The Integrated periodogram of a dependent extremal event sequence
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The Integrated periodogram of a dependent extremal event sequence. / Mikosch, Thomas Valentin; Zhao, Yuwei.
In: Stochastic Processes and Their Applications, Vol. 125, No. 8, 2015, p. 3126-3169.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - The Integrated periodogram of a dependent extremal event sequence
AU - Mikosch, Thomas Valentin
AU - Zhao, Yuwei
PY - 2015
Y1 - 2015
N2 - 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 covariance structure is in general unfamiliar, but in the i.i.d. 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 Cramér–von Mises tests which are based only on the extremes in the sample. We apply the test statistics to simulated and real-life data.
AB - 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 covariance structure is in general unfamiliar, but in the i.i.d. 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 Cramér–von Mises tests which are based only on the extremes in the sample. We apply the test statistics to simulated and real-life data.
U2 - 10.1016/j.spa.2015.02.017
DO - 10.1016/j.spa.2015.02.017
M3 - Journal article
VL - 125
SP - 3126
EP - 3169
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
IS - 8
ER -
ID: 137618757