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Adaptive Long Memory Testing Under Heteroskedasticity

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  • Harris, David
  • Kew, Hsein

Abstract

This paper considers adaptive hypothesis testing for the fractional differencing parameter in a parametric ARFIMA model with unconditional heteroskedasticity of unknown form. A weighted score test based on a nonparametric variance estimator is proposed and shown to be asymptotically equivalent, under the null and local alternatives, to the Neyman-Rao effective score test constructed under Gaussianity and known variance process. The proposed test is therefore asymptotically efficient under Gaussianity. The finite sample properties of the test are investigated in a Monte Carlo experiment and shown to provide potentially large power gains over the usual unweighted long memory test.

Suggested Citation

  • Harris, David & Kew, Hsein, 2017. "Adaptive Long Memory Testing Under Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 33(3), pages 755-778, June.
    • Handle: RePEc:cup:etheor:v:33:y:2017:i:03:p:755-778_00
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    Cited by:

    1. 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.
    2. Harris, David & Kew, Hsein & Taylor, A.M. Robert, 2020. "Level shift estimation in the presence of non-stationary volatility with an application to the unit root testing problem," Journal of Econometrics, Elsevier, vol. 219(2), pages 354-388.
    3. Lujia Bai & Weichi Wu, 2021. "Detecting long-range dependence for time-varying linear models," Papers 2110.08089, arXiv.org, revised Mar 2023.
    4. Zhang, Erhua & Wu, Jilin, 2020. "Adaptive estimation of AR∞ models with time-varying variances," Economics Letters, Elsevier, vol. 197(C).

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