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The Strong Consistency of Quasi-Maximum Likelihood Estimators for p-order Random Coefficient Autoregressive (RCA) Models

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  • Mohammed Benmoumen

    (University Mohammed Premier)

  • Imane Salhi

    (University Mohammed Premier)

Abstract

In this paper, we investigate the strong consistency of the quasi-maximum likelihood estimators derived through the Kalman filter for stationary random coefficient autoregressive (RCA) models. The estimators in question are the subject of Benmoumen et al. (2019) work. The suggested proof exploits both the ergodic theorem and Kalman filter asymptotic proprieties.

Suggested Citation

  • Mohammed Benmoumen & Imane Salhi, 2023. "The Strong Consistency of Quasi-Maximum Likelihood Estimators for p-order Random Coefficient Autoregressive (RCA) Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 617-632, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-021-00269-w
    DOI: 10.1007/s13171-021-00269-w
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    References listed on IDEAS

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    1. Pagan, Adrian, 1980. "Some identification and estimation results for regression models with stochastically varying coefficients," Journal of Econometrics, Elsevier, vol. 13(3), pages 341-363, August.
    2. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737, September.
    3. Alexander Aue & Lajos Horváth & Josef Steinebach, 2006. "Estimation in Random Coefficient Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 61-76, January.
    4. Mohammed Benmoumen & Jelloul Allal & Imane Salhi, 2019. "Parameter Estimation for p-Order Random Coefficient Autoregressive (RCA) Models Based on Kalman Filter," Journal of Applied Mathematics, Hindawi, vol. 2019, pages 1-5, May.
    5. Ghosh, Damayanti, 1989. "Maximum likelihood estimation of the dynamic shock-error model," Journal of Econometrics, Elsevier, vol. 41(1), pages 121-143, May.
    6. István Berkes & Lajos Horváth & Shiqing Ling, 2009. "Estimation in nonstationary random coefficient autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(4), pages 395-416, July.
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