On the squared residual autocorrelations in non-linear time series with conditional heteroskedasticity

Time series with a changing conditional variance have been found useful in many applications. Residual autocorrelations from traditional autoregressive moving‐average models have been found useful in model diagnostic checking. By analogy, squared residual autocorrelations from fitted conditional heteroskedastic time series models would be useful in checking the adequacy of such models. In this paper, a general class of squared residual autocorrelations is defined and their asymptotic distribution is obtained. The result leads to some useful diagnostic tools for statisticians using conditional heteroskedastic time series models. Some simulation results and an illustrative example are also reported. Copyright © 1994 Wiley Blackwell. All rights reserved.