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A use of the Stein-Chen method in time series analysis

Published online by Cambridge University Press:  14 July 2016

Sun-Tsung Kim*
Affiliation:
Universität Zürich
*
Postal address: c/o A. D. Barbour, Abteilung für angewandte Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland. Email address: [email protected]

Abstract

In this paper, a statistic that has been introduced to test for space-time correlation is considered in a time series context. The null hypothesis is white noise; the alternative is any kind of continuous functional dependence. For an autoregressive process close to the null hypothesis, a bound on the distance between the distribution of the statistic and a Poisson distribution is proved, using the Stein-Chen method. The main difficulty in the proof is that the dependence in the time series is not locally restricted. The result implies asymptotically certain discrimination for a reasonable choice of the thresholds.

Type
Short Communications
Copyright
Copyright © by the Applied Probability Trust 2000 

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References

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