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Article overview
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The integrated periodogram of a dependent extremal event sequence | | Thomas Mikosch
; Yuwei Zhao
; | | Date: |
13 Mar 2015 | | Abstract: | We investigate the asymptotic properties of the integrated periodogram
calculated from a sequence of indicator functions of dependent extremal events.
An event in Euclidean space is extreme if it occurs far away from the origin.
We use a regular variation condition on the underlying stationary sequence to
make these notions precise. Our main result is a functional central limit
theorem for the integrated periodogram of the indicator functions of dependent
extremal events. The limiting process is a continuous Gaussian process whose
covari- ance structure is in general unfamiliar, but in the iid case a Brownian
bridge appears. In the general case, we propose a stationary bootstrap
procedure for approximating the distribution of the limiting process. The
developed theory can be used to construct classical goodness-of-fit tests such
as the Grenander- Rosenblatt and Cram’{e}r-von Mises tests which are based
only on the extremes in the sample. We apply the test statistics to simulated
and real-life data. | | Source: | arXiv, 1503.4022 | | Services: | Forum | Review | PDF | Favorites | |
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