9.055340 0.0000
Test critical values: 1% level -3.471454 5% level -2.879494 10% level -2.576422 *MacKinnon (1996) one-sided p-values.
Aufgabe 9-b a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Dependent Variable: EURUSD Method: Least Squares Date: 08/20/12 Time: 20:50 Sample (adjusted): 2 162 Included observations: 161 after adjustments EURUSD=C(1)*EURUSD(-1)
Coefficient Std. Error t-Statistic Prob. C(1) 1.000804 0.001945 514.4293 0.0000 R-squared 0.978581 Mean dependent var 1.194565
Adjusted R-squared 0.978581 S.D. dependent var 0.204164 S.E. of regression 0.029880 Akaike info criterion -4.177067 Sum squared resid 0.142850 Schwarz criterion -4.157928 Log likelihood 337.2539 Hannan-Quinn criter. -4.169296 Durbin-Watson stat 1.356494
Dependent Variable: DEURUSD Method: Least Squares Date: 08/20/12 Time: 20:50 Sample (adjusted): 14 162 Included observations: 149 after adjustments DEURUSD=C(1)*DEURUSD(-1)
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Coefficient Std. Error t-Statistic Prob. C(1) 0.924209 0.031225 29.59874 0.0000 R-squared 0.836023 Mean dependent var 3.619195
Adjusted R-squared 0.836023 S.D. dependent var 9.896786 S.E. of regression 4.007607 Akaike info criterion 5.620954 Sum squared resid 2377.015 Schwarz criterion 5.641115 Log likelihood -417.7611 Hannan-Quinn criter. 5.629145 Durbin-Watson stat 1.531426
Dependent Variable: DLOG(EURUSD) Method: Least Squares Date: 08/20/12 Time: 20:51 Sample (adjusted): 3 162 Included observations: 160 after adjustments DLOG(EURUSD)=C(1)*DLOG(EURUSD(-1))
Coefficient Std. Error t-Statistic Prob. C(1) 0.319997 0.075054 4.263562 0.0000 R-squared 0.099552 Mean dependent var 0.001401
Adjusted R-squared 0.099552 S.D. dependent var 0.024125 S.E. of regression 0.022892 Akaike info criterion -4.709802 Sum squared resid 0.083325 Schwarz criterion -4.690582 Log likelihood 377.7842 Hannan-Quinn criter. -4.701998 Durbin-Watson stat 1.921460
Aufgabe 9-c
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Dependent Variable: DLOG(EURUSD) Method: Least Squares Date: 08/20/12 Time: 21:44 Sample (adjusted): 12 156 Included observations: 145 after adjustments DLOG(EURUSD)=C(1)*DLOG(EURUSD(-1))+C(2)*DLOG(EURUSD(-2)) +C(3)+C(4)*DLOG(BIPNOM(-1))+C(5)*DERDOL+C(6) *DLOG(EZBKREDITE(-1))+C(7)*DLOG(M1)+C(8)*DLOG(M2(-2))+C(9) *DLOG(LOHN(3))+C(10)*DLOG(MINDBIET(3))+C(11) *DLOG(ZINS1TAG(2))+C(12)*DLOG(ZINS1MT(3))+C(13) *DLOG(ZINS3MT(3))+C(14)*DLOG(ZINS6MT(4))+C(15)
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
*DLOG(ZINS1J(3))+C(16)*DLOG(ZINSUS10J(2)) Coefficient Std. Error t-Statistic Prob. C(1) 0.342029 0.081458 4.198846 0.0000
C(2) -0.225018 0.079868 -2.817385 0.0056 C(3) 0.006571 0.003112 2.111541 0.0367 C(4) -0.491215 0.305727 -1.606710 0.1106 C(5) -0.000121 5.39E-05 -2.244763 0.0265 C(6) -0.006418 0.037410 -0.171548 0.8641 C(7) -0.289249 0.145868 -1.982951 0.0495 C(8) 0.491845 0.338878 1.451395 0.1491 C(9) 0.040030 0.020448 1.957636 0.0524
C(10) 0.053046 0.034547 1.535486 0.1271 C(11) -0.037218 0.020824 -1.787224 0.0762 C(12) 0.043026 0.042633 1.009221 0.3148 C(13) 0.010236 0.062718 0.163200 0.8706 C(14) 0.039475 0.046094 0.856404 0.3934 C(15) -0.017361 0.048804 -0.355733 0.7226 C(16) 0.048030 0.029949 1.603700 0.1112
R-squared 0.341494 Mean dependent var 0.002437
Adjusted R-squared 0.264924 S.D. dependent var 0.024718 S.E. of regression 0.021192 Akaike info criterion -4.766581 Sum squared resid 0.057936 Schwarz criterion -4.438114 Log likelihood 361.5771 Hannan-Quinn criter. -4.633114 F-statistic 4.459869 Durbin-Watson stat 1.976834 Prob(F-statistic) 0.000001
