Abstract
We study the asymptotic behavior of the integrated periodogram for α-stable linear processes. For α ∈ (1,2) we prove a functional limit theorem for the integrated periodogram. The limit is an α-stable analogue to the Brownian bridge. We apply our results to investigate some specific goodness-of-fit tests for heavy-tailed linear processes.
| Original language | English |
|---|---|
| Pages (from-to) | 1855-1879 |
| Number of pages | 25 |
| Journal | Annals of Statistics |
| Volume | 24 |
| Issue number | 5 |
| DOIs | |
| State | Published - Oct 1996 |
Keywords
- Frequency domain
- Functional limit theorem
- Goodness-of-fit test
- Integrated periodogram
- Linear process
- Moving average process
- Quadratic form
- Stable process