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A frequency-domain test for long range dependence

Author

Listed:
  • Gennadi Gromykov

    (Carleton University)

  • Mohamedou Ould Haye

    (Carleton University)

  • Anne Philippe

    (Université de Nantes)

Abstract

A new frequency-domain test statistic is introduced to test for short memory versus long memory. We provide its asymptotic distribution under the null hypothesis and show that it is consistent under any long memory alternative. Some simulation studies show that this test is more robust than various standard tests in terms of empirical size when the normality of observed process is lost.

Suggested Citation

  • Gennadi Gromykov & Mohamedou Ould Haye & Anne Philippe, 2018. "A frequency-domain test for long range dependence," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 513-526, October.
    • Handle: RePEc:spr:sistpr:v:21:y:2018:i:3:d:10.1007_s11203-017-9164-6
    DOI: 10.1007/s11203-017-9164-6
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    References listed on IDEAS

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    1. R. S. Deo, 1997. "Asymptotic theory for certain regression models with long memory errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(4), pages 385-393, July.
    2. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus & Teyssiere, Gilles, 2003. "Rescaled variance and related tests for long memory in volatility and levels," Journal of Econometrics, Elsevier, vol. 112(2), pages 265-294, February.
    3. GIRAITIS, Liudas & KOKOSZKA, Piotr & LEIPUS, Remigijus & TEYSSIÈRE, Gilles, 2003. "Rescaled variance and related tests for long memory in volatility and levels," LIDAM Reprints CORE 1594, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Lee, Dongin & Schmidt, Peter, 1996. "On the power of the KPSS test of stationarity against fractionally-integrated alternatives," Journal of Econometrics, Elsevier, vol. 73(1), pages 285-302, July.
    5. Valdério A. Reisen & Eric Moulines & Philippe Soulier & Glaura C. Franco, 2010. "On the properties of the periodogram of a stationary long‐memory process over different epochs with applications," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(1), pages 20-36, January.
    6. Bailey, Natalia & Giraitis, Liudas, 2016. "Spectral approach to parameter-free unit root testing," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 4-16.
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    Cited by:

    1. Massimiliano Giacalone & Demetrio Panarello, 2022. "A Nonparametric Approach for Testing Long Memory in Stock Returns’ Higher Moments," Mathematics, MDPI, vol. 10(5), pages 1-21, February.

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