Brief Sketch of Solutions: Tutorial 3. 3) unit root tests
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1 Brief Sketch of Solutions: Tutorial 3 3) unit root tests Null Hypothesis: has a unit root Exogenous: None Lag Length: (Automatic based on SIC, MAXLAG=24) 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() Method: Least Squares Date: 7/12/11 Time: 9:49 Sample (adjusted): 1/2/21 4/3/27 Included observations: 165 after adjustments Variable Coefficient Std. Error t-statistic Prob. (-1) R-squared Mean dependent var -2.39E-6
2 Adjusted R-squared S.D. dependent var S.E. of regression.8473 Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter Durbin-Watson stat Null Hypothesis: has a unit root Exogenous: None Lag Length: (Automatic based on SIC, MAXLAG=24) 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() Method: Least Squares Date: 7/12/11 Time: 9:5 Sample (adjusted): 1/2/21 4/3/27 Included observations: 165 after adjustments Variable Coefficient Std. Error t-statistic Prob. (-1) R-squared Mean dependent var -1.16E-5 Adjusted R-squared S.D. dependent var S.E. of regression.9526 Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter Durbin-Watson stat Null Hypothesis: has a unit root Exogenous: None Lag Length: (Automatic based on SIC, MAXLAG=24) 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() Method: Least Squares
3 Date: 7/12/11 Time: 9:51 Sample (adjusted): 1/2/21 4/3/27 Included observations: 165 after adjustments Variable Coefficient Std. Error t-statistic Prob. (-1) R-squared Mean dependent var 1.3E-6 Adjusted R-squared S.D. dependent var S.E. of regression.1328 Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter Durbin-Watson stat 2668 Null Hypothesis: has a unit root Exogenous: None Lag Length: (Automatic based on SIC, MAXLAG=24) 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() Method: Least Squares Date: 7/12/11 Time: 9:52 Sample (adjusted): 1/2/21 4/3/27 Included observations: 165 after adjustments Variable Coefficient Std. Error t-statistic Prob. (-1) R-squared Mean dependent var 1.66E-6 Adjusted R-squared S.D. dependent var 229 S.E. of regression 432 Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter Durbin-Watson stat
4 4) VAR Lag Order Selection Criteria Endogenous variables: Exogenous variables: C Date: 7/12/11 Time: 9:53 Sample: 12/29/2 4/3/27 Included observations: 1643 Lag LogL LR FPE AIC SC HQ NA 1.7e * e * * 1.65e-17* * e e e e e e * indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion Vector Autoregression Estimates Date: 7/12/11 Time: 9:53 Sample (adjusted): 1/5/21 4/3/27 Included observations: 1647 after adjustments Standard errors in ( ) & t-statistics in [ ] (-1) (.2769) (.2444) (.3832) (.1288) [ ] [ ] [ ] [ ] (-2) (.2789) (.2462) (.3859) (.1297) [ ] [ ] [ ] [.28123] (-3) (.2788) (.2461) (.3858) (.1297) [-.7994] [.15291] [-.3194] [ 1.269] (-4) (.2777) (.2451) (.3843) (.1292) [ ] [ ] [-127] [.58613] (-1) (.327) (.2831) (.4439) (.1492) [ ] [ ] [ ] [ ] (-2)
