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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:101

Article

Galtchouk, Leonid¹  Konev, Victor² 

[1] Strasbourg Univ, IRMA, Dept Math, F-67084 Strasbourg, France

[2] Tomsk VV Kuibyshev State Univ, Dept Appl Math & Cybernet, Tomsk 634050, Russia

关键词: Autoregressive process;    Least squares estimate;    Sequential estimation;    Asymptotic normality;   

DOI  :  10.1016/j.jmva.2010.07.009

来源: Elsevier

【 摘 要 】

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. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free