Diagnostic testing of univariate time series models

The portmanteau statistic for testing the adequacy of an autoregressive-moving average model is based on the first m autocorrelations of the residuals from the fitted model. This paper examines the properties of this test for various choices of m. A modification which allows the use of small values of m is shown to result in a more powerful test. The Lagrange multiplier statistic (Godfrey, 1979) and a test statistic examined by Newbold (1980) are also discussed.