5 (.3214) (.2837) (.4448) (.1495) [ ] [.1373] [ ] [ ] (-3) (.328) (.2831) (.4439) (.1492) [ ] [-.812] [.19557] [ ] (-4) (.3181) (.288) (.443) (.148) [-.145] [ ] [ ] [ ] (-1) (.1851) (.1634) (.2562) (.861) [-.5948] [ ] [ ] [ ] (-2) (.1855) (.1637) (.2567) (.863) [-.7148] [ ] [ ] [ ] (-3) (.1854) (.1636) (.2565) (.862) [ ] [.88119] [ ] [ ] (-4) (.1848) (.1631) (.2558) (.86) [.67477] [ ] [ ] [.138] (-1) (.5366) (.4737) (.7426) (.2496) [ ] [-.5691] [ 1.351] [.3237] (-2) (.5369) (.4739) (.743) (.2497) [-1.413] [ ] [.18278] [-.484] (-3) (.5378) (.4748) (.7444) (.252) [-1.119] [ ] [ ] [ ] (-4) (.5379) (.4748) (.7444) (.252) [-.555] [ ] [ ] [.86431] C (24) (21) (33) (11) [ ] [.81376] [ ] [ 286] R-squared Adj. R-squared Sum sq. resids S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent S.D. dependent Determinant resid covariance (dof adj.) 1.62E-17 Determinant resid covariance 1.56E-17 Log likelihood Akaike information criterion Schwarz criterion
6 5) Block Exogeneity Test VAR Granger Causality/Block Exogeneity Wald Tests Date: 7/12/11 Time: 9:54 Sample: 12/29/2 4/3/27 Included observations: 1647 Dependent variable: All Dependent variable: All Dependent variable: All Dependent variable: All
7 6) Impulse Response functions Response to Cholesky One S.D. Innovations ± 2 S.E. Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to
8 Variance Decomposition of Variance Decomposition of Variance Decomposition of Variance Decomposition of ) Same procedure again VAR Lag Order Selection Criteria Endogenous variables: Exogenous variables: C Date: 7/12/11 Time: 1: Sample: 5/1/27 11/3/29 Included observations: 666 Lag LogL LR FPE AIC SC HQ
9 NA 2.2e e * * e-15* * e * 1.55e e e e e * indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion Vector Autoregression Estimates Date: 7/12/11 Time: 1: Sample (adjusted): 5/4/27 11/3/29 Included observations: 672 after adjustments Standard errors in ( ) & t-statistics in [ ] (-1) (.552) (.2377) (.38) (.778) [ ] [ ] [ ] [.6913] (-2) (.5163) (.2231) (.2891) (.73) [ ] [ ] [ ] [ ] (-1) (.14275) (.6167) (.7992) (.219) [ ] [ ] [.37679] [.99738] (-2) (.13166) (.5688) (.7371) (.1862) [ ] [ ] [ ] [ ] (-1) E-5 (.8159) (.3525) (.4568) (.1154) [ ] [ ] [ ] [ 44] (-2) (.812) (.358) (.4546) (.1148) [ ] [ ] [ ] [ ] (-1) (.27574) (.11913) (.15438) (.3899) [ ] [.1866] [ ] [ ] (-2) (.27645) (.11944) (.15477) (.399) [ ] [.74692] [.2639] [ ] C
10 (.142) (62) (8) (2) [ ] [ ] [-.6263] [ ] R-squared Adj. R-squared Sum sq. resids S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent S.D. dependent Determinant resid covariance (dof adj.) 1.41E-15 Determinant resid covariance 1.34E-15 Log likelihood Akaike information criterion Schwarz criterion VAR Granger Causality/Block Exogeneity Wald Tests Date: 7/12/11 Time: 1: Sample: 5/1/27 11/3/29 Included observations: 672 Dependent variable: All Dependent variable: All Dependent variable: All
11 Dependent variable: All Response to Cholesky One S.D. Innovations ± 2 S.E. Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to Response of to
12 Variance Decomposition of Variance Decomposition of Variance Decomposition of Variance Decomposition of ) similar results including hedge fund index VAR Lag Order Selection Criteria Endogenous variables: DHEDGE Exogenous variables: C Date: 7/12/11 Time: 1:3 Sample: 5/1/27 11/3/29 Included observations: 666 Lag LogL LR FPE AIC SC HQ NA 9.53e e * * e e * 6.62e-21* * e e e
