An algorithm for testing goodness of fit of ARMA (P,Q) models

Clarke, B.R. (1983) An algorithm for testing goodness of fit of ARMA (P,Q) models. Applied Statistics Journal , 32 (3). pp. 335-344.

Abstract

The algorithm presented here enables diagnostic checking on the adequacy of an initially specified invertible ARMA (p, q) model to a series of observations by using the estimated residuals. Tue theoretical motivation for this technique is given in Godolphin (1980), and a comparison with other methods in Clarke and Godolphin (1983) highlights this test, The algorithm evaluates a chi-squared statistic based on a quadratic form, the vectors in which are of length m, equal to the degrees of freedom; they are also approximately the maximum likelihood estimate of the assumed non-zero asymptotic residual means of a transformed vector of the residual serial correlations.