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Log-volatility enhanced GARCH models for single asset returns

Author

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  • Tomasz Skoczylas

    (University of Warsaw, Faculty of Economic Sciences)

Abstract

This paper presents an alternative approach to modelling and forecasting single asset return volatility. A new, flexible framework is proposed, one which may be considered a development of single-equation GARCH-type models. In this approach an additional equation is added, which binds logarithms of conditional volatility and observed volatility, as measured by the Garman-Klass variance estimator. It enables more information to be retrieved from data. Proposed models are compared with benchmark GARCH and range-based GARCH (RGARCH) models in terms of prediction accuracy. All models are estimated with the maximum likelihood method, using time series of EUR/PLN, EUR/USD, EUR/GBP spot rates quotations as well as WIG20, Dow Jones industrial and DAX indexes. Results are encouraging, especially for foreasting Value-at-Risk. Log-volatility enhanced models achieved lesser rates of VaR exception, as well as lower coverage test statistics, without being more conservative than their single-equation counterparts, as their forecast error measures are to some degree similar.

Suggested Citation

  • Tomasz Skoczylas, 2015. "Log-volatility enhanced GARCH models for single asset returns," Bank i Kredyt, Narodowy Bank Polski, vol. 46(5), pages 411-432.
    • Handle: RePEc:nbp:nbpbik:v:46:y:2015:i:5:p:411-432
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    References listed on IDEAS

    as
    1. Garman, Mark B & Klass, Michael J, 1980. "On the Estimation of Security Price Volatilities from Historical Data," The Journal of Business, University of Chicago Press, vol. 53(1), pages 67-78, January.
    2. Wiggins, James B, 1991. "Empirical Tests of the Bias and Efficiency of the Extreme-Value Variance Estimator for Common Stocks," The Journal of Business, University of Chicago Press, vol. 64(3), pages 417-432, July.
    3. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 429-434, October.
    4. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    5. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    6. Beckers, Stan, 1983. "Variances of Security Price Returns Based on High, Low, and Closing Prices," The Journal of Business, University of Chicago Press, vol. 56(1), pages 97-112, January.
    7. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    8. Brandt, Michael W. & Jones, Christopher S., 2006. "Volatility Forecasting With Range-Based EGARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 470-486, October.
    9. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    10. Chou, Ray Yeutien, 2005. "Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 561-582, June.
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    More about this item

    Keywords

    GARCH; range-based volatility estimators; observed volatility; Value-at-Risk; volatility forecasting;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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