On matricial measures of dependence in vector ARCH models with applications to diagnostic checking
Multivariate conditional heteroscedasticity models form an important class of nonlinear time series for modelling economic and financial data. Residual autocorrelations from classical autoregressive and moving-average models have been found useful for checking the adequacy of a particular model. In this paper, a general class of matricial measures of dependence is proposed, that corresponds to sample autocovariance matrices of the vector time series of squared (standardized) residuals and cross products of (standardized) residuals. We derive the asymptotic distribution of these residual autocovariance matrices, using an approach similar to Li and Mak (J. Time Ser. Anal. 15 (1994) 627). As an application, this result leads to some test statistics for diagnostic checking. Some simulation results are reported.
Volume (Year): 68 (2004)
Issue (Month): 2 (June)
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