Gaussian limit fields for the integrated periodogram

Claudia Klüppelberg, Thomas Mikosch

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Functional of a two-parameter integrated periodogram have been used for detecting a change in the spectral distribution of a stationary sequence. The bases for these results are functional central limit theorems for the integrated periodogram with a Gaussian limit field. We prove functional central limit theorems for a general linear sequence having a finite fourth moment which is shown to be the optimal moment condition. Our approach is via an approximation of the integrated periodogram by a finite linear combination of sample autocovariances. This gives special insight into the structure of the Gaussian limit field.

Original languageEnglish
Pages (from-to)969-991
Number of pages23
JournalAnnals of Applied Probability
Volume6
Issue number3
StatePublished - Aug 1996
Externally publishedYes

Keywords

  • Changepoint
  • Empirical process
  • Functional central limit theorem
  • Gaussian field
  • Integrated periodogram
  • Kiefer process
  • Moving average process
  • Sample autocovariance
  • Spectral distribution

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