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

Part of: Nonparametric inference Distribution theory Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

Sun-Tsung Kim
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]
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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.

Keywords

Stein-Chen methodtime seriespower of tests

MSC classification

Primary: 62E17: Approximations to distributions (nonasymptotic)
Secondary: 62G10: Hypothesis testing 62M10: Time series, auto-correlation, regression, etc.
Type
Short Communications
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 1129 - 1136
Copyright
Copyright © by the Applied Probability Trust 2000 

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References

[1] Abramowitz, M., and Stegun, I. A. (eds) (1964). Handbook of Mathematical Functions. National Bureau of Standards/US Government Printing Office, Washington, DC.Google Scholar
[2] Barbour, A. D., Holst, L., and Janson, S. (1992). Poisson Approximation (Oxford Studies in Probability 2). Clarendon Press, Oxford.Google Scholar
[3] Knox, G. (1964). Epidemiology of childhood leukaemia in Northumberland and Durham. Brit. J. Prev. Soc. Med. 18, 17–24.Google ScholarPubMed