Abstract
Abstract Box and Pierce [3] showed that the residual autocorrelations computed from an autoregressive-moving average time series model (single variate) can be successfully utilized for testing the goodness of fit. Here we extend their results to multiple autoregressive time series models. It is shown that the residual autocorrelations can be approximately represented as a singular linear transform of the corresponding white noise autocorrelations and that they possess a multivariate singular normal distribution. Finally a simple, approximate chi-square statistic is proposed to test the fit.
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