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Nonparametric estimation of a time-varying GARCH model

Author

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  • Neelabh Rohan
  • T. V. Ramanathan

Abstract

In this paper, a non-stationary time-varying GARCH (tvGARCH) model has been introduced by allowing the parameters of a stationary GARCH model to vary as functions of time. It is shown that the tvGARCH process is locally stationary in the sense that it can be locally approximated by stationary GARCH processes at fixed time points. We develop a two-step local polynomial procedure for the estimation of the parameter functions of the proposed model. Several asymptotic properties of the estimators have been established, including the asymptotic optimality. It is found that the tvGARCH model performs better than many of the standard GARCH models for various real data sets.

Suggested Citation

  • Neelabh Rohan & T. V. Ramanathan, 2013. "Nonparametric estimation of a time-varying GARCH model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 33-52, March.
    • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:33-52
    DOI: 10.1080/10485252.2012.728600
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    Cited by:

    1. Rohan, Neelabh, 2013. "A time varying GARCH(p,q) model and related statistical inference," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 1983-1990.
    2. Hajar Nasrazadani & Maria Pilar Mu oz Gracia, 2017. "Comparing Iranian and Spanish Electricity Markets with Nonlinear Time Series," International Journal of Energy Economics and Policy, Econjournals, vol. 7(2), pages 262-286.
    3. Rydlewski, Jerzy P. & Snarska, Małgorzata, 2014. "On geometric ergodicity of skewed—SVCHARME models," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 192-197.
    4. Pan, Zhiyuan & Wang, Qing & Wang, Yudong & Yang, Li, 2018. "Forecasting U.S. real GDP using oil prices: A time-varying parameter MIDAS model," Energy Economics, Elsevier, vol. 72(C), pages 177-187.
    5. Grigoryeva, Lyudmila & Ortega, Juan-Pablo & Peresetsky, Anatoly, 2018. "Volatility forecasting using global stochastic financial trends extracted from non-synchronous data," Econometrics and Statistics, Elsevier, vol. 5(C), pages 67-82.
    6. Pourkhanali, Armin & Tafakori, Laleh & Bee, Marco, 2023. "Forecasting Value-at-Risk using functional volatility incorporating an exogenous effect," International Review of Financial Analysis, Elsevier, vol. 89(C).
    7. Sayar Karmakar & Arkaprava Roy, 2020. "Bayesian modelling of time-varying conditional heteroscedasticity," Papers 2009.06007, arXiv.org, revised Mar 2021.
    8. Karmakar, Sayar & Richter, Stefan & Wu, Wei Biao, 2022. "Simultaneous inference for time-varying models," Journal of Econometrics, Elsevier, vol. 227(2), pages 408-428.
    9. Yudong Wang & Zhiyuan Pan & Chongfeng Wu, 2017. "Time‐Varying Parameter Realized Volatility Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(5), pages 566-580, August.
    10. Mishra Anuj & Ramanathan Thekke Variyam, 2017. "Nonstationary autoregressive conditional duration models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(4), pages 1-22, September.

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