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

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

3.  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

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

5. Histogram of original data Correlogram of original data

6. 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-0.051649 0.9519 Test critical values:1% level-3.456302 5% level-2.872857 10% level-2.572875 *MacKinnon (1996) one-sided p-values.

7. 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-1.402074 0.5812 Test critical values:1% level-3.456302 5% level-2.872857 10% level-2.572875 *MacKinnon (1996) one-sided p-values.

8. Line graph Histogram

9. 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 - 12.67345 0.0000 Test critical values: 1% level - 3.456302 5% level - 2.872857 10% level - 2.572875 *MacKinnon (1996) one-sided p-values.

10. AICStd. ar1 ma1 ma4-3.164650.054171 ar1 ma1 ar4-3.183180.052654 ar1 ma4-3.152110.054871 ma1 ma4-3.13290.055395 ar1 ar4-3.176360.053344 ma1 ar4-3.167070.053945 ar1-3.149680.055969 ma1-3.134320.056211 ar1 ma1-3.145130.056056

11. 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. C0.0151450.0027915.4264340.0000 AR(1)0.5786540.1275974.5349970.0000 AR(4)-0.2539790.048822-5.2021750.0000 MA(1)-0.4303780.150243-2.8645470.0045 R-squared0.133199 Mean dependent var0.014791 Adjusted R-squared0.122542 S.D. dependent var0.055381 S.E. of regression0.051877 Akaike info criterion-3.063875 Sum squared resid0.656665 Schwarz criterion-3.007206 Log likelihood383.9205 F-statistic12.49830 Durbin-Watson stat2.031919 Prob(F-statistic)0.000000 Inverted AR Roots.68-.46i.68+.46i -.39+.48i-.39-.48i Inverted MA Roots.43 Regression with AR(1) MA(1) MA(4)

12. CorrelogramCorrelogram with residuals squared

13. ARCH Test: F-statistic7.160676 Probability0.000951 Obs*R-squared13.69126 Probability0.001064 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. C0.0018590.0003944.7143570.0000 RESID^2(-1)0.1599840.0634462.5215780.0123 RESID^2(-2)0.1456410.0634342.2959390.0225 R-squared0.055656 Mean dependent var0.002669 Adjusted R-squared0.047883 S.D. dependent var0.005322 S.E. of regression0.005193 Akaike info criterion-7.670838 Sum squared resid0.006553 Schwarz criterion-7.628090 Log likelihood946.5130 F-statistic7.160676 Durbin-Watson stat2.036030 Prob(F-statistic)0.000951

14. 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. C0.0161060.0031095.1800120.0000 AR(1)0.6210960.2082252.9828140.0029 AR(4)-0.1584120.058175-2.7230250.0065 MA(1)-0.4571220.242386-1.8859250.0593 Variance Equation C0.0002599.44E-052.7410820.0061 RESID(-1)^20.1531630.0376434.0688730.0000 GARCH(-1)0.7435740.06040312.310260.0000 R-squared0.118040 Mean dependent var0.014791 Adjusted R-squared0.096082 S.D. dependent var0.055381 S.E. of regression0.052654 Akaike info criterion-3.183176 Sum squared resid0.668149 Schwarz criterion-3.084006 Log likelihood401.7138 F-statistic5.375835 Durbin-Watson stat2.027874 Prob(F-statistic)0.000031 Inverted AR Roots.64+.38i.64-.38i -.33-.42i-.33+.42i Inverted MA Roots.46

15. Correlogram Correlogram with residuals squared

17. ARCH Test: F-statistic0.335499 Probability0.715312 Obs*R-squared0.677412 Probability0.712692 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. C1.0353580.1625256.3704640.0000 STD_RESID^2(-1)0.0307620.0640840.4800290.6316 STD_RESID^2(-2)-0.0434370.064055-0.6781210.4983 R-squared0.002754 Mean dependent var1.022628 Adjusted R-squared-0.005454 S.D. dependent var2.106837 S.E. of regression2.112575 Akaike info criterion4.345812 Sum squared resid1084.503 Schwarz criterion4.388560 Log likelihood-531.5349 F-statistic0.335499 Durbin-Watson stat1.998539 Prob(F-statistic)0.715312

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