A Small Sample Study of Goodness-of-Fit Tests for Time Series Models
15 Pages Posted: 31 Oct 2008
Date Written: 2000
We study the small sample behaviour of two goodness-of-fit tests for time series models whichhave been proposed recently in the literature. Both tests are generalizations of the popular Box-Ljung-Pierce portmanteau test, one in the time domain and the other in the frequency domain.The tests are found to be oversized under the null of white noise but undersized under othernull hypotheses. The cause for this effect is investigated and a finite sample correction proposedwhich ameliorates this effect. It is found that the corrected versions of the tests have markedlybetter size properties. The correction is also found to result in an overall increase in power whichcan be significant in certain alternatives. Furthermore, the corrected tests also have uniformlybetter power than the Box-Ljung-Pierce portmanteau test, unlike the uncorrected versions.
Keywords: frequency domain, portmanteau test
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