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On uniform asymptotic normality of sequential least squares estimators for the parameters in a stable AR(p)

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  • Galtchouk, L.
  • Konev, V.

Abstract

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.

Suggested Citation

  • Galtchouk, L. & Konev, V., 2004. "On uniform asymptotic normality of sequential least squares estimators for the parameters in a stable AR(p)," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 119-142, November.
    • Handle: RePEc:eee:jmvana:v:91:y:2004:i:2:p:119-142
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    References listed on IDEAS

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    1. Lai, T. L. & Wei, C. Z., 1983. "Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters," Journal of Multivariate Analysis, Elsevier, vol. 13(1), pages 1-23, March.
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    Cited by:

    1. Kohtaro Hitomi & Keiji Nagai & Yoshihiko Nishiyama & Junfan Tao, 2021. "Joint Asymptotic Properties of Stopping Times and Sequential Estimators for Stationary First-order Autoregressive Models," KIER Working Papers 1060, Kyoto University, Institute of Economic Research.
    2. Keiji Nagai & Yoshihiko Nishiyama & Kohtaro Hitomi, 2018. "Sequential test for unit root in AR(1) model," KIER Working Papers 1003, Kyoto University, Institute of Economic Research.
    3. Galtchouk, Leonid & Konev, Victor, 2010. "On asymptotic normality of sequential LS-estimate for unstable autoregressive process AR(2)," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2616-2636, November.

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