Sequential estimation for a functional of the spectral density of a Gaussian stationary process

Takayuki Shiohama, Masanobu Taniguchi

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Abstract

Integral functional of the spectral density of stationary process is an important index in time series analysis. In this paper we consider the problem of sequential point and fixed-width confidence interval estimation of an integral functional of the spectral density for Gaussian stationary process. The proposed sequential point estimator is based on the integral functional replaced by the periodogram in place of the spectral density. Then it is shown to be asymptotically risk efficient as the cost per observation tends to zero. Next we provide a sequential interval estimator, which is asymptotically efficient as the width of the interval tends to zero. Finally some numerical studies will be given.

Original languageEnglish
Pages (from-to)142-158
Number of pages17
JournalAnnals of the Institute of Statistical Mathematics
Volume53
Issue number1
DOIs
Publication statusPublished - 2001 Jan 1

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Keywords

  • Integral functional
  • Periodogram
  • Sequential interval estimation
  • Sequential point estimation
  • Spectral density
  • Stationary process

ASJC Scopus subject areas

  • Statistics and Probability

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