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Diagnostics - Choice

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

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Diagnostics - Choice

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  1. Diagnostics - Choice

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

  3. Modeling for Forecast The Base Model Linear Trend Data Forecast 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 • Yt ~ iid N(m, s) Random Series • et ~ iid N(0, s) White Noise

  7. Random Series Data Generation • Independent observations at every t from the normal distribution(m, s) Y Yt t

  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 Summarizes A, F, R Graph Ref. Diebold, Ch.1: Appendix

  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 • H0 : r = 0 • H1 : r > 0 -> positive auto-correlated residual

  14. Some Key Values of DW Stat • E(DW) = 2 if H0 • Low DW -> H1 (consult with a table)

  15. Test of Significance of Coefficients • Model: Yt = b0 + b1 t + e e : WN (0, s) • Hypotheses: • H0 : b1 = 0 • H1: b1 = 0 • Test statistics: • t-stat • p-value

  16. Review of Significance Tests in Regression • F - Test H0:b1=b2=…, bk= 0 H1: at least onebinot zero • T - Test of a coefficient, bj. H0 :bj =0 H1:bj =0or > 0 or < 0

  17. Truth H0 H1 Accept H0 OK Type II Your Inference OK Reject H0 Type I Risks in Hypothesis Testing

  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.

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