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# notes8 - Notes 8 Diagnostics Checking Recall j Ztj at Zt =...

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Notes 8 Diagnostics Checking : Recall Z t = j =1 π j Z t - j + a t Put ˆ a t = Z t - j =1 ˆ π j Z t - j Residual = actual value - estimated value Residual Analysis 1. Plot residuals ˆ a t against t (See whether trend exists) 2. Histogram of ˆ a t (or standardized residuals), normal-score correlation test (Check normality) 3. Plot ˆ a t against ˆ Z t (check constant variance) 4. Check autocorrelation of residuals. We consider the sample autocorrelation of the residuals, { ˆ r k } . If the residuals follows a white noise process, then the sample acf are approximately uncorrelated and each { ˆ r k } is distributed approximately as Normal with mean 0 and variance 1 /n , where n is the series length. However, residuals, even with a corrected specified model with efficiently estimated parameters, have different properties. Properties of the sample acf of residuals for some models For AR(1) model, for large n V ar r 1 ) φ 2 n V ar r k ) 1 - (1 - φ 2 ) φ 2( k - 1) n , k > 1 .

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notes8 - Notes 8 Diagnostics Checking Recall j Ztj at Zt =...

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