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foundations of econometrics phần 5

Báo cáo tỷ lệ của thời gian mỗi khoảng tin cậy bao gồm các giá trị đích thực của các thông số. Trên cơ sở những kết quả này, trong đó ước tính hiệp phương sai ma trận bạn sẽ khuyên bạn nên sử dụng trong thực tế Viết xuống một mở rộng thứ hai, | 7.7 Testing for Serial Correlation 279 the alternative that p 0. An investigator will reject the null hypothesis if d dL fail to reject if d dư and come to no conclusion if dL d dư. For example for a test at the .05 level when n 100 and k 8 including the constant term the bounding critical values are dL 1.528 and dư 1-826. Therefore one would reject the null hypothesis if d 1-528 and not reject it if d 1.826. Notice that even for this not particularly small sample size the indeterminate region between 1.528 and 1.826 is quite large. It should by now be evident that the Durbin-Watson statistic despite its popularity is not very satisfactory. Using it with standard tables is relatively cumbersome and often yields inconclusive results. Moreover the standard tables only allow us to perform one-tailed tests against the alternative that p 0. Since the alternative that p 0 is often of interest as well the inability to perform a two-tailed test or a one-tailed test against this alternative using standard tables is a serious limitation. Although exact P values for both onetailed and two-tailed tests which depend on the X matrix can be obtained by using appropriate software many computer programs do not offer this capability. In addition the DW statistic is not valid when the regressors include lagged dependent variables and it cannot easily be generalized to test for higher-order processes. Happily the development of simulation-based tests has made the DW statistic obsolete. Monte Carlo Tests for Serial Correlation We discussed simulation-based tests including Monte Carlo tests and bootstrap tests at some length in Section 4.6. The techniques discussed there can readily be applied to the problem of testing for serial correlation in linear and nonlinear regression models. All the test statistics we have discussed namely ÍGNR tsR and d are pivotal under the null hypothesis that p 0 when the assumptions of the classical normal linear model are satisfied. This makes it possible