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Realized Wavelet Jump-GARCH model: Can time-frequency decomposition of volatility improve its forecasting?

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  • Jozef Barunik
  • Lukas Vacha

Abstract

In this paper, we propose a forecasting model for volatility based on its decomposition to several investment horizons and jumps. As a forecasting tool, we use Realized GARCH framework which models jointly returns and realized measures of volatility. Using jump wavelet two scale realized volatility estimator (JWTSRV), we first decompose the returns volatility into several investment horizons and jumps and then utilise this decomposition in a newly proposed Realized Jump-GARCH and Realized Wavelet-Jump GARCH models. On currency futures data covering the period of recent financial crisis we moreover compare the forecasts from Realized GARCH model using several additional realized volatility measures. Namely, we use the realized volatility, bipower variation, two-scale realized volatility, realized kernel and jump wavelet two scale realized volatility. We find that in-sample as well as out-of-sample performance of the model significantly differs based on the realized measure used. When JWTSRV estimator is used, model produces significantly best forecasts. Our Realized Wavelet-Jump GARCH model proves to further improve the volatility forecasts. We conclude that realized volatility measurement in the time-frequency domain and inclusion of jumps improves the volatility forecasting considerably.

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File URL: http://arxiv.org/pdf/1204.1452
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1204.1452.

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Date of creation: Apr 2012
Date of revision: Feb 2013
Handle: RePEc:arx:papers:1204.1452

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References

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  1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
  2. Lanne, Markku, 2007. "Forecasting realized exchange rate volatility by decomposition," International Journal of Forecasting, Elsevier, vol. 23(2), pages 307-320.
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  5. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 7(2), pages 174-196, Spring.
  6. Nielsen, Morten Ørregaard & Frederiksen, Per, 2008. "Finite sample accuracy and choice of sampling frequency in integrated volatility estimation," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 265-286, March.
  7. Torben G. Andersen & Tim Bollerslev & Xin Huang, 2007. "A Reduced Form Framework for Modeling Volatility of Speculative Prices based on Realized Variation Measures," CREATES Research Papers 2007-14, School of Economics and Management, University of Aarhus.
  8. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  9. Jozef Barunik & Lukas Vacha, 2012. "Realized wavelet-based estimation of integrated variance and jumps in the presence of noise," Papers 1202.1854, arXiv.org, revised Feb 2013.
  10. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
  11. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  12. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
  13. Ramazan Gencay & Nikola Gradojevic & Faruk Selcuk & Brandon Whitcher, 2010. "Asymmetry of information flow between volatilities across time scales," Quantitative Finance, Taylor and Francis Journals, vol. 10(8), pages 895-915.
  14. Peter Reinhard Hansen & Zhuo (Albert) Huang & Howard Howan Shek, . "Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility," CREATES Research Papers 2010-13, School of Economics and Management, University of Aarhus.
  15. Fleming, Jeff & Paye, Bradley S., 2011. "High-frequency returns, jumps and the mixture of normals hypothesis," Journal of Econometrics, Elsevier, vol. 160(1), pages 119-128, January.
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Cited by:
  1. Jozef Barunik & Michaela Barunikova, 2012. "Revisiting the fractional cointegrating dynamics of implied-realized volatility relation with wavelet band spectrum regression," Papers 1208.4831, arXiv.org, revised Feb 2013.

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