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

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Presentation transcript:

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

Identification

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

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

Pre-Whitening

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

Dependent Variable: DLNPRICE Method: Least Squares Sample (adjusted): 5/17/ /22/2008 Included observations: 815 after adjustments Convergence achieved after 6 iterations Backcast: 1/11/1993 5/10/1993 VariableCoefficientStd. Errort-StatisticProb. C AR(1) AR(2) AR(3) AR(5) MA(8) MA(18) 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 F-statistic Durbin-Watson stat Prob(F-statistic)

Model Validation-1

Model Validation-2 Breusch-Godfrey Serial Correlation LM Test: F-statistic Prob. F(2,806) Obs*R-squared Prob. Chi-Square(2) ARCH Test: F-statistic Prob. F(1,812) Obs*R-squared Prob. Chi-Square(1)

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. C AR(1) AR(2) AR(3) AR(5) MA(8) MA(18) Variance Equation C6.94E E RESID(-1)^ GARCH(-1)

Model Validation-ARCH GARCH (1)

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. C AR(1) AR(2) AR(4) AR(5) MA(9) MA(18) Variance Equation C7.30E E RESID(-1)^ GARCH(-1)

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. C AR(1) AR(2) AR(4) MA(18) Variance Equation C7.55E E RESID(-1)^ GARCH(-1)

Model Validation-ARCH GARCH (3)

Correlogram

Correlogram of Residual 2

Histogram

ARCH Test ARCH Test: F-statistic Prob. F(1,812) Obs*R-squared Prob. Chi-Square(1)

Forecast

Recolor

Comparison

A Little Bit Further

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 ” James D. Hamilton, UCSD (2009)