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On matricial measures of dependence in vector ARCH models with applications to diagnostic checking

  • Duchesne, Pierre

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.

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Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 68 (2004)
Issue (Month): 2 (June)
Pages: 149-160

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Handle: RePEc:eee:stapro:v:68:y:2004:i:2:p:149-160
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  1. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  2. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  3. Engle, Robert F. & Granger, C. W. J. & Kraft, Dennis, 1984. "Combining competing forecasts of inflation using a bivariate arch model," Journal of Economic Dynamics and Control, Elsevier, vol. 8(2), pages 151-165, November.
  4. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  5. H. Wong & W. Li, 2002. "Detecting and Diagnostic Checking Multivariate Conditional Heteroscedastic Time Series Models," Annals of the Institute of Statistical Mathematics, Springer, vol. 54(1), pages 45-59, March.
  6. Y. K. Tse, 2002. "Residual-based diagnostics for conditional heteroscedasticity models," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 358-374, 06.
  7. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February.
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