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The periodogram of an i.i.d. sequence

  • Fay, Gilles
  • Soulier, Philippe
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    Periodogram ordinates of a Gaussian white-noise computed at Fourier frequencies are well known to form an i.i.d. sequence. This is no longer true in the non-Gaussian case. In this paper, we develop a full theory for weighted sums of non-linear functionals of the periodogram of an i.i.d. sequence. We prove that these sums are asymptotically Gaussian under conditions very close to those which are sufficient in the Gaussian case, and that the asymptotic variance differs from the Gaussian case by a term proportional to the fourth cumulant of the white noise. An important consequence is a functional central limit theorem for the spectral empirical measure. The technique used to obtain these results is based on the theory of Edgeworth expansions for triangular arrays.

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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 92 (2001)
    Issue (Month): 2 (April)
    Pages: 315-343

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    Handle: RePEc:eee:spapps:v:92:y:2001:i:2:p:315-343
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    1. Velasco, Carlos, 1998. "Non-Gaussian log-periodogram regression," DES - Working Papers. Statistics and Econometrics. WS 4553, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Kokoszka, Piotr & Mikosch, Thomas, 2000. "The periodogram at the Fourier frequencies," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 49-79, March.
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