Fall 2008 under econometrics prof keunkwan ryu 5

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Fall 2008 under Econometrics Prof. Keunkwan Ryu 5 Testing for AR(1) Serial Correlation (continued) If the regressors are not strictly exogenous, then neither the t or DW test will work Regress the residual (or y ) on the lagged residual and all of the x ’s The inclusion of the x ’s allows each x tj to be correlated with u t-1 , so don’t need assumption of strict exogeneity
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Fall 2008 under Econometrics Prof. Keunkwan Ryu 6 Testing for Higher Order S.C. Can test for AR( q ) serial correlation in the same basic manner as AR(1) Just include q lags of the residuals in the regression and test for joint significance Can use F test or LM test, where the LM version is called a Breusch-Godfrey test and is ( n-q ) R 2 using R 2 from residual regression Can also test for seasonal forms
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Fall 2008 under Econometrics Prof. Keunkwan Ryu 7 Correcting for Serial Correlation Start with case of strictly exogenous regressors, and maintain all G-M assumptions except no serial correlation Assume errors follow AR(1) so u t = ρ u t-1 + e t , t =2,…, n Var( u t ) = σ 2 e / (1- ρ 2 ) We need to try and transform the equation so we have no serial correlation in the errors
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Fall 2008 under Econometrics Prof. Keunkwan Ryu 8 Correcting for S.C. (continued) Consider that since y t = β 0 + β 1 x t + u t , then y t-1 = β 0 + β 1 x t-1 + u t-1 If you multiply the second equation by ρ , and subtract if from the first you get y t ρ y t-1 = (1 ρ ) β 0 + β 1 (x
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