Weighted Portmanteau Statistics

• Activity Number: 406
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Colin Gallagher*+ and Thomas Fisher
• Companies: Clemson University and University of Missouri-Kansas City
• Keywords: ARMA Process ; correlation ; Goodness-of-fit

Abstract

The commonly used Ljung-Box test for time series goodness of fit is a weighted sum of squared sample autocorrelations at lags 1,2,.,m. In this case the weight for the lag-k correlation comes from the approximate variance and the weights increase as the lag increases. In practice m typically increases with the sample size. The performance of the Ljung-Box statistic is fairly sensitive to the choice of m and the asymptotic chi-square approximation is less reliable for larger m. A Portmanteau type statistic can be created by taking any weighted sum of squared sample autocorrelations. We consider the asymptotic behavior of this type of statistic when m is fixed and when m depends on the sample size. In the latter case we consider sequences of weights with convergent partial sums and sequences with divergent partial sums. We discuss some different weighting schemes. It appears that the test statistics tend to be less sensitive to the choice of m when the weights decrease as the lag of the autocorrelation increases.