Welche Fragen sind bei den einzelnen Aufgaben zu ... fileUniversität zu Köln Univ.-Professor Dr....

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?


c. Welche Theorie(n) könnten relevant sein?



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)



-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



Aufgabe b

a. Was zeigt die nachfolgende Darstellung?



-.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)



Aufgabe c




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



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




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


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




Aufgabe d




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





Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=13)




Null Hypothesis: DM3 has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=13)




Null Hypothesis: DLOG(M3) has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=13)



*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)






Aufgabe e




Aufgabe f




-.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)



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




Pairwise Granger Causality Tests Date: 04/05/12 Time: 11:42 Sample: 1 158 Lags: 2

Null Hypothesis: Obs F-Statistic Prob.



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?


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





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






C(3) 2.297894 0.481042 4.776908 0.0000 C(4) -0.380303 0.089447 -4.251711 0.0000




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


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


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




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



C(3) 2.870851 0.529761 5.419144 0.0000 C(4) -0.464364 0.093957 -4.942282 0.0000


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



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



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




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








C(3) -0.579991 0.113220 -5.122669 0.0000 C(4) 0.144821 0.027231 5.318223 0.0000


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








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


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)



*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)


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


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



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


Aufgabe 2-a






xM1=Geldschöpfungsmultiplikator M1 und Kreditschöpfungsmultiplikator

Aufgabe 2-b

a. Was zeigt die nachfolgenden

Darstellungen?


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



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


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)


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





Aufgabe 2-c




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


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


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





Null Hypothesis: Obs F-Statistic Prob.



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


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






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




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



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: 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)


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





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


C(10) 0.270463 0.076668 3.527713 0.0005 C(17) 0.001227 0.000173 7.074039 0.0000



Aufgabe 2-f






C(3) 1.465408 0.366108 4.002661 0.0001 C(4) -0.102859 0.028285 -3.636539 0.0004


Equation: DM1 = C(1)*DM1(-1) + C(3) + C(4)*DKREDMFI Observations: 127



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


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






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)


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





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


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





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



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



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))


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


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



X(-4)) +C(7)*DLOG(BIPREAL(3)) GARCH = C(8) + C(9)*RESID(-1)^2 + C(10)*GARCH(-1)


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



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)


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





Aufgabe 3-b




Null Hypothesis: ZINS1TAG has a unit root Exogenous: Constant Lag Length: 2 (Automatic based on SIC, MAXLAG=13)


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)



Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLOG(ZINS1TAG)) Method: Least Squares Date: 08/19/12 Time: 21:40 Sample (adjusted): 5 162



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


Aufgabe 3-c




0

5

10

15

20

25

30

1 2 3 4 5

Series: ZINS1TAGSample 1 162Observations 162





Aufgabe 3-d





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




Sample: 3 154 Included observations: 152 Total system (balanced) observations 152 Presample covariance: backcast (parameter =0.7) Convergence achieved after 20 iterations


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



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


C(2) -0.159465 0.050840 -3.136585 0.0017 C(5) 0.627491 0.032437 19.34493 0.0000




C(7) 0.223279 0.053747 4.154218 0.0000 C(8) 0.824973 0.021769 37.89659 0.0000



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






Null Hypothesis: ZINS10J has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=13)


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





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)



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




Aufgabe 4-b




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)


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





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


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



Dependent Variable: DLOG(ZINS10J) Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/20/12 Time: 08:45



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



Aufgabe 4-c





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



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


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



Dependent Variable: DLOG(ZINS10J) Method: ML - ARCH (Marquardt) - Normal distribution Date: 08/20/12 Time: 08:53



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))


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



Aufgabe 4-d





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



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


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




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



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


C(2) 0.000399 3.96E-05 10.05592 0.0001 R-squared 0.943989 Mean dependent var 3.023875


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



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)


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


-.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




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_


C(2) -4.368231 0.227162 -19.22961 0.0000 R-squared 0.984033 Mean dependent var 3.023875




-.08

-.04

.00

.04

.082.4

2.8

3.2

3.6

4.0

4.4

1 2 3 4 5 6 7 8




Thema 6: Die affine Zinsstrukturtheorie (II): Empirische

Analysen und theoretische Grundlagen

Aufgabe 6-a




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




Aufgabe 6-b




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




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



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



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



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






(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)


C(3) -0.025384 0.009501 -2.671785 0.0083 C(4) 8.695867 2.434096 3.572524 0.0005



-.8

-.6

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.0

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.6

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25 50 75 100 125 150




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))


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

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.6

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25 50 75 100 125 150






Thema 7: Der Kreditmarkt im Eurowährungsgebiet,

empirische Analysen und theoretische Grundlagen

Aufgabe 7-a




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)



Null Hypothesis: LOG(KREDITEMFI) has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=13)



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




Null Hypothesis: DKREDMFI has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=13)



-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





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)



Null Hypothesis: DLOG(KREDITEMFI) has a unit root Exogenous: Constant Lag Length: 2 (Automatic based on SIC, MAXLAG=13)