Dependent Variable: DLOG(EURUSD) Method: Least Squares Date: 08/20/12 Time: 21:50 Sample (adjusted): 3 156 Included observations: 154 after adjustments DLOG(EURUSD)=C(1)*DLOG(EURUSD(-1))+C(9)*DLOG(LOHN(3))
Coefficient Std. Error t-Statistic Prob. C(1) 0.311520 0.074619 4.174803 0.0001
C(9) 0.061944 0.019273 3.214062 0.0016 R-squared 0.154736 Mean dependent var 0.001760
Adjusted R-squared 0.149175 S.D. dependent var 0.024299 S.E. of regression 0.022413 Akaike info criterion -4.745407 Sum squared resid 0.076359 Schwarz criterion -4.705966 Log likelihood 367.3963 Hannan-Quinn criter. -4.729386 Durbin-Watson stat 1.892833
Dependent Variable: DLOG(EURUSD) Method: ML - ARCH (Marquardt) - Normal distribution
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Date: 08/20/12 Time: 21:50 Sample (adjusted): 3 156 Included observations: 154 after adjustments Convergence achieved after 20 iterations Presample variance: backcast (parameter = 0.7) DLOG(EURUSD)=C(1)*DLOG(EURUSD(-1))+C(9)*DLOG(LOHN(3)) GARCH = C(10) + C(11)*RESID(-1)^2 + C(12)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob. C(1) 0.330428 0.073049 4.523350 0.0000
C(9) 0.059617 0.020687 2.881935 0.0040 Variance Equation C 1.56E-05 7.47E-06 2.091421 0.0365
RESID(-1)^2 -0.069538 0.035478 -1.960027 0.0500 GARCH(-1) 1.046222 0.051448 20.33572 0.0000
R-squared 0.154309 Mean dependent var 0.001760
Adjusted R-squared 0.148746 S.D. dependent var 0.024299 S.E. of regression 0.022419 Akaike info criterion -4.822764 Sum squared resid 0.076398 Schwarz criterion -4.724162 Log likelihood 376.3528 Hannan-Quinn criter. -4.782712 Durbin-Watson stat 1.925042
Dependent Variable: DLOG(EURUSD) Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/20/12 Time: 21:51 Sample (adjusted): 3 156 Included observations: 154 after adjustments Convergence achieved after 28 iterations Presample variance: backcast (parameter = 0.7) DLOG(EURUSD)=C(1)*DLOG(EURUSD(-1))+C(9)*DLOG(LOHN(3)) LOG(GARCH) = C(10) + C(11)*ABS(RESID(-1)/@SQRT(GARCH(-1))) + C(12)*RESID(-1)/@SQRT(GARCH(-1)) + C(13)*LOG(GARCH(-1))
Variable Coefficient Std. Error z-Statistic Prob. C(1) 0.352175 0.070230 5.014621 0.0000
C(9) 0.066604 0.020177 3.301050 0.0010 Variance Equation C(10) -0.190237 0.100193 -1.898718 0.0576
C(11) -0.207964 0.106757 -1.948011 0.0514 C(12) 0.057421 0.049683 1.155747 0.2478 C(13) 0.952792 0.005997 158.8891 0.0000
R-squared 0.152704 Mean dependent var 0.001760
Adjusted R-squared 0.147129 S.D. dependent var 0.024299 S.E. of regression 0.022440 Akaike info criterion -4.820245 Sum squared resid 0.076543 Schwarz criterion -4.701922 Log likelihood 377.1589 Hannan-Quinn criter. -4.772183 Durbin-Watson stat 1.960061
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Aufgabe 9-d
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Dependent Variable: DEURUSD Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/20/12 Time: 22:02 Sample (adjusted): 15 161 Included observations: 147 after adjustments Convergence achieved after 64 iterations Presample variance: backcast (parameter = 0.7) DEURUSD = C(1)*DEURUSD(-1) + C(2)*DEURUSD(-2) + C(4) *ZINSUS10J(1)+C(5)*ZINS10J(-1) GARCH = C(6) + C(7)*RESID(-1)^2 + C(8)*GARCH(-1)
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Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Variable Coefficient Std. Error z-Statistic Prob. C(1) 1.144984 0.082174 13.93366 0.0000
C(2) -0.246475 0.081132 -3.037955 0.0024 C(4) -0.984142 0.554433 -1.775043 0.0759 C(5) 1.102643 0.562892 1.958888 0.0501
Variance Equation C 0.520810 0.141884 3.670685 0.0002
RESID(-1)^2 -0.084465 0.034234 -2.467282 0.0136 GARCH(-1) 1.060962 0.045580 23.27677 0.0000
R-squared 0.842316 Mean dependent var 3.833810
