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I wonder why the Durbin-Watson test table has the critical values of dL and dU. This is different from other tests, Z, t, chi-squire, F.

It has confused me. A test statistic has the sampling distribution and then I can get the definite critical value at 95% cumulative probability. So is the DW statistic. Knowing the autocorrelation coefficient helps to fit data model.

Today, I find a figure in Instagram about finding sampling distribution of the DW statistic. I try to download, run and plot the chart. It seems true, but I cannot sure it is true.

kjetil b halvorsen
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Coadak
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    The problem with the DW test is that its distribution, unlike - as you correctly point out - that of almost all other tests, depends on the distribution of the regressors, which typically is unknown. But Durbin and Watson were successful in providing bounds that are valid for any distribution of the regressors. – Christoph Hanck Nov 16 '21 at 08:51
  • There is no longer a need for the bounds, as the exact critical value can be computed. It is available in standard software. – BigBendRegion Nov 16 '21 at 13:18
  • Thank you, bigbendregion. It seems the sampling distribution of DW statistic have been found, so there is the exact critical value can be computed. It is doubtful that what the sampling distribution of DW statistic is. Does it have constant pdf so that we can get the exact critical value? Or the pdf doesn’t have constant form. The latter will increase the difficulty in finding the probability distribution function. – Coadak Nov 19 '21 at 18:47

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