Asymptotic behaviour of the portmanteau tests in an integer-valued AR model

Abstract

The portmanteau test has been popular for diagnostic checking in time series models. Asymptotic properties of portmanteau tests have been exhaustively studied for real-valued time series model though, similar results for integer-valued autoregressive (INAR) models are not well documented, nevertheless. In view of this, we investigate the asymptotic behaviour of the Box-Pierce and Ljung-Box portmanteau tests in an INAR model. It turns out that these tests are chi-squared distributed asymptotically under mild conditions regardless of the process being stable or nearly unstable.