Adjusted R-squared 0.839008 S.D. dependent var 9.789303 S.E. of regression 3.927837 Akaike info criterion 5.474315 Sum squared resid 2206.191 Schwarz criterion 5.616717 Log likelihood -395.3622 Hannan-Quinn criter. 5.532175 Durbin-Watson stat 1.965872
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Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Thema 10: Die Rohstoffmärkte, empirische Analyse der
Rohstoffpreise (Ölpreis und Gesamtindex)
Aufgabe 10-a
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
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Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
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Series: DERDOLSample 1 162Observations 151
Mean 19.68609Median 22.00000Maximum 191.0000Minimum -55.00000Std. Dev. 38.71037Skewness 0.847175Kurtosis 5.602444
Jarque-Bera 60.67393Probability 0.000000
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Null Hypothesis: DERDOL has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -5.347166 0.0000
Test critical values: 1% level -3.474567 5% level -2.880853 10% level -2.577147 *MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(DERDOL) Method: Least Squares Date: 08/21/12 Time: 06:35 Sample (adjusted): 14 162 Included observations: 149 after adjustments
Aufgabe 10-b
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
System: UNTITLED Estimation Method: Least Squares Date: 08/21/12 Time: 07:29 Sample: 14 151 Included observations: 138 Total system (balanced) observations 138
Coefficient Std. Error t-Statistic Prob. C(1) 0.862143 0.080650 10.68993 0.0000
C(2) -0.172083 0.075446 -2.280876 0.0243 C(3) -24.54161 12.33751 -1.989188 0.0490 C(4) 0.040500 0.101497 0.399027 0.6906 C(5) 0.412293 0.323890 1.272938 0.2055 C(6) 1.224517 0.777354 1.575236 0.1178 C(7) -1.982130 1.555583 -1.274204 0.2051 C(8) 1.598103 0.627743 2.545793 0.0122 C(9) 0.100354 0.122836 0.816975 0.4156
C(10) 9.310891 2.606993 3.571507 0.0005 C(11) -19.84689 10.79991 -1.837690 0.0686 C(12) 1.656983 11.11444 0.149084 0.8817 C(13) 6.574976 5.897472 1.114880 0.2671 C(14) -2.208947 8.503847 -0.259759 0.7955
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
C(15) 8.505936 10.31055 0.824974 0.4110 C(16) 2.627439 9.392271 0.279745 0.7802 C(17) -1.402092 7.162171 -0.195764 0.8451 C(18) 0.830661 5.392811 0.154031 0.8778
Determinant residual covariance 135.3651
Equation: DERDOL = C(1)*DERDOL(-1) + C(2)*DERDOL(-2) + C(3) + C(4) *DAKTIENINDEX + C(5)*DARBEITSLOSE(9) + C(6)*DBIPNOM(8) + C(7)*DBIPREAL(5) + C(8)*DM1(-2) + C(9)*DROHSTOFFE + C(10) *INFLATIONSRATE(7) + C(11)*MINDBIET(-7) + C(12)*ZINS1TAG(-7) + C(13)*ZINS1MT(-5) + C(14)*ZINS3MT(-8) + C(15)*ZINS6MT(-7) + C(16) *ZINS1J(-8) + C(17)*ZINS2J(-10) + C(18)*ZINS5J(-11) Observations: 138 R-squared 0.892634 Mean dependent var 17.46377 Adjusted R-squared 0.877424 S.D. dependent var 35.63689 S.E. of regression 12.47677 Sum squared resid 18680.39 Durbin-Watson stat 1.868550
Dependent Variable: DERDOL Method: Least Squares Date: 08/21/12 Time: 07:36 Sample (adjusted): 14 155 Included observations: 142 after adjustments DERDOL = C(1)*DERDOL(-1) + C(2)*DERDOL(-2) +C(10) *INFLATIONSRATE(7) + C(11)*MINDBIET(-7)
Coefficient Std. Error t-Statistic Prob. C(1) 0.946991 0.076449 12.38727 0.0000
C(2) -0.190308 0.069771 -2.727609 0.0072 C(10) 5.659320 1.077599 5.251784 0.0000 C(11) -3.211020 0.735575 -4.365320 0.0000
R-squared 0.873613 Mean dependent var 17.83803
Adjusted R-squared 0.870865 S.D. dependent var 35.19986 S.E. of regression 12.64918 Akaike info criterion 7.940826 Sum squared resid 22080.23 Schwarz criterion 8.024089 Log likelihood -559.7986 Hannan-Quinn criter. 7.974661 Durbin-Watson stat 1.842641