13 e * indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion Vector Autoregression Estimates Date: 7/12/11 Time: 1:3 Sample (adjusted): 5/8/27 11/3/29 Included observations: 67 after adjustments Standard errors in ( ) & t-statistics in [ ] DHEDGE (-1) (.587) () (.2512) (.3238) (.825) [ ] [ ] [ ] [ ] [.34648] (-2) (.6123) (21) (.2649) (.3414) (.87) [ ] [ ] [ ] [ ] [ ] (-3) (.6157) (24) (.2664) (.3433) (.875) [-1.737] [ ] [-.29] [ ] [ ] (-4) (.5548) (.382) (.24) (.394) (.788) [.8286] [ ] [-.4771] [.91977] [ ] DHEDGE(-1) (.742) (.4846) (.3467) (.39268) (.16) [-.1979] [ 4.548] [ ] [ ] [ ] DHEDGE(-2) (.794) (.4823) (.3326) (.3986) (.9959) [.5585] [ ] [.1865] [.6529] [ ] DHEDGE(-3) (.69489) (.4782) (.364) (.38749) (.9873) [ ] [ 387] [-.9446] [ ] [ ] DHEDGE(-4) (.69989) (.4816) (.328) (.3927) (.9944) [-.5777] [ ] [.31699] [ ] [.13346] (-1) (.16331) (.1124) (.765) (.916) (.232) [ ] [ ] [ ] [ ] [ ] (-2) (.16271) (.112) (.739) (.973) (.2312) [ ] [ ] [ ] [ ] [ ]
14 (-3) (.16416) (.113) (.712) (.9154) (.2332) [ ] [ ] [ 2.26] [.62333] [.83845] (-4) (.15378) (58) (.6653) (.8575) (.2185) [ ] [.2758] [ ] [-.4731] [ ] (-1) (.835) (71) (.3593) (.4631) (.118) [-.3443] [-.343] [-.8464] [ ] [.954] (-2) (.8321) (73) (.36) (.464) (.1182) [ ] [ ] [ ] [ 1.521] [ ] (-3) (.834) (74) (.368) (.465) (.1185) [ ] [ ] [ ] [ ] [ ] (-4) (.8266) (69) (.3576) (.469) (.1174) [ ] [.64155] [ ] [.5784] [ ] (-1) (.2832) (.1929) (.12128) (.15631) (.3983) [ ] [ ] [.11679] [ ] [ ] (-2) (.281) (.1927) (.12114) (.15614) (.3978) [ ] [ ] [.68216] [.4961] [ ] (-3) (.28142) (.1937) (.12176) (.15693) (.3999) [ ] [.3845] [.52846] [-.1679] [.54687] (-4) (.2814) (.1936) (.12175) (.15691) (.3998) [.37979] [-.7868] [ ] [.37726] [ ] C E (.144) (9.9E-5) (62) (8) (2) [ ] [-.7773] [ ] [ ] [ ] R-squared Adj. R-squared Sum sq. resids S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent S.D. dependent Determinant resid covariance (dof adj.) 5.57E-21 Determinant resid covariance 4.75E-21 Log likelihood Akaike information criterion Schwarz criterion
15 VAR Granger Causality/Block Exogeneity Wald Tests Date: 7/12/11 Time: 1:4 Sample: 5/1/27 11/3/29 Included observations: 67 Dependent variable: DHEDGE All Dependent variable: DHEDGE All Dependent variable: DHEDGE All Dependent variable: DHEDGE All Dependent variable: DHEDGE
16 All Response to Cholesky One S.D. Innovations ± 2 S.E. Response of to Response of to DHEDGE Response of to Response of to Response of to Response of DHEDGE to Response of DHEDGE to DHEDGE Response of DHEDGE to Response of DHEDGE to Response of DHEDGE to Response of to Response of to DHEDGE Response of to Response of to Response of to Response of to Response of to DHEDGE Response of to Response of to Response of to Response of to Response of to DHEDGE Response of to Response of to Response of to
17 1 Variance Decomposition of 1 Variance Decomposition of DHEDGE DHEDGE DHEDGE 6 Variance Decomposition of 8 Variance Decomposition of DHEDGE DHEDGE Variance Decomposition of DHEDGE
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