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Deciding between GARCH and Stochastic Volatility via Strong Decision Rules

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  • Hafner, C.
  • Preminger, A.

Abstract

The GARCH and stochastic volatility (SV) models are two competing, well-known and often used models to explain the volatility of financial series. In this paper, we consider a closed form estimator for a stochastic volatility model and derive its asymptotic properties. We confirm our theoretical results by a simulation study. In addition, we propose a set of simple, strongly consistent decision rules to compare the ability of the GARCH and the SV model to fit the characteristic features observed in high frequency financial data such as high kurtosis and slowly decaying autocorrelation function of the squared observations. These rules are based on a number of moment conditions that is allowed to increase with sample size. We show that our selection procedure leads to choosing the best and simple model with probability one as the sample size increases. The finite sample size behaviour of our procedure is analyzed via simulations. Finally, we provide an application to stocks in the Dow Jones industrial average index.
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Suggested Citation

  • Hafner, C. & Preminger, A., 2010. "Deciding between GARCH and Stochastic Volatility via Strong Decision Rules," LIDAM Reprints ISBA 2010032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2010032
    Note: In : Journal of Statistical Planning and Inference, vol. 140, no. 3, p. 791-805 (2010)
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    Cited by:

    1. Messow, Philip & Krämer, Walter, 2013. "Spurious persistence in stochastic volatility," Economics Letters, Elsevier, vol. 121(2), pages 221-223.
    2. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Ender Demir & Ka Wai Terence Fung & Zhou Lu, 2016. "Capital Asset Pricing Model and Stochastic Volatility: A Case Study of India," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 52(1), pages 52-65, January.
    4. Andrei Rusu, 2020. "Multivariate VaR: A Romanian Market study," The Review of Finance and Banking, Academia de Studii Economice din Bucuresti, Romania / Facultatea de Finante, Asigurari, Banci si Burse de Valori / Catedra de Finante, vol. 12(1), pages 79-95, June.
    5. Krämer, Walter & Messow, Philip, 2012. "Structural Change and Spurious Persistence in Stochastic Volatility," Ruhr Economic Papers 310, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    6. Qiao, Gaoxiu & Jiang, Gongyue & Yang, Jiyu, 2022. "VIX term structure forecasting: New evidence based on the realized semi-variances," International Review of Financial Analysis, Elsevier, vol. 82(C).
    7. Fung, Ka Wai Terence & Lau, Chi Keung Marco & Chan, Kwok Ho, 2014. "The conditional equity premium, cross-sectional returns and stochastic volatility," Economic Modelling, Elsevier, vol. 38(C), pages 316-327.
    8. Fung, Ka Wai Terence & Lau, Chi Keung Marco & Chan, Kwok Ho, 2013. "The Conditional CAPM, Cross-Section Returns and Stochastic Volatility," MPRA Paper 52469, University Library of Munich, Germany.
    9. Walter Krämer & Philip Mess, 2012. "Structural Change and Spurious Persistence in Stochastic Volatility," Ruhr Economic Papers 0310, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    10. Liu, Wei-han, 2016. "A re-examination of maturity effect of energy futures price from the perspective of stochastic volatility," Energy Economics, Elsevier, vol. 56(C), pages 351-362.
    11. Będowska-Sójka, Barbara & Kliber, Agata, 2021. "Is there one safe-haven for various turbulences? The evidence from gold, Bitcoin and Ether," The North American Journal of Economics and Finance, Elsevier, vol. 56(C).
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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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