System: UNTITLED Estimation Method: ARCH Maximum Likelihood (Marquardt) Covariance specification: Diagonal VECH Date: 08/21/12 Time: 07:34
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Sample: 14 155 Included observations: 142 Total system (balanced) observations 142 Presample covariance: backcast (parameter =0.7) Convergence achieved after 32 iterations
Coefficient Std. Error z-Statistic Prob. C(1) 0.975288 0.021594 45.16387 0.0000
C(2) -0.209897 0.032476 -6.463220 0.0000 C(10) 5.920234 1.050468 5.635804 0.0000 C(11) -3.373738 0.742504 -4.543729 0.0000
Variance Equation Coefficients C(12) 13.50800 2.384563 5.664771 0.0000
C(13) -0.140394 0.033426 -4.200104 0.0000 C(14) 1.038422 0.044825 23.16629 0.0000
Log likelihood -547.1321 Schwarz criterion 7.950388
Avg. log likelihood -3.853043 Hannan-Quinn criter. 7.863888 Akaike info criterion 7.804678
Equation: DERDOL = C(1)*DERDOL(-1) + C(2)*DERDOL(-2) +C(10) *INFLATIONSRATE(7) + C(11)*MINDBIET(-7) R-squared 0.873199 Mean dependent var 17.83803 Adjusted R-squared 0.870443 S.D. dependent var 35.19986 S.E. of regression 12.66985 Sum squared resid 22152.48 Durbin-Watson stat 1.887749
Dependent Variable: DERDOL Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/21/12 Time: 07:37 Sample (adjusted): 14 155 Included observations: 142 after adjustments Convergence achieved after 26 iterations Presample variance: backcast (parameter = 0.7) DERDOL = C(1)*DERDOL(-1) + C(2)*DERDOL(-2) +C(10) *INFLATIONSRATE(7) + C(11)*MINDBIET(-7) LOG(GARCH) = C(12) + C(13)*ABS(RESID(-1)/@SQRT(GARCH(-1))) + C(14)*RESID(-1)/@SQRT(GARCH(-1)) + C(15)*LOG(GARCH(-1))
Variable Coefficient Std. Error z-Statistic Prob. C(1) 0.990230 0.084300 11.74646 0.0000
C(2) -0.169714 0.074831 -2.267964 0.0233 C(10) 4.744598 1.102086 4.305107 0.0000 C(11) -2.721528 0.793303 -3.430626 0.0006
Variance Equation C(12) 0.633022 0.265537 2.383932 0.0171
C(13) -0.081741 0.082764 -0.987630 0.3233
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
C(14) 0.130181 0.071032 1.832697 0.0668 C(15) 0.881679 0.054200 16.26716 0.0000
R-squared 0.869771 Mean dependent var 17.83803
Adjusted R-squared 0.866940 S.D. dependent var 35.19986 S.E. of regression 12.84001 Akaike info criterion 7.877733 Sum squared resid 22751.49 Schwarz criterion 8.044258 Log likelihood -551.3190 Hannan-Quinn criter. 7.945402 Durbin-Watson stat 1.882755
Dependent Variable: DERDOL Method: Least Squares Date: 08/21/12 Time: 07:42 Sample (adjusted): 14 155 Included observations: 142 after adjustments DERDOL = C(1)*DERDOL(-1) + C(2)*DERDOL(-2) + C(4) *INFLATIONSRATE(7)
Coefficient Std. Error t-Statistic Prob. C(1) 1.042444 0.077868 13.38741 0.0000
C(2) -0.227942 0.073596 -3.097205 0.0024 C(4) 1.617474 0.586014 2.760130 0.0066
R-squared 0.856161 Mean dependent var 17.83803
Adjusted R-squared 0.854091 S.D. dependent var 35.19986 S.E. of regression 13.44566 Akaike info criterion 8.056090 Sum squared resid 25129.23 Schwarz criterion 8.118537 Log likelihood -568.9824 Hannan-Quinn criter. 8.081466 Durbin-Watson stat 1.819408
Aufgabe 10-c
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
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Series: DROHSTOFFESample 1 162Observations 162
Mean 6.540741Median 3.400000Maximum 54.70000Minimum -25.00000Std. Dev. 16.95216Skewness 0.829216Kurtosis 3.702886
Jarque-Bera 21.90003Probability 0.000018
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Null Hypothesis: DROHSTOFFE has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=13)
t-Statistic Prob.* Augmented Dickey-Fuller test statistic -2.842833 0.0546
Test critical values: 1% level -3.471454 5% level -2.879494 10% level -2.576422 *MacKinnon (1996) one-sided p-values.
