ON WEIGHTED PORTMANTEAU TESTS FOR TIME‐SERIES GOODNESS‐OF‐FIT

Recent work in the literature has shown weighted variants of the classic portmanteau test for time series can be more powerful in many situations. In this article, we study the asymptotic distribution of weighted sums of the squared residual autocorrelations where both the sample size n and maximum lag of the statistic m grow large. Several weighting schemes are introduced, including a data‐adaptive statistic in which the weights are determined by a function of the sample partial autocorrelations. These statistics can provide more power than other portmanteau tests found in the literature and are much less sensitive to the choice of the maximum correlation lag. The efficacy of the proposed methods is further demonstrated through an analysis of Australian red wine sales.