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Modelling Different Volatility Components

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  • Feng, Yuanhua

Abstract

This paper considers simultaneous modelling of seasonality, slowly changing un- conditional variance and conditional heteroskedasticity in high-frequency fiancial returns. A new approach, called a seasonal SEMIGARCH model, is proposed to perform this by introducing multiplicative seasonal and trend components into the GARCH model. A data-driven semiparametric algorithm is developed for estimat- ing the model. Asymptotic properties of the proposed estimators are investigated briefly. An approximate significance test of seasonality and the use of Monte Carlo confidence bounds for the trend are proposed. Practical performance of the pro- posal is investigated in detail using some German stock price returns. The approach proposed here provides a useful semiparametric extension of the GARCH model.

Suggested Citation

  • Feng, Yuanhua, 2002. "Modelling Different Volatility Components," CoFE Discussion Papers 02/18, University of Konstanz, Center of Finance and Econometrics (CoFE).
    • Handle: RePEc:zbw:cofedp:0218
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    References listed on IDEAS

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    1. He, Changli & Teräsvirta, Timo, 1999. "FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS," Econometric Theory, Cambridge University Press, vol. 15(6), pages 824-846, December.
    2. Beran, Jan, 1999. "SEMIFAR Models - A Semiparametric Framework for Modelling Trends, Long Range Dependence and Nonstationarity," CoFE Discussion Papers 99/16, University of Konstanz, Center of Finance and Econometrics (CoFE).
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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    5. Feng, Yuanhua, 2004. "Simultaneously Modeling Conditional Heteroskedasticity And Scale Change," Econometric Theory, Cambridge University Press, vol. 20(3), pages 563-596, June.
    6. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    7. Mercurio, Danilo & Spokoiny, Vladimir G., 2002. "Statistical inference for time-inhomogeneous volatility models," SFB 373 Discussion Papers 2002,61, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
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