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Real time estimation of stochastic volatility processes

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  • László Gerencsér
  • Zsanett Orlovits

Abstract

Autoregressive conditional heteroscedastic (ARCH) processes and their extensions known as generalized ARCH (GARCH) processes are widely accepted for modelling financial time series, in particular stochastic volatility processes. The off-line estimation of ARCH and GARCH processes have been analyzed under a variety of conditions in the literature. The main contribution of this paper is a rigorous convergence analysis of a recursive estimation method for GARCH processes with restricted stability margin under reasonable technical conditions. The main tool in the convergence analysis is an appropriate modification of the theory of recursive estimation within a Markovian framework developed in Benveniste et al. (Adaptive Algorithms and Stochastic Approximations. Springer, Berlin, 1990 ). The basic elements of this theory will also be summarized. The viability of the method will be demonstrated by experimental results both for simulated and real data. Copyright Springer Science+Business Media, LLC 2012

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  • László Gerencsér & Zsanett Orlovits, 2012. "Real time estimation of stochastic volatility processes," Annals of Operations Research, Springer, vol. 200(1), pages 223-246, November.
    • Handle: RePEc:spr:annopr:v:200:y:2012:i:1:p:223-246:10.1007/s10479-011-0976-2
    DOI: 10.1007/s10479-011-0976-2
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    References listed on IDEAS

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    7. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    8. 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.
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    Cited by:

    1. Bal'azs Csan'ad Cs'aji, 2018. "Score Permutation Based Finite Sample Inference for Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) Models," Papers 1807.08390, arXiv.org.
    2. Yanlin Shi, 2023. "Long memory and regime switching in the stochastic volatility modelling," Annals of Operations Research, Springer, vol. 320(2), pages 999-1020, January.

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