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Zhen Tian Jeff Lee Visut Hemithi Huan Zhang Diana Aguilar Yuli Yan A Deep Analysis of A Random Walk.

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Presentation on theme: "Zhen Tian Jeff Lee Visut Hemithi Huan Zhang Diana Aguilar Yuli Yan A Deep Analysis of A Random Walk."— Presentation transcript:

1 Zhen Tian Jeff Lee Visut Hemithi Huan Zhang Diana Aguilar Yuli Yan A Deep Analysis of A Random Walk

2 Identification

3

4 Unit Root Null Hypothesis: PRICE has a unit root Exogenous: Constant Lag Length: 3 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic-2.431974 0.1332 Test critical values:1% level-3.438129 5% level-2.864863 10% level-2.568594

5 Pre-Whitening Log Transformation Trend in Var. Difference Trend in Mean

6 Pre-Whitening

7 Unit Root Null Hypothesis: DLNPRICE has a unit root Exogenous: Constant Lag Length: 4 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic-9.819079 0.0000 Test critical values:1% level-3.438149 5% level-2.864872 10% level-2.568599

8 Dependent Variable: DLNPRICE Method: Least Squares Sample (adjusted): 5/17/1993 12/22/2008 Included observations: 815 after adjustments Convergence achieved after 6 iterations Backcast: 1/11/1993 5/10/1993 VariableCoefficientStd. Errort-StatisticProb. C0.0004210.0017690.2380030.8119 AR(1)0.5038030.03477114.489200.0000 AR(2)0.1040440.0394202.6393310.0085 AR(3)0.1434440.0364663.9336790.0001 AR(5)-0.1243640.032993-3.7694390.0002 MA(8)0.1033320.0370232.7910070.0054 MA(18)0.1181550.0364993.2371940.0013 R-squared0.389743 Mean dependent var0.000545 Adjusted R-squared0.385211 S.D. dependent var0.019718 S.E. of regression0.015461 Akaike info criterion-5.492468 Sum squared resid0.193141 Schwarz criterion-5.452073 Log likelihood2245.181 F-statistic86.00538 Durbin-Watson stat2.000720 Prob(F-statistic)0.000000

9 Model Validation-1

10 Model Validation-2 Breusch-Godfrey Serial Correlation LM Test: F-statistic0.105569 Prob. F(2,806)0.899825 Obs*R-squared0.213376 Prob. Chi-Square(2)0.898806 ARCH Test: F-statistic204.8519 Prob. F(1,812)0.000000 Obs*R-squared163.9859 Prob. Chi-Square(1)0.000000

11 ARCH GARCH (1) Dependent Variable: DLNPRICE Method: ML - ARCH (Marquardt) - Normal distribution MA backcast: 1/11/1993 5/10/1993, Variance backcast: ON GARCH = C(8) + C(9)*RESID(-1)^2 + C(10)*GARCH(-1) CoefficientStd. Errorz-StatisticProb. C0.0002250.0012730.1768570.8596 AR(1)0.5332510.03793414.057180.0000 AR(2)0.1504970.0394323.8166790.0001 AR(3)0.0326060.0384750.8474500.3967 AR(5)-0.0633880.027109-2.3383080.0194 MA(8)0.0284880.0354750.8030350.4220 MA(18)0.1048790.0287093.6531850.0003 Variance Equation C6.94E-061.17E-065.9568910.0000 RESID(-1)^20.2906650.0392117.4128290.0000 GARCH(-1)0.7278340.02938424.770130.0000

12 Model Validation-ARCH GARCH (1)

13 ARCH GARCH (2) Dependent Variable: DLNPRICE Method: ML - ARCH (Marquardt) - Normal distribution MA backcast: 1/11/1993 5/10/1993, Variance backcast: ON GARCH = C(8) + C(9)*RESID(-1)^2 + C(10)*GARCH(-1) CoefficientStd. Errorz-StatisticProb. C0.0001210.0011620.1043850.9169 AR(1)0.5433730.03777714.383740.0000 AR(2)0.1880200.0387194.8559930.0000 AR(4)-0.0950350.036572-2.5985550.0094 AR(5)0.0060740.0303100.2003930.8412 MA(9)-0.0344530.033775-1.0200790.3077 MA(18)0.1056560.0280833.7622910.0002 Variance Equation C7.30E-061.18E-066.1894020.0000 RESID(-1)^20.2889110.0401337.1988880.0000 GARCH(-1)0.7243860.03155422.957160.0000

14 ARCH GARCH (3) Dependent Variable: DLNPRICE Method: ML - ARCH (Marquardt) - Normal distribution MA backcast: 1/11/1993 5/10/1993, Variance backcast: ON GARCH = C(8) + C(9)*RESID(-1)^2 + C(10)*GARCH(-1) CoefficientStd. Errorz-StatisticProb. C0.0003590.0011980.2994880.7646 AR(1)0.5395750.03738214.434180.0000 AR(2)0.1984000.0384565.1591690.0000 AR(4)-0.0948420.030904-3.0689370.0021 MA(18)0.1062560.0276123.8482500.0001 Variance Equation C7.55E-061.21E-066.2526620.0000 RESID(-1)^20.2944220.0403147.3032730.0000 GARCH(-1)0.7182100.03128522.957310.0000

15 Model Validation-ARCH GARCH (3)

16 Correlogram

17 Correlogram of Residual 2

18 Histogram

19 ARCH Test ARCH Test: F-statistic0.190541 Prob. F(1,812)0.662583 Obs*R-squared0.190965 Prob. Chi-Square(1)0.662115

20 Forecast

21

22 Recolor

23 Comparison

24 A Little Bit Further

25 Story Behind the Scene To Investigate the Sources of Shock Geopolitical Events (War & Disasters) GDP / Mean Personal Income Vehicle Sales (SUV Sales) China Petro Consumption Speculation (Future Contract Price) Key Bibliography “Causes and Consequences of the Oil Shock of 2007-08” James D. Hamilton, UCSD (2009)

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