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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.

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