Diagnostics - Choice

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Diagnostics - Choice
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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

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Modeling for Forecast
The Base Model
Linear Trend
Forecast
Data
Logistic Growth
Others Models
Look for a best approximation of the truth
Forecasting Skill
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Random Series is The Base Model to Compare With
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Fixed Trend Models
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Notation

• WN (white noise) uncorrelated
• iid independent and identically distributed
• Yt iid N(m, s) Random Series
• et iid N(0, s) White Noise

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Random Series Data Generation

• Independent observations at every t from
• the normal distribution (m, s)

Y
Yt
t
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Generating a Random Series Using Eviews

• Command nrnd generates a RND N(0, 1)

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Fitting the Base Model
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Eviews ls View/ Equation Output
Summarizes A, F, R Graph
Ref. Diebold, Ch.1 Appendix
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Eviews lsView/Actual,Fitted, Residual Graph
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Durbin Watson Statistic

• See Diebold page 25.
• DW appreciably below 2 is a warning sign of
  serially correlated residuals

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Trend Model for DW Test
H0 r 0 H1 r gt 0 -gt positive
auto-correlated residual
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Some Key Values of DW Stat

• E(DW) 2 if H0
• Low DW -gt H1 (consult with a table)

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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

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Review of Significance Tests in Regression

• F - Test
• H0 b1 b2 , bk 0
• H1 at least one bi not zero
• T - Test of a coefficient, bj.
• H0 bj 0
• H1 bj 0 or gt 0 or lt 0

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Risks in Hypothesis Testing
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Log likelihood, AIC and SC
(Maximized)
(Minimized)
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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.