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Data Driven Order Selection for Projection Estimator of the Spectral Density of Time Series with Long Range Dependence

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  • Eric Moulines
  • Philippe Soulier

Abstract

Fractional exponential (FEXP) models have been introduced by Robinson (1991) and Beran (1993) to model the spectral density of a covariance stationary long‐range dependent process. In this class of models, the spectral density f(x) of the process is decomposed as f(x) = |1 − exp(ix)|−2df*(x), where f*(x) accounts for the short‐memory component. In this contribution, FEXP models are used to construct semi‐parametric estimates of the fractional differencing coefficient and of the spectral density, by considering an infinite Fourier series expansion of log f*(x). A data‐driven order selection procedure, adapted from the Mallows' Cp procedure, is proposed to determine the order of truncation. The optimality of the data‐driven procedure is established, under mild assumptions on the short‐memory component f*(x). A limited Monte‐Carlo experiment is presented to support our claims.

Suggested Citation

  • Eric Moulines & Philippe Soulier, 2000. "Data Driven Order Selection for Projection Estimator of the Spectral Density of Time Series with Long Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(2), pages 193-218, March.
    • Handle: RePEc:bla:jtsera:v:21:y:2000:i:2:p:193-218
    DOI: 10.1111/1467-9892.00181
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    Cited by:

    1. Masaki Narukawa & Yasumasa Matsuda, 2008. "Broadband semiparametric estimation of the long-memory parameter by the likelihood-based FEXP approach," TERG Discussion Papers 239, Graduate School of Economics and Management, Tohoku University.
    2. Bhansali, R.J. & Giraitis, L. & Kokoszka, P.S., 2006. "Estimation of the memory parameter by fitting fractionally differenced autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2101-2130, November.
    3. Uwe Hassler & Marc-Oliver Pohle, 2019. "Forecasting under Long Memory and Nonstationarity," Papers 1910.08202, arXiv.org.
    4. Jan Beran & Sucharita Ghosh, 2020. "Estimating the Mean Direction of Strongly Dependent Circular Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 210-228, March.
    5. Hurvich, Clifford M., 2002. "Multistep forecasting of long memory series using fractional exponential models," International Journal of Forecasting, Elsevier, vol. 18(2), pages 167-179.

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