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Limit theorems for the shifting level process

Published online by Cambridge University Press:  14 July 2016

Daren B. H. Cline
Daren B. H. Cline*
Affiliation:
Colorado State University
*
∗ Postal address: Department of Statistics, Colorado State University, Fort Collins, CO 80523, U.S.A.
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Abstract

This paper studies the asymptotic properties of moment estimators for the general shifting level process (SLP). A law of large numbers and a weak convergence theorem are obtained under conditions involving the unobservable processes which make up SLP. Specific conditions about those underlying processes are added to give explicit results, applicable to a large class of moment estimators. Actual formulae for asymptotic variances, etc. are obtained for a simple example, the GNN model.

Keywords

SHIFTING LEVEL PROCESSLAW OF LARGE NUMBERSWEAK CONVERGENCEMOMENT ESTIMATORSERGODICITYϑ-MIXINGl-DEPENDENCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 322 - 337
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

Research supported by the National Science Foundation under Grants ENG77-26729, ENG79-19300 and CEE81-10782.

References

Billingsley, P. (1968) Weak Convergence of Probability Measures. Wiley, New York.Google Scholar
Boes, D. C. and Salas, J. D. (1978) Nonstationarity of the mean and the Hurst phenomenon. Water Resources Res. 14, 135–143.Google Scholar
Breiman, L. (1968) Probability. Addison-Wesley, Reading, MA.Google Scholar
Chung, K. L. (1974) A Course in Probability Theory, 2nd edn. Academic Press, New York.Google Scholar
Durrett, R. T. and Resnick, S. I. (1977) Weak convergence with random indices. Stoch. Proc. Appl. 5, 213–220.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and its Applications, 2nd edn. Wiley, New York.Google Scholar
Hurst, H. E. (1957) A suggested model of some time series which occur in nature. Nature, London 180, 194.Google Scholar
Klemes, V. (1974) The Hurst phenomenon: a puzzle? Water Resources Res. 10, 675–688.Google Scholar
Serfozo, R. F. (1972) Semi-stationary processes. Z. Wahrscheinlichkeitsth. 23, 125–132.Google Scholar