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Modelling Volatility by Variance Decomposition

Author

Listed:
  • Cristina Amado

    (University of Minho and NIPE)

  • Timo Teräsvirta

    (Aarhus University, School of Economics and Management and CREATES)

Abstract

In this paper, we propose two parametric alternatives to the standard GARCH model. They allow the variance of the model to have a smooth time-varying structure of either additive or multiplicative type. The suggested parameterisations describe both nonlinearity and structural change in the conditional and unconditional variances where the transition between regimes over time is smooth. The main focus is on the multiplicative decomposition that decomposes the variance into an unconditional and conditional component. A modelling strategy for the time-varying GARCH model based on the multiplicative decomposition of the variance is developed. It is heavily dependent on Lagrange multiplier type misspeci?cation tests. Finite-sample properties of the strategy and tests are examined by simulation. An empirical application to daily stock returns and another one to daily exchange rate returns illustrate the functioning and properties of our modelling strategy in practice. The results show that the long memory type behaviour of the sample autocorrelation functions of the absolute returns can also be explained by deterministic changes in the unconditional variance.

Suggested Citation

  • Cristina Amado & Timo Teräsvirta, 2011. "Modelling Volatility by Variance Decomposition," CREATES Research Papers 2011-01, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2011-01
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    1. Christian T. Brownlees & Giampiero M. Gallo, 2010. "Comparison of Volatility Measures: a Risk Management Perspective," Journal of Financial Econometrics, Oxford University Press, vol. 8(1), pages 29-56, Winter.
    2. Song, Peter X.K. & Fan, Yanqin & Kalbfleisch, John D., 2005. "Maximization by Parts in Likelihood Inference," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1145-1158, December.
    3. Meitz, Mika & Saikkonen, Pentti, 2011. "Parameter Estimation In Nonlinear Ar–Garch Models," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1236-1278, December.
    4. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    5. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Persistence in Variance, Structural Change, and the GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 225-234, April.
    6. Robert F. Engle & Jose Gonzalo Rangel, 2008. "The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes," The Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1187-1222, May.
    7. Fiorentini, Gabriele & Calzolari, Giorgio & Panattoni, Lorenzo, 1996. "Analytic Derivatives and the Computation of GARCH Estimates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(4), pages 399-417, July-Aug..
    8. VAN BELLEGEM, Sébastien, 2011. "Locally stationary volatility modelling," LIDAM Discussion Papers CORE 2011041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Mishra, Santosh & Su, Liangjun & Ullah, Aman, 2010. "Semiparametric Estimator of Time Series Conditional Variance," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 256-274.
    10. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    11. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    12. Terasvirta, Timo & Tjostheim, Dag & Granger, Clive W. J., 2010. "Modelling Nonlinear Economic Time Series," OUP Catalogue, Oxford University Press, number 9780199587155, Decembrie.
    13. Van Bellegem, Sebastien & von Sachs, Rainer, 2004. "Forecasting economic time series with unconditional time-varying variance," International Journal of Forecasting, Elsevier, vol. 20(4), pages 611-627.
    14. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    15. Kim, Tae-Hwan & White, Halbert, 2004. "On more robust estimation of skewness and kurtosis," Finance Research Letters, Elsevier, vol. 1(1), pages 56-73, March.
    16. Baillie, Richard T. & Morana, Claudio, 2009. "Modelling long memory and structural breaks in conditional variances: An adaptive FIGARCH approach," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1577-1592, August.
    17. Thomas Mikosch & Cătălin Stărică, 2004. "Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 378-390, February.
    18. A. Ronald Gallant, 1984. "The Fourier Flexible Form," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 66(2), pages 204-208.
    19. Eitrheim, Oyvind & Terasvirta, Timo, 1996. "Testing the adequacy of smooth transition autoregressive models," Journal of Econometrics, Elsevier, vol. 74(1), pages 59-75, September.
    20. Enrique Sentana, 1995. "Quadratic ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(4), pages 639-661.
    21. Jacek Osiewalski & Anna Pajor, 2009. "Bayesian Analysis for Hybrid MSF-SBEKK Models of Multivariate Volatility," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 1(2), pages 179-202, November.
    22. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    23. Berkes, István & Gombay, Edit & Horváth, Lajos & Kokoszka, Piotr, 2004. "SEQUENTIAL CHANGE-POINT DETECTION IN GARCH(p,q) MODELS," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1140-1167, December.
    24. Cristina Amado & Timo Teräsvirta, 2014. "Conditional Correlation Models of Autoregressive Conditional Heteroscedasticity With Nonstationary GARCH Equations," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 69-87, January.
    25. Teräsvirta, Timo, 1996. "Smooth Transition Models," SSE/EFI Working Paper Series in Economics and Finance 132, Stockholm School of Economics.
    26. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    27. Timo Terasvirta & Zhenfang Zhao, 2011. "Stylized facts of return series, robust estimates and three popular models of volatility," Applied Financial Economics, Taylor & Francis Journals, vol. 21(1-2), pages 67-94.
    28. Lin, Chien-Fu Jeff & Terasvirta, Timo, 1994. "Testing the constancy of regression parameters against continuous structural change," Journal of Econometrics, Elsevier, vol. 62(2), pages 211-228, June.
    29. 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.
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    More about this item

    Keywords

    Conditional heteroskedasticity; Structural change; Lagrange multiplier test; Misspeci?cation test; Nonlinear time series; Time-varying parameter model.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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