ch12 - Time Series Data yt = 0 1xt1 kxtk ut 2 Further...

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Economics 20 - Prof. Anderson 1 Time Series Data y t = β 0 + β 1 x t1 + . . .+ β k x tk + u t 2. Further Issues
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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
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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
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Economics 20 - Prof. Anderson 4 Testing for AR(1) Serial Correlation (continued) If the regressors are not strictly exogenous,
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