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

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. 1 2 ∗ The second author is partially supported by the RFFI-Grant 04-01-00855. 1 AMS 2000 Subject Classification : 62L10, 62L12 2 Key words: Autoregressive process, least squares estimate, sequential estimation, asymptotic normality . 1 hal-00271136,version1-8Apr2008 

• Type: Journal
• Year: 2010
• Where: MA
• Authors: Leonid Galtchouk, Victor Konev
• Keywords: AMS 2000 Subject, Communications, MA 2010, Observed Fisher Information, Sequential