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Estimation of Long Memory in Volatility Using Wavelets

Author

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  • Jozef Baruník

    (Institute of Economic Studies, Faculty of Social Sciences, Charles University in Prague, Smetanovo nábreží 6, 111 01 Prague 1, Czech Republic
    Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod Vodarenskou Vezi 4, 182 00, Prague, Czech Republic)

  • Lucie Kraicová

    (Institute of Economic Studies, Faculty of Social Sciences, Charles University in Prague, Smetanovo nábreží 6, 111 01 Prague 1, Czech Republic)

Abstract

In this work we focus on the application of wavelet-based methods in volatility modeling. We introduce a new, wavelet-based estimator (wavelet Whittle estimator) of a FIEGARCH model, ARCH-family model capturing long-memory and asymmetry in volatility, and study its properties. Based on an extensive Monte Carlo experiment, both the behavior of the new estimator in various situations and its relative performance with respect to two more traditional estimators (maximum likelihood estimator and Fourier-based Whittle estimator) are assessed, along with practical aspects of its application. Possible solutions are proposed for most of the issues detected, including suggestion of a new speci cation of the estimator. This uses maximal overlap discrete wavelet transform, which improves the estimator perfor- mance, as we show in the experiment extension. Next, we study all the estimators in case of a FIEGARCH-Jump model, which brings interesting insights to their mechanism. We conclude that, after optimization of the estimation setup, the wavelet-based estimator may become an attractive robust alternative to the traditional methods

Suggested Citation

  • Jozef Baruník & Lucie Kraicová, 2014. "Estimation of Long Memory in Volatility Using Wavelets," Working Papers IES 2014/33, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Sep 2014.
    • Handle: RePEc:fau:wpaper:wp2014_33
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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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