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Robust Tests For White Noise And Cross-Correlation

Author

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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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    Cited by:

    1. NguyenHuu, Tam, 2022. "The impacts of rare disasters on asset returns and risk premiums in advanced economies (1870–2015)," Finance Research Letters, Elsevier, vol. 45(C).
    2. Giraitis, Liudas & Li, Yufei & Phillips, Peter C.B., 2024. "Reprint of: Robust inference on correlation under general heterogeneity," Journal of Econometrics, Elsevier, vol. 244(2).
    3. Guastella, Gianni & Mazzarano, Matteo & Pareglio, Stefano & Xepapadeas, Anastasios, 2022. "Climate reputation risk and abnormal returns in the stock markets: A focus on large emitters," International Review of Financial Analysis, Elsevier, vol. 84(C).
    4. Kyriazopoulos Georgios & Sariannidis Nikolaos & Parpoutzidou Androniki, 2020. "Evaluation of the main African Stock Exchanges Markets for Foreign Direct Investments. A Statistical Approach," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 10(5), pages 1-13.
    5. Axel Bücher & Holger Dette & Florian Heinrichs, 2023. "A portmanteau-type test for detecting serial correlation in locally stationary functional time series," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 255-278, July.
    6. Morelli, Giacomo, 2023. "Stochastic ordering of systemic risk in commodity markets," Energy Economics, Elsevier, vol. 117(C).
    7. Todd Henry & Peter C.B. Phillips, 2020. "Forecasting Economic Activity Using the Yield Curve: Quasi-Real-Time Applications for New Zealand, Australia and the US," Cowles Foundation Discussion Papers 2259, Cowles Foundation for Research in Economics, Yale University.
    8. Uwe Hassler & Marc-Oliver Pohle & Tanja Zahn, 2025. "Simultaneous Inference Bands for Autocorrelations," Papers 2503.18560, arXiv.org, revised Aug 2025.
    9. Zhang, Qi & Chen, Chun & Xue, Hong & Park, Kayoung & Wang, Youfa, 2021. "Revisiting the relationship between WIC participation and breastfeeding among low-income children in the U.S. after the 2009 WIC food package revision," Food Policy, Elsevier, vol. 101(C).
    10. Assaf, Ata & Mokni, Khaled & Youssef, Manel, 2023. "COVID-19 and information flow between cryptocurrencies, and conventional financial assets," The Quarterly Review of Economics and Finance, Elsevier, vol. 89(C), pages 73-81.
    11. Giraitis, Liudas & Li, Yufei & Phillips, Peter C.B., 2024. "Robust inference on correlation under general heterogeneity," Journal of Econometrics, Elsevier, vol. 240(1).
    12. Fiorentini, Gabriele & Sentana, Enrique, 2021. "New testing approaches for mean–variance predictability," Journal of Econometrics, Elsevier, vol. 222(1), pages 516-538.
    13. Philipp Wegmueller & Christian Glocker, 2024. "Capturing Swiss economic confidence," Swiss Journal of Economics and Statistics, Springer;Swiss Society of Economics and Statistics, vol. 160(1), pages 1-17, December.
    14. Wegmüller, Philipp & Glocker, Christian & Guggia, Valentino, 2023. "Weekly economic activity: Measurement and informational content," International Journal of Forecasting, Elsevier, vol. 39(1), pages 228-243.
    15. Charles Darko, 2021. "An Evaluation of How Students Use Blackboard and the Possible Link to Their Grades," SAGE Open, , vol. 11(4), pages 21582440211, December.
    16. Marcel Bräutigam & Michel Dacorogna & Marie Kratz, 2023. "Pro‐cyclicality beyond business cycle," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 308-341, April.
    17. Ziwei Mei & Zhentao Shi & Peter C. B. Phillips, 2022. "The boosted HP filter is more general than you might think," Cowles Foundation Discussion Papers 2348, Cowles Foundation for Research in Economics, Yale University.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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