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On the distribution of the residual cross-correlations of infinite order vector autoregressive series and applications

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  • Bouhaddioui, Chafik
  • Roy, Roch

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.

Suggested Citation

  • Bouhaddioui, Chafik & Roy, Roch, 2006. "On the distribution of the residual cross-correlations of infinite order vector autoregressive series and applications," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 58-68, January.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:1:p:58-68
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    References listed on IDEAS

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    1. Hong, Yongmiao, 1996. "Testing for independence between two covariance stationary time series," MPRA Paper 108731, University Library of Munich, Germany.
    2. Marc Hallin & Abdessamad Saidi, 2005. "Testing Non‐Correlation and Non‐Causality between Multivariate ARMA Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 83-105, January.
    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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