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Robust Tests For White Noise And Cross-Correlation

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  • Dalla, Violetta
  • Giraitis, Liudas
  • Phillips, Peter C. B.

Abstract

Commonly used tests to assess evidence for the absence of autocorrelation in a univariate time series or serial cross-correlation between time series rely on procedures whose validity holds for i.i.d. data. When the series are not i.i.d., the size of correlogram and cumulative Ljung–Box tests can be significantly distorted. This paper adapts standard correlogram and portmanteau tests to accommodate hidden dependence and nonstationarities involving heteroskedasticity, thereby uncoupling these tests from limiting assumptions that reduce their applicability in empirical work. To enhance the Ljung–Box test for non-i.i.d. data, a new cumulative test is introduced. Asymptotic size of these tests is unaffected by hidden dependence and heteroskedasticity in the series. Related extensions are provided for testing cross-correlation at various lags in bivariate time series. Tests for the i.i.d. property of a time series are also developed. An extensive Monte Carlo study confirms good performance in both size and power for the new tests. Applications to real data reveal that standard tests frequently produce spurious evidence of serial correlation.

Suggested Citation

  • Dalla, Violetta & Giraitis, Liudas & Phillips, Peter C. B., 2022. "Robust Tests For White Noise And Cross-Correlation," Econometric Theory, Cambridge University Press, vol. 38(5), pages 913-941, October.
    • Handle: RePEc:cup:etheor:v:38:y:2022:i:5:p:913-941_4
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    References listed on IDEAS

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    10. Liudas Giraitis & Yufei Li & Peter C.B. Phillips, 2023. "Robust Inference on Correlation under General Heterogeneity," Cowles Foundation Discussion Papers 2354, Cowles Foundation for Research in Economics, Yale University.
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    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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