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 language | English |
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Pages (from-to) | 969-991 |
Number of pages | 23 |
Journal | Annals of Applied Probability |
Volume | 6 |
Issue number | 3 |
State | Published - Aug 1996 |
Externally published | Yes |
Keywords
- Changepoint
- Empirical process
- Functional central limit theorem
- Gaussian field
- Integrated periodogram
- Kiefer process
- Moving average process
- Sample autocovariance
- Spectral distribution