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On local asymptotic normality for functional autoregressive processes

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  • Kara-Terki, Nesrine
  • Mourid, Tahar

Abstract

We establish Local Asymptotic Normality (LAN) and Uniform Local Asymptotic Normality (ULAN) conditions for a class of function space valued autoregressive processes when the correlation operator depends on an unknown one-dimensional parameter. We then derive Hajek minimax bound, consistency, asymptotic normality and efficiency of the conditional maximum likelihood estimator yielding their optimality. A simulation studies illustrate the performance of the estimators.

Suggested Citation

  • Kara-Terki, Nesrine & Mourid, Tahar, 2016. "On local asymptotic normality for functional autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 120-140.
    • Handle: RePEc:eee:jmvana:v:148:y:2016:i:c:p:120-140
    DOI: 10.1016/j.jmva.2016.02.017
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    References listed on IDEAS

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    1. Swensen, Anders Rygh, 1985. "The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend," Journal of Multivariate Analysis, Elsevier, vol. 16(1), pages 54-70, February.
    2. Loges, Wilfried, 1986. "Estimation of parameters for Hilbert space-valued partially observable stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 161-174, October.
    3. Young Hwang, Sun & Basawa, I. V., 1993. "Asymptotic optimal inference for a class of nonlinear time series models," Stochastic Processes and their Applications, Elsevier, vol. 46(1), pages 91-113, May.
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