System: UNTITLED Estimation Method: Least Squares Date: 08/21/12 Time: 09:01 Sample: 18 152 Included observations: 135 Total system (balanced) observations 135
Coefficient Std. Error t-Statistic Prob. C(1) 0.972936 0.087301 11.14460 0.0000
C(2) -0.054288 0.090442 -0.600252 0.5495 C(3) 8.823474 7.728392 1.141696 0.2559 C(4) 0.009781 0.016516 0.592214 0.5549 C(5) 0.201175 0.185943 1.081919 0.2815 C(6) 0.099749 0.580373 0.171871 0.8638 C(7) 0.040524 0.020708 1.956960 0.0527 C(8) 0.006585 0.033492 0.196627 0.8445 C(9) -0.018947 0.354532 -0.053443 0.9575
C(10) -2.403537 1.488924 -1.614278 0.1092 C(11) -2.153803 1.728217 -1.246257 0.2152 C(12) 1.111037 1.501438 0.739982 0.4608 C(13) 6.211145 3.129507 1.984704 0.0495 C(14) -0.672878 4.013469 -0.167655 0.8671 C(15) 0.418184 7.319977 0.057129 0.9545 C(16) -5.424543 4.535858 -1.195924 0.2341 C(17) -0.437398 1.001361 -0.436804 0.6631 C(18) -0.982950 1.575105 -0.624054 0.5338
Determinant residual covariance 19.52570
Equation: DROHSTOFFE = C(1)*DROHSTOFFE(-1) + C(2)*DROHSTOFFE( -2) + C(3) + C(4)*AKTIENINDEX + C(5)*DARBEITSLOSE(-5) + C(6) *DBIPREAL(3) + C(7)*DERDOL + C(8)*DEZBKREDITE(-3) + C(9)*DM1( -3) + C(10)*INFLATIONSRATE(-3) + C(11)*LOHN(-3) + C(12) *ZINS1TAG(-3) + C(13)*ZINS1MT(-7) + C(14)*ZINS3MT(-8) + C(15) *ZINS6MT(-8) + C(16)*ZINS1J(-8) + C(17)*ZINS2J(10) + C(18)*ZINS5J( -9) Observations: 135 R-squared 0.936998 Mean dependent var 7.415556 Adjusted R-squared 0.927844 S.D. dependent var 17.67017
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
S.E. of regression 4.746541 Sum squared resid 2635.969 Durbin-Watson stat 1.979983
Dependent Variable: DROHSTOFFE Method: Least Squares Date: 08/21/12 Time: 09:17 Sample (adjusted): 18 162 Included observations: 145 after adjustments DROHSTOFFE = C(1)*DROHSTOFFE(-1) + C(4)*AKTIENINDEX +C(5) *DARBEITSLOSE(-5) + C(7)*DERDOL + C(10)*INFLATIONSRATE(-3)
Coefficient Std. Error t-Statistic Prob. C(1) 0.887727 0.026908 32.99158 0.0000
C(4) 0.011518 0.003692 3.119566 0.0022 C(5) 0.133450 0.043939 3.037206 0.0028 C(7) 0.043830 0.015085 2.905587 0.0043
C(10) -1.627430 0.467463 -3.481409 0.0007 R-squared 0.929078 Mean dependent var 6.789655
Adjusted R-squared 0.927051 S.D. dependent var 17.23050 S.E. of regression 4.653792 Akaike info criterion 5.947116 Sum squared resid 3032.090 Schwarz criterion 6.049762 Log likelihood -426.1659 Hannan-Quinn criter. 5.988825 Durbin-Watson stat 1.664871
Dependent Variable: DROHSTOFFE Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/21/12 Time: 09:17 Sample (adjusted): 18 162 Included observations: 145 after adjustments Convergence achieved after 37 iterations Presample variance: backcast (parameter = 0.7) DROHSTOFFE = C(1)*DROHSTOFFE(-1) + C(4)*AKTIENINDEX +C(5) *DARBEITSLOSE(-5) + C(7)*DERDOL + C(10)*INFLATIONSRATE(-3) GARCH = C(11) + C(12)*RESID(-1)^2 + C(13)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob. C(1) 0.886870 0.027792 31.91075 0.0000
C(4) 0.012181 0.003584 3.398468 0.0007 C(5) 0.117575 0.041630 2.824273 0.0047 C(7) 0.045659 0.017195 2.655365 0.0079
C(10) -1.725649 0.528208 -3.266991 0.0011 Variance Equation C 10.31023 10.18019 1.012774 0.3112
