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**Unformatted text preview: **Economics 20 - Prof. Anderson 1 Time Series Data y t = β + β 1 x t1 + . . .+ β k x tk + u t 2. Further Issues Economics 20 - Prof. Anderson 2 Testing for AR(1) Serial Correlation Want to be able to test for whether the errors are serially correlated or not Want to test the null that ρ = 0 in u t = ρ u t-1 + e t , t =2,…, n , where u t is the model error term and e t is iid With strictly exogenous regressors, the test is very straightforward – simply regress the residuals on lagged residuals and use a t-test Economics 20 - Prof. Anderson 3 Testing for AR(1) Serial Correlation (continued) An alternative is the Durbin-Watson (DW) statistic, which is calculated by many packages If the DW statistic is around 2, then we can reject serial correlation, while if it is significantly < 2 we cannot reject Critical values are difficult to calculate, making the t test easier to work with Economics 20 - Prof. Anderson 4 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 Economics 20 - Prof. Anderson 5 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 Economics 20 - Prof. Anderson 6 Correcting for Serial Correlation Start with case of strictly exogenous regressors, and maintain all G-M...

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