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Simultaneously Modelling Conditional Heteroskedasticity and Scale Change

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  • Feng, Yuanhua

Abstract

This paper proposes a semiparametric approach by introducing a smooth scale function into the standard GARCH model so that conditional heteroskedasticity and scale change in a financial time series can be modelled simultaneously. An estimation procedure combining kernel estimation of the scale function and maximum likelihood estimation of the GARCH parameters is proposed. Asymptotic proper- ties of the kernel estimator are investigated in detail. An iterative plug-in algorithm is developed for selecting the bandwidth. Practical performance of the proposal is illustrated by simulation. The proposal is applied to the daily S&P 500 and DAX 100 returns. It is shown that there are simultaneously significant conditional heteroskedasticity and scale change in these series.

Suggested Citation

  • Feng, Yuanhua, 2002. "Simultaneously Modelling Conditional Heteroskedasticity and Scale Change," CoFE Discussion Papers 02/12, University of Konstanz, Center of Finance and Econometrics (CoFE).
    • Handle: RePEc:zbw:cofedp:0212
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    References listed on IDEAS

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    1. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    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. Hall, Peter & Hart, Jeffrey D., 1990. "Nonparametric regression with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 36(2), pages 339-351, December.
    4. Feng, Yuanhua, 2002. "An Iterative Plug-In Algorithm for Nonparametric Modelling of Seasonal Time Series," CoFE Discussion Papers 02/04, University of Konstanz, Center of Finance and Econometrics (CoFE).
    5. Beran, Jan & Ocker, Dirk, 2001. "Volatility of Stock-Market Indexes--An Analysis Based on SEMIFAR Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 103-116, January.
    6. Karanasos, Menelaos, 1999. "The second moment and the autocovariance function of the squared errors of the GARCH model," Journal of Econometrics, Elsevier, vol. 90(1), pages 63-76, May.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Semiparametric GARCH; conditional heteroskedasticity; scale change; nonparametric regression with dependence; bandwidth selection;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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