Diagnostic checking for non-stationary ARMA models with an application to financial data

This paper first derives the limiting distributions of the residual and the squared residual autocorrelation functions of the nonstationary autoregressive moving-average model, respectively. We then use them to construct two portmanteau statistics for testing the adequacy of the fitted model. Simulation results show that the tests have reasonable empirical sizes and powers in the finite samples. Finally, we use the daily SP500 data to illustrate our theory and approach.