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Bandwidth Choice, Optimal Rates and Adaptivity in Semiparametric Estimation of Long Memory

In: Long Memory in Economics

Author

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  • Marc Henry

    (Columbia University)

Abstract

Summary Semiparametric estimation of long memory refers to periodogram based estimation of the shape of the spectral density f(λ) at low frequencies, where all but the lowest harmonics of the periodogram are discarded, so as to forego specification of the short range dynamic structure of the time series, and avoid bias incurred when the latter is misspecified. Such a procedure entails an order of magnitude loss of efficiency with respect to parametric estimation, but may be warranted when long series (earth scientific or financial) can be obtained. This paper presents strategies proposed for the choice of bandwidth, i.e. the number of periodogram harmonics used in estimation, with the aim of minimizing this loss of efficiency. Such strategies are assessed with respect to minimax rates of convergence, that depend on the smoothness of |λ|−2d f(λ) (where d is the long memory parameter) in the neighbourhood of frequency zero. The plug-in strategy is discussed in the case where the degree of local smoothness is known a priori, and adaptive estimation of d is discussed for the case where the degree of local smoothness is unknown.

Suggested Citation

  • Marc Henry, 2007. "Bandwidth Choice, Optimal Rates and Adaptivity in Semiparametric Estimation of Long Memory," Springer Books, in: Gilles Teyssière & Alan P. Kirman (ed.), Long Memory in Economics, pages 157-172, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34625-8_6
    DOI: 10.1007/978-3-540-34625-8_6
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    Cited by:

    1. Bouezmarni, Taoufik & Van Bellegem, Sébastien, 2009. "Nonparametric Beta Kernel Estimator for Long Memory Time Series," IDEI Working Papers 633, Institut d'Économie Industrielle (IDEI), Toulouse.
    2. Gil-Alana, Luis A. & Gupta, Rangan, 2014. "Persistence and cycles in historical oil price data," Energy Economics, Elsevier, vol. 45(C), pages 511-516.

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