Brief Sketch of Solutions: Tutorial 1. 2) descriptive statistics and correlogram. Series: LGCSI Sample 12/31/ /11/2009 Observations 2596

Transcription

1 Brief Sketch of Solutions: Tutorial 1 2) descriptive statistics and correlogram Series: LGCSI Sample 12/31/ /11/2009 Observations 2596 Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability Series: LJPM Sample 12/31/ /11/2009 Observations 2596 Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability

2 Correlogram of lgcsi Date: 07/12/11 Time: 08:58 Sample: 12/31/ /11/2009 Included observations: 2596 ******* ******* ******* ******* ******* ******* ******* ******* ******* ******* ******* Correlogram of ljpm Date: 07/12/11 Time: 08:57 Sample: 12/31/ /11/2009 Included observations: 2596 ******* ******* ******* ******* ******* ******* ******* ******* ******* ******* *******

3 Correlogram of differences of lgsci Date: 07/12/11 Time: 08:59 Sample: 12/31/ /11/2009 Included observations: 2595 * * Correlogram of differences of ljpm Date: 07/12/11 Time: 09:00 Sample: 12/31/ /11/2009 Included observations: ) Unit Root Test Null Hypothesis: LGCSI has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=27) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level

4 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LGCSI) Date: 07/12/11 Time: 09:02 after adjustments LGCSI(-1) D(LGCSI(-1)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) Null Hypothesis: D(LGCSI) has a unit root Exogenous: None Lag Length: 0 (Automatic based on SIC, MAXLAG=27) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LGCSI,2) Date: 07/12/11 Time: 09:04 after adjustments D(LGCSI(-1)) R-squared Mean dependent var 6.26E-06 Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter Durbin-Watson stat

5 Null Hypothesis: LJPM has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Automatic based on SIC, MAXLAG=27) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LJPM) Date: 07/12/11 Time: 09:06 Sample (adjusted): 1/03/ /11/2009 Included observations: 2595 after adjustments LJPM(-1) C E E R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) Null Hypothesis: D(LJPM) has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=27) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LJPM,2) Date: 07/12/11 Time: 09:06 after adjustments

6 D(LJPM(-1)) C E R-squared Mean dependent var -4.58E-06 Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) ) Dependent Variable: DGCSI Date: 06/20/11 Time: 18:32 after adjustments Convergence achieved after 3 iterations AR(1) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter Durbin-Watson stat Inverted AR Roots -.07 Date: 07/12/11 Time: 09:08 Sample: 1/04/ /11/2009 Q-statistic probabilities adjusted for 1 ARMA term(s)

7 5) and 6) Dependent Variable: DJPM Date: 06/20/11 Time: 18:39 after adjustments Convergence achieved after 12 iterations MA Backcast: 1/03/2000 AR(1) MA(1) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter Durbin-Watson stat Inverted AR Roots -.76 Inverted MA Roots -.79 Date: 07/12/11 Time: 09:09 Sample: 1/04/ /11/2009 Q-statistic probabilities adjusted for 2 ARMA term(s)

8 7) (keep in mind: poor forecast quality) Forecast: DGCSIF Actual: DGCSI Forecast sample: 12/31/ /11/... Adjusted sample: 1/04/ /11/2009 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion DGCSIF ± 2 S.E Forecast: DGCSIF Actual: DGCSI Forecast sample: 12/31/ /11/... Adjusted sample: 1/04/ /11/2009 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion DGCSIF ± 2 S.E.

9 Forecast: DJPMF Actual: DJPM Forecast sample: 12/31/ /11/... Adjusted sample: 1/04/ /11/2009 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion DJPMF ± 2 S.E Forecast: DJPMF Actual: DJPM Forecast sample: 12/31/ /11/... Adjusted sample: 1/04/ /11/2009 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion DJPMF ± 2 S.E.