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An asymptotic Wiener-Itô representation for the low frequency ordinates of the periodogram of a long memory time series

Author

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  • Terrin, Norma
  • Hurvich, Clifford M.

Abstract

We consider a general long memory time series, assumed stationary and linear, but not necessarily Gaussian or generated by a finite-parameter model. For such a process, we derive the asymptotic joint distribution of the normalized periodogram at a fixed, finite collection of Fourier frequencies. The limiting distribution is represented in terms of Wiener-Itô integrals, and, for a single periodogram ordinate, it is an unequally weighted linear combination of independent [chi]21 random variables. This result was previously known only in the Gaussian case. Our theorem may be useful for generalizing, beyond the Gaussian case, the applicability of a semiparametric method of estimating the long memory parameter based on log-periodogram regression.

Suggested Citation

  • Terrin, Norma & Hurvich, Clifford M., 1994. "An asymptotic Wiener-Itô representation for the low frequency ordinates of the periodogram of a long memory time series," Stochastic Processes and their Applications, Elsevier, vol. 54(2), pages 297-307, December.
    • Handle: RePEc:eee:spapps:v:54:y:1994:i:2:p:297-307
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    Cited by:

    1. Hsieh, Meng-Chen & Hurvich, Clifford M. & Soulier, Philippe, 2007. "Asymptotics for duration-driven long range dependent processes," Journal of Econometrics, Elsevier, vol. 141(2), pages 913-949, December.
    2. Willa Chen & Clifford Hurvich, 2004. "Semiparametric Estimation of Fractional Cointegrating Subspaces," Econometrics 0412007, University Library of Munich, Germany.
    3. Gabriel Lang & Philippe Soulier, 2000. "Convergence de mesures spectrales aléatoires et applications à des principes d'invariance," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 41-51, January.

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