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Estimation in Random Coefficient Autoregressive Models

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  • Alexander Aue
  • Lajos Horváth
  • Josef Steinebach

Abstract

. We propose the quasi‐maximum likelihood method to estimate the parameters of an RCA(1) process, i.e. a random coefficient autoregressive time series of order 1. The strong consistency and the asymptotic normality of the estimators are derived under optimal conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:1:p:61-76
    DOI: 10.1111/j.1467-9892.2005.00453.x
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    Cited by:

    1. Chi Yao & Wei Yu & Xuejun Wang, 2023. "Strong Consistency for the Conditional Self-weighted M Estimator of GRCA(p) Models," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-21, March.
    2. Daisuke Nagakura, 2009. "Inconsistency of a Unit Root Test against Stochastic Unit Root Processes," IMES Discussion Paper Series 09-E-23, Institute for Monetary and Economic Studies, Bank of Japan.
    3. Aknouche, Abdelhakim, 2015. "Unified quasi-maximum likelihood estimation theory for stable and unstable Markov bilinear processes," MPRA Paper 69572, University Library of Munich, Germany.
    4. Zheqi Wang & Dehui Wang & Jianhua Cheng, 2023. "A new autoregressive process driven by explanatory variables and past observations: an application to PM 2.5," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(2), pages 619-658, June.
    5. Lorenzo Trapani, 2021. "Testing for strict stationarity in a random coefficient autoregressive model," Econometric Reviews, Taylor & Francis Journals, vol. 40(3), pages 220-256, April.
    6. Boukhiar, Souad & Mourid, Tahar, 2022. "Resolvent estimators for functional autoregressive processes with random coefficients," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    7. Proïa, Frédéric & Soltane, Marius, 2021. "Comments on the presence of serial correlation in the random coefficients of an autoregressive process," Statistics & Probability Letters, Elsevier, vol. 170(C).
    8. Daisuke Nagakura, 2007. "Testing for Coefficient Stability of AR(1) Model When the Null is an Integrated or a Stationary Process," IMES Discussion Paper Series 07-E-20, Institute for Monetary and Economic Studies, Bank of Japan.
    9. 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.
    10. Aknouche, Abdelhakim & Gouveia, Sonia & Scotto, Manuel, 2023. "Random multiplication versus random sum: auto-regressive-like models with integer-valued random inputs," MPRA Paper 119518, University Library of Munich, Germany, revised 18 Dec 2023.
    11. Tao, Yubo & Phillips, Peter C.B. & Yu, Jun, 2019. "Random coefficient continuous systems: Testing for extreme sample path behavior," Journal of Econometrics, Elsevier, vol. 209(2), pages 208-237.
    12. Horváth, Lajos & Trapani, Lorenzo, 2019. "Testing for randomness in a random coefficient autoregression model," Journal of Econometrics, Elsevier, vol. 209(2), pages 338-352.
    13. Jonathan Hill & Liang Peng, 2014. "Unified Interval Estimation For Random Coefficient Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 282-297, May.
    14. 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.
    15. Bercu, Bernard & Blandin, Vassili, 2015. "A Rademacher–Menchov approach for random coefficient bifurcating autoregressive processes," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1218-1243.
    16. Trapani, Lorenzo, 2021. "A test for strict stationarity in a random coefficient autoregressive model of order 1," Statistics & Probability Letters, Elsevier, vol. 177(C).
    17. Nielsen, Heino Bohn & Rahbek, Anders, 2014. "Unit root vector autoregression with volatility induced stationarity," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 144-167.
    18. Horváth, Lajos & Trapani, Lorenzo, 2016. "Statistical inference in a random coefficient panel model," Journal of Econometrics, Elsevier, vol. 193(1), pages 54-75.
    19. Abdelhakim Aknouche, 2015. "Quadratic random coefficient autoregression with linear-in-parameters volatility," Statistical Inference for Stochastic Processes, Springer, vol. 18(2), pages 99-125, July.
    20. Thorsten Fink & Jens-Peter Kreiss, 2013. "Bootstrap For Random Coefficient Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 646-667, November.
    21. Johansen, Søren & Lange, Theis, 2013. "Least squares estimation in a simple random coefficient autoregressive model," Journal of Econometrics, Elsevier, vol. 177(2), pages 285-288.
    22. Nagakura, Daisuke, 2009. "Asymptotic theory for explosive random coefficient autoregressive models and inconsistency of a unit root test against a stochastic unit root process," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2476-2483, December.
    23. Autcha Araveeporn, 2020. "Comparing Parameter Estimation of Random Coefficient Autoregressive Model by Frequentist Method," Mathematics, MDPI, vol. 8(1), pages 1-17, January.
    24. Lorenzo Trapani & Emily Whitehouse, 2020. "Sequential monitoring for cointegrating regressions," Papers 2003.12182, arXiv.org.
    25. Yoon, Gawon, 2016. "Stochastic unit root processes: Maximum likelihood estimation, and new Lagrange multiplier and likelihood ratio tests," Economic Modelling, Elsevier, vol. 52(PB), pages 725-732.

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