The Annals of Statistics

Asymptotic Conditional Inference for Regular Nonergodic Models with an Application to Autoregressive Processes

I. V. Basawa and P. J. Brockwell

Full-text: Open access

Abstract

A conditional limit theorem is derived for a certain class of stochastic processes whose distributions constitute a nonergodic family. The limit theorem allows us to study the asymptotic behaviour under the conditional model of some standard statistical procedures by making use of results for ergodic families. Explosive Gaussian autoregressive processes are studied in some detail. Here the conditional process is shown to be a nonexplosive Gaussian autoregression bearing a simple relation to the original process. Some optimality results under the conditional model are given for estimators and tests based on the unconditional likelihood.

Article information

Source
Ann. Statist., Volume 12, Number 1 (1984), 161-171.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346399

Digital Object Identifier
doi:10.1214/aos/1176346399

Mathematical Reviews number (MathSciNet)
MR733506

Zentralblatt MATH identifier
0546.62059

JSTOR
links.jstor.org

Subjects
Primary: 62M07: Non-Markovian processes: hypothesis testing
Secondary: 62M09: Non-Markovian processes: estimation 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Nonergodic processes asymptotic conditionality principle conditionally locally asymptotically normal families maximum likelihood estimators score tests conditional limit theorem

Citation

Basawa, I. V.; Brockwell, P. J. Asymptotic Conditional Inference for Regular Nonergodic Models with an Application to Autoregressive Processes. Ann. Statist. 12 (1984), no. 1, 161--171. doi:10.1214/aos/1176346399. https://projecteuclid.org/euclid.aos/1176346399


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