Angela Sordello Christopher Friedberg Can Shen Hui Lai Hui Wang Fang Guo

 Introduction  Original Data  Pre Whitening  Comparison of Models  Modeling  Model Validation  Forecasting  Conclusion

 Gross Private Domestic Investment (GPDI) is a measure of fixed investment and the change in private inventories  Used as an indicator to assess the state of the economy  We wanted to see if the United States economy is still in a recession

 St. Louis Federal Reserve Bank  The data is quarterly and has been seasonally adjusted  GDPI is measured in billions of US dollars

Histogram of original data Correlogram of original data

Null Hypothesis: GPDI has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=15) t-Statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values:1% level % level % level *MacKinnon (1996) one-sided p-values.

Null Hypothesis: LNVAL has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=15) t-Statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values:1% level % level % level *MacKinnon (1996) one-sided p-values.

Line graph Histogram

Null Hypothesis: DLNVAL has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=15) t-Statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values.

AICStd. ar1 ma1 ma ar1 ma1 ar ar1 ma ma1 ma ar1 ar ma1 ar ar ma ar1 ma

Dependent Variable: DLN Method: Least Squares Sample (adjusted): 1948Q2 2010Q1 Included observations: 248 after adjustments Convergence achieved after 8 iterations Backcast: 1948Q1 VariableCoefficientStd. Errort-StatisticProb. C AR(1) AR(4) 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 F-statistic Durbin-Watson stat Prob(F-statistic) Inverted AR Roots i i i i Inverted MA Roots.43 Regression with AR(1) MA(1) MA(4)

CorrelogramCorrelogram with residuals squared

ARCH Test: F-statistic Probability Obs*R-squared Probability Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: Time: 15:25 Sample (adjusted): 1948Q4 2010Q1 Included observations: 246 after adjustments VariableCoefficientStd. Errort-StatisticProb. C RESID^2(-1) RESID^2(-2) 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)

Dependent Variable: DLN Method: ML - ARCH (Marquardt) - Normal distribution Sample (adjusted): 1948Q2 2010Q1 Included observations: 248 after adjustments Convergence achieved after 17 iterations MA backcast: 1948Q1, Variance backcast: ON GARCH = C(5) + C(6)*RESID(-1)^2 + C(7)*GARCH(-1) CoefficientStd. Errorz-StatisticProb. C AR(1) AR(4) MA(1) Variance Equation C E RESID(-1)^ GARCH(-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 F-statistic Durbin-Watson stat Prob(F-statistic) Inverted AR Roots i i i i Inverted MA Roots.46

Correlogram Correlogram with residuals squared

ARCH Test: F-statistic Probability Obs*R-squared Probability Test Equation: Dependent Variable: STD_RESID^2 Method: Least Squares Date: Time: 15:27 Sample (adjusted): 1948Q4 2010Q1 Included observations: 246 after adjustments VariableCoefficientStd. Errort-StatisticProb. C STD_RESID^2(-1) STD_RESID^2(-2) 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)

The GDPI is increasing. It is signaling the US economy is recovering.