A Note On Diagnostic Checking Of The Double Autoregressive Model

Abstract

The double autoregressive model finds its use in the modelling of conditional heteroscedasticity of time series data. In view of its growing popularity, the goodness-of-fit of the model is examined. The asymptotic distributions of the residual and squared residual autocorrelations are derived. Two test statistics are then constructed which can be used to measure the adequacy of the conditional mean and conditional variance components of a fitted model. Our goodness-of-fit tests out-perform other benchmark tests such as the Ljung-Box test in simulation studies. To illustrate the testing procedure, the model is fitted to the weekly log-return series of the Hang Seng Index.