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)




0

10

20

30

40

-0.02 -0.01 -0.00 0.01 0.02

Series: DLOG(KREDITEMFI)Sample 1 162Observations 161







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


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


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


C(22) -0.060152 0.014227 -4.228048 0.0000 C(23) 1.040732 0.029193 35.65014 0.0000



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



DLOG(KREDITEMFI) = C(6)*DLOG(BARGELD) +C(10)*DLOG(M3)+C(17) *ZINS2J


C(10) 0.270463 0.076668 3.527713 0.0005 C(17) 0.001227 0.000173 7.074039 0.0000



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)


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



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 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))


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





Thema 8: Die Aktienmärkte, empirische Analysen und


Aufgabe 8-a




-.03

-.02

-.01

.00

.01

.02

-.03

-.02

-.01

.00

.01

.02

.03

25 50 75 100 125 150




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



Null Hypothesis: DAKTIENINDEX has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=13)



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





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






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




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))


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



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



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))


C(13) 0.250963 0.068034 3.688773 0.0003 R-squared 0.158206 Mean dependent var -0.001998






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



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






.001

.002

.003

.004

.005

.006

.007

25 50 75 100 125 150

Var(DLOG(AKTIENINDEX))

Conditional Covariance

1

2

3

4

5

6

7

25 50 75 100 125

Conditional standard deviation



Aufgabe 8-d




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)


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



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)


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


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)


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


RESID(-1)^2 0.083685 0.080364 1.041327 0.2977



GARCH(-1) 0.539801 0.477018 1.131614 0.2578 R-squared 0.936535 Mean dependent var -0.288971


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))


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





Aufgabe 8-e




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

-20

-10

0

10

20

-60

-40

-20

0

20

40

60

25 50 75 100 125 150




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)



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




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AKTIENINDEX Trend Cycle




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Thema 9: Die Devisenmärkte, empirische Analyse der Devisenkurse (EUR-USD) und theoretische Grundlagen

Aufgabe 9-a




.02

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Conditional standard deviation



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Series: EURUSDSample 1 162Observations 162





Null Hypothesis: EURUSD has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=13)



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Null Hypothesis: DEURUSD has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=13)



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Series: DEURUSDSample 1 162Observations 150





Null Hypothesis: DLOG(EURUSD) has a unit root

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Series: DLOG(EURUSD)Sample 1 162Observations 161





Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=13)



Aufgabe 9-b a. Was zeigt die nachfolgenden Darstellungen?



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)



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)





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))



Aufgabe 9-c




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)



*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



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))


C(9) 0.061944 0.019273 3.214062 0.0016 R-squared 0.154736 Mean dependent var 0.001760


Dependent Variable: DLOG(EURUSD) Method: ML - ARCH (Marquardt) - Normal distribution



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)


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



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))


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





Aufgabe 9-d




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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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


RESID(-1)^2 -0.084465 0.034234 -2.467282 0.0136 GARCH(-1) 1.060962 0.045580 23.27677 0.0000



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Thema 10: Die Rohstoffmärkte, empirische Analyse der

Rohstoffpreise (Ölpreis und Gesamtindex)

Aufgabe 10-a




0

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ER

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Series: DERDOLSample 1 162Observations 151





Null Hypothesis: DERDOL has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=13)



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






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



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


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)


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



System: UNTITLED Estimation Method: ARCH Maximum Likelihood (Marquardt) Covariance specification: Diagonal VECH Date: 08/21/12 Time: 07:34



Sample: 14 155 Included observations: 142 Total system (balanced) observations 142 Presample covariance: backcast (parameter =0.7) Convergence achieved after 32 iterations


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



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))


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



C(14) 0.130181 0.071032 1.832697 0.0668 C(15) 0.881679 0.054200 16.26716 0.0000



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)


C(2) -0.227942 0.073596 -3.097205 0.0024 C(4) 1.617474 0.586014 2.760130 0.0066



Aufgabe 10-c






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Series: DROHSTOFFESample 1 162Observations 162





Null Hypothesis: DROHSTOFFE has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=13)





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


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



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)


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


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)


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



RESID(-1)^2 -0.054922 0.034993 -1.569496 0.1165 GARCH(-1) 0.548478 0.501284 1.094147 0.2739



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))


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





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DROHSTOFFEF ± 2 S.E.

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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Thema 11: Die Wirkungen der Geldpolitik und die Taylor-

Regel

Aufgabe 11-a






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


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




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



Aufgabe 11-b




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Aufgabe 11-c




Dependent Variable: ZINS1TAG Method: Least Squares Date: 08/21/12 Time: 09:54 Sample: 1 162 Included observations: 162 ZINS1TAG=C(1)*INFLATIONSRATE



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SR

AT

E



Aufgabe 11-d




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

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SR

AT

E(5

)



. |**** | . |**** | 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




Pairwise Granger Causality Tests



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



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



Aufgabe 11-f




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

)



.*| . | ***| . | 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.

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