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A multivariate test against spurious long memory

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  • Sibbertsen, Philipp
  • Leschinski, Christian
  • Busch, Marie

Abstract

This paper provides a multivariate score-type test against spurious long memory. We prove the consistency of the test against the alternatives of random level shifts and smooth trends. The test statistic is based on the weighted sum of the partial derivatives of the multivariate local Whittle likelihood function. To apply the test to fractionally cointegrated series, the test statistic is calculated for the linearly transformed system after estimating the cointegrating matrix. We derive the limiting distribution and show consistency of this procedure. The test is applied to log-absolute returns and log-realized volatilities of the S&P 500, DAX, FTSE, and NIKKEI.

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  • Sibbertsen, Philipp & Leschinski, Christian & Busch, Marie, 2018. "A multivariate test against spurious long memory," Journal of Econometrics, Elsevier, vol. 203(1), pages 33-49.
    • Handle: RePEc:eee:econom:v:203:y:2018:i:1:p:33-49
    DOI: 10.1016/j.jeconom.2017.07.005
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    Cited by:

    1. Ata Assaf & Luis Alberiko Gil-Alana & Khaled Mokni, 2022. "True or spurious long memory in the cryptocurrency markets: evidence from a multivariate test and other Whittle estimation methods," Empirical Economics, Springer, vol. 63(3), pages 1543-1570, September.
    2. Kunal Saha & Vinodh Madhavan & Chandrashekhar G. R. & David McMillan, 2020. "Pitfalls in long memory research," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1733280-173, January.
    3. Alia Afzal & Philipp Sibbertsen, 2023. "Long Memory, Spurious Memory: Persistence in Range-Based Volatility of Exchange Rates," Open Economies Review, Springer, vol. 34(4), pages 789-811, September.
    4. Wenger, Kai & Leschinski, Christian & Sibbertsen, Philipp, 2017. "The Memory of Volatility," Hannover Economic Papers (HEP) dp-601, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    5. Kai Wenger & Christian Leschinski & Philipp Sibbertsen, 2019. "Change-in-mean tests in long-memory time series: a review of recent developments," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(2), pages 237-256, June.
    6. Mwasi Paza Mboya & Philipp Sibbertsen, 2023. "Optimal forecasts in the presence of discrete structural breaks under long memory," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(7), pages 1889-1908, November.
    7. Leschinski, Christian & Sibbertsen, Philipp, 2018. "The Periodogram of Spurious Long-Memory Processes," Hannover Economic Papers (HEP) dp-632, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    8. Assaf, Ata & Mokni, Khaled & Yousaf, Imran & Bhandari, Avishek, 2023. "Long memory in the high frequency cryptocurrency markets using fractal connectivity analysis: The impact of COVID-19," Research in International Business and Finance, Elsevier, vol. 64(C).
    9. Becker, Janis & Leschinski, Christian & Sibbertsen, Philipp, 2019. "Robust Multivariate Local Whittle Estimation and Spurious Fractional Cointegration," Hannover Economic Papers (HEP) dp-660, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    10. Lujia Bai & Weichi Wu, 2021. "Detecting long-range dependence for time-varying linear models," Papers 2110.08089, arXiv.org, revised Mar 2023.
    11. Dooruj Rambaccussing & Murat Mazibas, 2020. "True versus Spurious Long Memory in Cryptocurrencies," JRFM, MDPI, vol. 13(9), pages 1-11, August.
    12. Less, Vivien & Sibbertsen, Philipp, 2022. "Estimation and Testing in a Perturbed Multivariate Long Memory Framework," Hannover Economic Papers (HEP) dp-704, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    13. Sibbertsen, Philipp & Wenger, Kai & Wingert, Simon, 2020. "Testing for Multiple Structural Breaks in Multivariate Long Memory Time Series," Hannover Economic Papers (HEP) dp-676, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    14. Leschinski, Christian & Sibbertsen, Philipp, 2017. "Origins of Spurious Long Memory," Hannover Economic Papers (HEP) dp-595, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.

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    More about this item

    Keywords

    Multivariate long memory; Semiparametric estimation; Spurious long memory; Fractional cointegration; Volatility;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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