A Small Sample Study of Goodness-of-fit Tests for Time Series Models

Abstract

We study the small sample behaviour of two goodness-of-fit tests for time series models which have 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 other null hypotheses. The cause for this effect is investigated and a finite sample correction proposed which ameliorates this effect. It is found that the corrected versions of the tests have markedly better size properties. The correction is also found to result in an overall increase in power which can be significant in certain alternatives. Furthermore, the corrected tests also have uniformly better power than the Box-Ljung-Pierce portmanteau test, unlike the uncorrected versions.