On asymptotic normality of sequential LS-estimate for unstable autoregressive process AR(2)

Abstract

For estimating parameters in an unstable AR(2) model, the paper proposes a sequential least squares estimate with a special stopping time defined by the trace of the observed Fisher information matrix. It is shown that the sequential LSE is asymptotically normally distributed in the stability region and on its boundary in contrast to the usual LSE, having six different types of asymptotic distributions on the boundary depending on the values of the unknown parameters. The asymptotic behavior of the stopping time is studied.

Original language	English
Pages (from-to)	2616-2636
Number of pages	21
Journal	Journal of Multivariate Analysis
Volume	101
Issue number	10
DOIs	https://doi.org/10.1016/j.jmva.2010.07.009
Publication status	Published - Nov 2010

Keywords

Asymptotic normality
Autoregressive process
Least squares estimate
Sequential estimation

ASJC Scopus subject areas

Statistics, Probability and Uncertainty
Numerical Analysis
Statistics and Probability

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10.1016/j.jmva.2010.07.009

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abstract = "For estimating parameters in an unstable AR(2) model, the paper proposes a sequential least squares estimate with a special stopping time defined by the trace of the observed Fisher information matrix. It is shown that the sequential LSE is asymptotically normally distributed in the stability region and on its boundary in contrast to the usual LSE, having six different types of asymptotic distributions on the boundary depending on the values of the unknown parameters. The asymptotic behavior of the stopping time is studied.",

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author = "Leonid Galtchouk and Victor Konev",

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