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
RESID(-1)^2 -0.054922 0.034993 -1.569496 0.1165 GARCH(-1) 0.548478 0.501284 1.094147 0.2739
R-squared 0.928993 Mean dependent var 6.789655
Adjusted R-squared 0.926964 S.D. dependent var 17.23050 S.E. of regression 4.656563 Akaike info criterion 5.963779 Sum squared resid 3035.700 Schwarz criterion 6.128013 Log likelihood -424.3740 Hannan-Quinn criter. 6.030513 Durbin-Watson stat 1.655604
Dependent Variable: DROHSTOFFE Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/21/12 Time: 09:18 Sample (adjusted): 12 162 Included observations: 151 after adjustments Convergence achieved after 22 iterations Presample variance: backcast (parameter = 0.7) DROHSTOFFE = C(1)*DROHSTOFFE(-1) + C(4)*AKTIENINDEX +C(7) *DERDOL + C(10)*INFLATIONSRATE(-3) LOG(GARCH) = C(11) + C(12)*ABS(RESID(-1)/@SQRT(GARCH(-1))) + C(13)*RESID(-1)/@SQRT(GARCH(-1)) + C(14)*LOG(GARCH(-1))
Variable Coefficient Std. Error z-Statistic Prob. C(1) 0.842257 0.022631 37.21691 0.0000
C(4) 0.003876 0.002320 1.671113 0.0947 C(7) 0.051021 0.006516 7.830362 0.0000
C(10) -0.838026 0.263057 -3.185724 0.0014 Variance Equation C(11) 1.614758 0.380899 4.239327 0.0000
C(12) -0.447345 0.176184 -2.539073 0.0111 C(13) 0.565294 0.122404 4.618256 0.0000 C(14) 0.559459 0.119110 4.696982 0.0000
R-squared 0.916930 Mean dependent var 7.321854
Adjusted R-squared 0.915235 S.D. dependent var 17.08696 S.E. of regression 4.974766 Akaike info criterion 5.887221 Sum squared resid 3638.000 Schwarz criterion 6.047077 Log likelihood -436.4852 Hannan-Quinn criter. 5.952163 Durbin-Watson stat 1.385905
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
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Forecast: DROHSTOFFEFActual: DROHSTOFFEForecast sample: 1 162Adjusted sample: 13 162Included observations: 150Root Mean Squared Error 12.13539Mean Absolute Error 10.07276Mean Abs. Percent Error 324.5727Theil Inequality Coefficient 0.343310 Bias Proportion 0.002753 Variance Proportion 0.017263 Covariance Proportion 0.979984
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Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Thema 11: Die Wirkungen der Geldpolitik und die Taylor-
Regel
Aufgabe 11-a
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
System: UNTITLED Estimation Method: Least Squares Date: 08/21/12 Time: 09:39 Sample: 6 159 Included observations: 154 Total system (balanced) observations 154
Coefficient Std. Error t-Statistic Prob. C(1) 0.983084 0.010309 95.36575 0.0000
C(3) 0.076560 0.030842 2.482338 0.0142 C(4) -0.055658 0.015858 -3.509735 0.0006 C(5) 0.055303 0.006602 8.376939 0.0000
Determinant residual covariance 0.017502
Equation: ZINS1TAG = C(1)*ZINS1TAG(-1) + C(3) + C(4)*INFLATIONGAP( -5) + C(5)*OUTPUTGAP Observations: 154 R-squared 0.990520 Mean dependent var 2.530130 Adjusted R-squared 0.990331 S.D. dependent var 1.363206 S.E. of regression 0.134048 Sum squared resid 2.695312 Durbin-Watson stat 1.775149
