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 | |
| 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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Galtchouk, L., & Konev, V. (2010). On asymptotic normality of sequential LS-estimate for unstable autoregressive process AR(2). Journal of Multivariate Analysis, 101(10), 2616-2636. https://doi.org/10.1016/j.jmva.2010.07.009