Diagnostic checking of time series models

Abstract

Diagnostic checks have become a standard tool for identification of models before forecasting the data. The overall test for lack of fit for autoregressive moving average models proposed by Box and Pierce (1970) and a measure of lack of fit in time series models proposed by Ljung and Box (1978) are considered. In this paper, a modification is made and it is shown that a substantially improved approximation results from a simple improvement of this test. Cumulative periodogram check is also given.