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On the Distribution of the Residual Cross-Correlations between Two Uncorrelated Infinite Order Vector Autoregressive Series

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  • Chafik Bouhaddioui
  • Roch Roy

Abstract

Here we derive the asymptotic distribution of an arbitrary vector of residual cross-correlations resulting from the fitting of finite autoregressions to two uncorrelated infinite order vector autoregressive series. Its asymptotic distribution is the same multivariate normal as the one of the corresponding vector of cross-correlations between the two innovation series. The application of that result for testing the uncorrelatedness of two series is also discussed. Dans ce travail, nous obtenons la loi asymptotique d'un vecteur quelconque de corrélations croisées résiduelles résultant de l'ajustement d'autorégressions finies à deux séries non corrélées décrites par des processus autorégressifs multivariés d'ordre infini. La loi asymptotique est la même que celle du vecteur correspondant de corrélations croisées entre les deux séries d'innovations correspondantes qui est une loi multinormale. Nous discutons aussi l'application de ce résultat afin de tester l'hypothèse de non corrélation de deux séries multivariées.

Suggested Citation

  • Chafik Bouhaddioui & Roch Roy, 2003. "On the Distribution of the Residual Cross-Correlations between Two Uncorrelated Infinite Order Vector Autoregressive Series," CIRANO Working Papers 2003s-41, CIRANO.
    • Handle: RePEc:cir:cirwor:2003s-41
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    References listed on IDEAS

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    3. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
    4. Paparoditis, Efstathios, 1996. "Bootstrapping Autoregressive and Moving Average Parameter Estimates of Infinite Order Vector Autoregressive Processes," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 277-296, May.
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