Dependent Variable: ZINS1TAG Method: Least Squares Date: 08/21/12 Time: 09:45 Sample (adjusted): 3 154 Included observations: 152 after adjustments ZINS1TAG = C(1)*ZINS1TAG(-1) + C(2)*ZINS1TAG(-2) + C(3) + C(4) *INFLATIONGAP(8) + C(5)*OUTPUTGAP
Coefficient Std. Error t-Statistic Prob. C(1) 1.146897 0.083139 13.79496 0.0000
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
C(2) -0.178223 0.081045 -2.199073 0.0294 C(3) 0.095595 0.031884 2.998271 0.0032 C(4) 0.037222 0.019284 1.930196 0.0555 C(5) 0.040344 0.009645 4.182904 0.0000
R-squared 0.989616 Mean dependent var 2.600658
Adjusted R-squared 0.989333 S.D. dependent var 1.320054 S.E. of regression 0.136337 Akaike info criterion -1.115038 Sum squared resid 2.732389 Schwarz criterion -1.015568 Log likelihood 89.74287 Hannan-Quinn criter. -1.074630 F-statistic 3502.204 Durbin-Watson stat 2.032695 Prob(F-statistic) 0.000000
Aufgabe 11-b
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
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Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Aufgabe 11-c
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Dependent Variable: ZINS1TAG Method: Least Squares Date: 08/21/12 Time: 09:54 Sample: 1 162 Included observations: 162 ZINS1TAG=C(1)*INFLATIONSRATE
Coefficient Std. Error t-Statistic Prob. C(1) 1.145431 0.045181 25.35186 0.0000 R-squared 0.122076 Mean dependent var 2.500679
Adjusted R-squared 0.122076 S.D. dependent var 1.363879 S.E. of regression 1.277922 Akaike info criterion 3.334501 Sum squared resid 262.9265 Schwarz criterion 3.353560 Log likelihood -269.0946 Hannan-Quinn criter. 3.342239 Durbin-Watson stat 0.053776
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Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Aufgabe 11-d
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Date: 08/21/12 Time: 10:05 Sample: 1 162 Included observations: 162 Correlations are asymptotically consistent approximations
ZINS1TAG,INFLATIONSRA
TE(-i) ZINS1TAG,INFLATIONSRAT
E(+i) i lag lead
-1
0
1
2
3
4
5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
ZINS1TAG
INF
LAT
ION
SR
AT
E(5
)
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
. |**** | . |**** | 0 0.4309 0.4309
. |**** | . |**** | 1 0.4393 0.4179 . |**** | . |**** | 2 0.4352 0.3953 . |**** | . |**** | 3 0.4188 0.3675 . |**** | . |*** | 4 0.3898 0.3308 . |**** | . |*** | 5 0.3545 0.2909 . |*** | . |** | 6 0.3132 0.2429 . |*** | . |** | 7 0.2734 0.1895 . |** | . |*. | 8 0.2338 0.1339 . |** | . |*. | 9 0.1940 0.0789 . |*. | . | . | 10 0.1544 0.0274 . |*. | . | . | 11 0.1132 -0.0165 . |*. | .*| . | 12 0.0735 -0.0576 . | . | .*| . | 13 0.0432 -0.0952 . | . | .*| . | 14 0.0175 -0.1283 . | . | **| . | 15 0.0007 -0.1588 . | . | **| . | 16 -0.0105 -0.1855 . | . | **| . | 17 -0.0199 -0.2073 . | . | **| . | 18 -0.0255 -0.2259 . | . | **| . | 19 -0.0323 -0.2445 . | . | ***| . | 20 -0.0405 -0.2639 .*| . | ***| . | 21 -0.0430 -0.2818 .*| . | ***| . | 22 -0.0425 -0.2940 . | . | ***| . | 23 -0.0403 -0.3054 . | . | ***| . | 24 -0.0318 -0.3109 . | . | ***| . | 25 -0.0273 -0.3090 . | . | ***| . | 26 -0.0160 -0.3025 . | . | ***| . | 27 -0.0048 -0.2924 . | . | ***| . | 28 0.0079 -0.2774 . | . | ***| . | 29 0.0084 -0.2645 . | . | ***| . | 30 0.0098 -0.2477 . | . | **| . | 31 0.0092 -0.2276 . | . | **| . | 32 0.0034 -0.2024 . | . | **| . | 33 -0.0145 -0.1741 . | . | .*| . | 34 -0.0350 -0.1445 .*| . | .*| . | 35 -0.0585 -0.1114 .*| . | .*| . | 36 -0.0930 -0.0765
