1. Diagnostics - Choice

2. Model Diagnostics 1.Explains data well –R-Squared, and adjusted R-Squared 2.Residuals follow a white noise, as specified in the model –Durbin Watson test 3.Key coefficients are significant –t- test –F-test –These tests depend on 2, ie, WN residual

3. Modeling for Forecast Forecast Data The Base Model Linear Trend Logistic Growth Others Models Look for a best approximation of the truth Forecasting Skill

4. Random Series is The Base Model to Compare With

5. Fixed Trend Models

6. Notation WN (white noise) – uncorrelated iid: independent and identically distributed Y t ~ iid N( ,  ) Random Series  t ~ iid N(0,  ) White Noise

7. Random Series Data Generation Independent observations at every t from the normal distribution ( ,  ) t YtYt Y

8. Generating a Random Series Using Eviews Command: nrnd generates a RND N(0, 1)

9. Fitting the Base Model

10. Eviews ‘ls’ View/ Equation Output Ref. Diebold, Ch.1: Appendix Summarizes A, F, R Graph

11. Eviews ‘ls’ View/Actual,Fitted, Residual Graph

12. Durbin Watson Statistic See Diebold page 25. DW appreciably below 2 is a warning sign of serially correlated residuals

13. Trend Model for DW Test H 0 :  = 0 H 1 :  > 0 -> positive auto-correlated residual

14. Some Key Values of DW Stat E(DW) = 2 if H 0 Low DW -> H 1 (consult with a table)

15. Test of Significance of Coefficients Model: Y t =  0 +  1 t +  WN (0,  ) Hypotheses: –H 0 :  1 = 0 –H 1 :  1 = 0 Test statistics: –t-stat –p-value

16. Review of Significance Tests in Regression F - Test H 0 :  1 =  2 = …,  k = 0 H 1 : at least one  i not zero T - Test of a coefficient,  j. H 0 :  j = 0 H 1 :  j = 0 or > 0 or < 0

17. Risks in Hypothesis Testing Your Inference Truth Reject H 0 OK Type I Type II Accept H 0 H0H0 H1H1

18. Log likelihood, AIC and SC (Maximized) (Minimized)

19. Using AIC or SC Choice among models with: –the same dependent variable, –but different number of independent variables. Possibly a better guide than SE, but not intuitive. SC penalizes more for increasing the number of the independent variables.