If there is negative correlation, the statistic will lie somewhere between 2 and 4. Positive serial correlation is the most commonly observed form of dependence. As a rule of thumb, with 50 or more observations and only a few independent variables, a DW statistic below about 1.
See Johnston and DiNardo , Chapter 6. There are three main limitations of the DW test as a test for serial correlation.
First, the distribution of the DW statistic under the null hypothesis depends on the data matrix. The usual approach to handling this problem is to place bounds on the critical region, creating a region where the test results are inconclusive.
Second, if there are lagged dependent variables on the right-hand side of the regression, the DW test is no longer valid. Lastly, you may only test the null hypothesis of no serial correlation against the alternative hypothesis of first-order serial correlation. Two other tests of serial correlation—the Q -statistic and the Breusch-Godfrey LM test—overcome these limitations, and are preferred in most applications. If there is no serial correlation in the residuals, the autocorrelations and partial autocorrelations at all lags should be nearly zero, and all Q -statistics should be insignificant with large p -values.
The results of this regression using the Multiple Linear Regression data analysis tool are shown in Figure 3. Figure 3 — Breusch-Godfrey test results. We have also added the calculation of the Breusch-Godfrey test in the upper right side of Figure 3.
RT X6,X7. This indicates that there is third order autocorrelation, but not first or second order autocorrelation. Skip to content. Figure 3 — Breusch-Godfrey test results We have also added the calculation of the Breusch-Godfrey test in the upper right side of Figure 3. Retrive Password Enter right registered email to receive password! Enter your emailid Username. Login Here Create a new account. Assume that the error term follows the p-th order autoregressive, AR p scheme extension of the earlier AR 1 scheme , as follows where E, is a stochastic error as before.
The null hypothesis to be tested is: In it is hypothesized that there is no autocorrelation of any order. The BG test involves the following steps: 1 Estimate by OLS and obtain the residuals ti, 2 Regress u i , on the original x, as well as any other variables used as regressors ealier and where the latter are lagged values of the estimated residuals in step 1. In short, run the following regression: and obtain from this the auxiliary egression.
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