Aufgabe 11-e
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Pairwise Granger Causality Tests
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Date: 08/21/12 Time: 12:48 Sample: 1 162 Lags: 2
Null Hypothesis: Obs F-Statistic Prob. INFLATIONGAP(8) does not Granger Cause OUTPUTGAP 152 5.99308 0.0031
OUTPUTGAP does not Granger Cause INFLATIONGAP(8) 0.86394 0.4236
System: UNTITLED Estimation Method: Least Squares Date: 08/21/12 Time: 12:50 Sample: 2 154 Included observations: 153 Total system (balanced) observations 153
Coefficient Std. Error t-Statistic Prob. C(1) 0.936409 0.022334 41.92833 0.0000
C(4) 0.181695 0.057638 3.152353 0.0020 Determinant residual covariance 0.237853
Equation: OUTPUTGAP = C(1)*OUTPUTGAP(-1) + C(4)*INFLATIONGAP(8) Observations: 153 R-squared 0.931995 Mean dependent var -0.758170 Adjusted R-squared 0.931545 S.D. dependent var 1.876328 S.E. of regression 0.490921 Sum squared resid 36.39151 Durbin-Watson stat 2.019859
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
Aufgabe 11-f
a. Was zeigt die nachfolgenden Darstellungen?
b. Was fällt Ihnen dabei auf?
c. Welche Theorie(n) könnten relevant sein?
Date: 08/21/12 Time: 12:53 Sample: 1 162 Included observations: 149 Correlations are asymptotically consistent approximations
DEZBKREDITE,INFLATION
SRATE(-i) DEZBKREDITE,INFLATION
SRATE(+i) i lag lead **| . | **| . | 0 -0.2120 -0.2120
**| . | **| . | 1 -0.1830 -0.2393 **| . | ***| . | 2 -0.1500 -0.2528 .*| . | ***| . | 3 -0.1128 -0.2570
-3
-2
-1
0
1
2
3
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2
OUTPUTGAP
INF
LAT
ION
GA
P(8
)
Universität zu Köln
Univ.-Professor Dr. Ralph Anderegg Center for Macroeconomic Research (CMR)
.*| . | ***| . | 4 -0.0703 -0.2470 . | . | **| . | 5 -0.0294 -0.2274 . | . | **| . | 6 0.0155 -0.2090 . | . | **| . | 7 0.0474 -0.1852 . |*. | **| . | 8 0.0729 -0.1676 . |*. | .*| . | 9 0.1087 -0.1401 . |*. | .*| . | 10 0.1460 -0.1132 . |** | .*| . | 11 0.1955 -0.0904 . |** | .*| . | 12 0.2362 -0.0655 . |** | .*| . | 13 0.2495 -0.0424 . |** | . | . | 14 0.2505 -0.0201 . |** | . | . | 15 0.2358 0.0010 . |** | . | . | 16 0.2254 0.0242 . |** | . | . | 17 0.2242 0.0443 . |** | . |*. | 18 0.2195 0.0650 . |** | . |*. | 19 0.2219 0.0796 . |** | . |*. | 20 0.2239 0.0989 . |** | . |*. | 21 0.2024 0.1108 . |** | . |*. | 22 0.1652 0.1160 . |*. | . |*. | 23 0.1244 0.1215 . |*. | . |*. | 24 0.0610 0.1244 . | . | . |*. | 25 0.0017 0.1320 .*| . | . |*. | 26 -0.0745 0.1359 **| . | . |*. | 27 -0.1547 0.1352 **| . | . |*. | 28 -0.2458 0.1291 ***| . | . |*. | 29 -0.3267 0.1268 ****| . | . |*. | 30 -0.4129 0.1207 *****| . | . |*. | 31 -0.4999 0.1207 ******| . | . |*. | 32 -0.5669 0.1150 ******| . | . |*. | 33 -0.5943 0.1072 ******| . | . |*. | 34 -0.5874 0.1006 ******| . | . |*. | 35 -0.5515 0.0979 *****| . | . |*. | 36 -0.4622 0.0950
21.8.2012/an./Dr. Joanna Boerner/Dr. Barbara Schuler.