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A Zero Serial Cross‐Correlation Test Before Fitting Heteroscedasticity

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  • Yaolan Ma
  • Xiaohong Chen
  • Liang Peng
  • Rongmao Zhang

Abstract

Many statistical inferences for a multivariate innovation‐based copula time series model rely on the serial independence of innovation vectors after filtering the conditional means and conditional covariance. Zero (respectively nonzero) serial cross‐correlations for the heteroscedastic noises before filtering the conditional covariance may suggest the use of univariate (respectively multivariate) GARCH models. This paper develops a zero serial cross‐correlation test for the heteroscedastic noises with heavy tails before fitting a multivariate heteroscedasticity model. Applications to exchange rates and mutual fund returns show that this critical assumption could be problematic sometimes and conducting such a test is necessary before building and using a multivariate innovation‐based copula time series model.

Suggested Citation

  • Yaolan Ma & Xiaohong Chen & Liang Peng & Rongmao Zhang, 2026. "A Zero Serial Cross‐Correlation Test Before Fitting Heteroscedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 47(2), pages 364-377, March.
    • Handle: RePEc:bla:jtsera:v:47:y:2026:i:2:p:364-377
    DOI: 10.1111/jtsa.12807
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