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Quadratic random coefficient autoregression with linear-in-parameters volatility

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  • Abdelhakim Aknouche

Abstract

This paper proposes a class of generalized random coefficient autoregressions ( $$GRCA$$ G R C A ) in which the autoregressive coefficient is a linear regression of the innovation, so that the corresponding volatility is linear in parameters while having a quadratic expression. The proposed model allows a flexible representation, including level and volatility asymmetries, while being fairly simple to implement. We study the dynamic structure of the model and we propose a four-stage weighted least squares estimate ( $$4SWLSE$$ 4 S W L S E ) for which we establish consistency and asymptotic normality in both stationary and nonstationary cases. The proposed $$4SWLSE$$ 4 S W L S E , with a closed form, has the same asymptotic distribution as the quasi-maximum likelihood estimate under the same mild assumptions. Application to real data is given. Copyright Springer Science+Business Media Dordrecht 2015

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  • 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.
    • Handle: RePEc:spr:sistpr:v:18:y:2015:i:2:p:99-125
    DOI: 10.1007/s11203-014-9108-3
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    References listed on IDEAS

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    1. Min Chen & Dong Li & Shiqing Ling, 2014. "Non-Stationarity And Quasi-Maximum Likelihood Estimation On A Double Autoregressive Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 189-202, May.
    2. Shiqing Ling & Dong Li, 2008. "Asymptotic inference for a nonstationary double AR (1) model," Biometrika, Biometrika Trust, vol. 95(1), pages 257-263.
    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. S. Y. Hwang & I. V. Basawa, 2005. "Explosive Random‐Coefficient AR(1) Processes and Related Asymptotics for Least‐Squares Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 807-824, November.
    5. Paul D. Feigin & Richard L. Tweedie, 1985. "Random Coefficient Autoregressive Processes:A Markov Chain Analysis Of Stationarity And Finiteness Of Moments," Journal of Time Series Analysis, Wiley Blackwell, vol. 6(1), pages 1-14, January.
    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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    1. 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.

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