On uniform asymptotic normality of sequential least squares estimators for the parameters in a stable AR(\(p\)). (English) Zbl 1110.62107
Summary: For a stable autoregressive process of order \(p\) with unknown vector parameter \(\theta\), it is shown that under a sequential sampling scheme with the stopping time defined by the trace of the observed Fisher information matrix, the least-squares estimator of \(\theta\) is asymptotically normally distributed uniformly in \(\theta\) belonging to any compact set in the parameter region.
MSC:
| 62L12 | Sequential estimation |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62F12 | Asymptotic properties of parametric estimators |
Keywords:
Autoregressive process; Least-squares estimator; Sequential estimation; Uniform asymptotic normalityReferences:
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