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Estimation of long memory in volatility using wavelets

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  • Kraicova, Lucie
  • Barunik, Jozef

Abstract

This work studies wavelet-based Whittle estimator of the Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroscedasticity (FIEGARCH) model, often used for modeling long memory in volatility of financial assets. The newly proposed estimator approximates the spectral density using wavelet transform, which makes it more robust to certain types of irregularities in data. Based on an extensive Monte Carlo study, both behaviour of the proposed estimator and its relative performance with respect to traditional estimators are assessed. In addition, we study properties of the estimators in presence of jumps, which brings interesting discussion. We find that wavelet-based estimator may become an attractive robust and fast alternative to the traditional methods of estimation.

Suggested Citation

  • Kraicova, Lucie & Barunik, Jozef, 2015. "Estimation of long memory in volatility using wavelets," FinMaP-Working Papers 33, Collaborative EU Project FinMaP - Financial Distortions and Macroeconomic Performance: Expectations, Constraints and Interaction of Agents.
    • Handle: RePEc:zbw:fmpwps:33
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    References listed on IDEAS

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    1. Morten Ørregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 405-443.
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    5. Fan, Yanqin & Gençay, Ramazan, 2010. "Unit Root Tests With Wavelets," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1305-1331, October.
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    7. 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.
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    17. Alex Gonzaga & Michael Hauser, 2011. "A wavelet Whittle estimator of generalized long-memory stochastic volatility," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(1), pages 23-48, March.
    18. Jensen, Mark J., 2000. "An alternative maximum likelihood estimator of long-memory processes using compactly supported wavelets," Journal of Economic Dynamics and Control, Elsevier, vol. 24(3), pages 361-387, March.
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    More about this item

    Keywords

    volatility; long memory; FIEGARCH; wavelets; Whittle; Monte Carlo;
    All these keywords.

    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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