On the Distribution of Residual Autocorrelations in Box–Jenkins Models

Summary The large sample distribution of the residual autocorrelations in the arma model is derived. The main advantage of this derivation over that of Box and Pierce (1970) is that it extends directly to more general situations. Generalizations of the derived distribution are presented for the residual autocorrelations in the multiplicative seasonal arma model and for the autocorrelations of a subseries of the residuals.