Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31464
Normalizing Logarithms of Realized Volatility in an ARFIMA Model

Authors: G. L. C. Yap


Modelling realized volatility with high-frequency returns is popular as it is an unbiased and efficient estimator of return volatility. A computationally simple model is fitting the logarithms of the realized volatilities with a fractionally integrated long-memory Gaussian process. The Gaussianity assumption simplifies the parameter estimation using the Whittle approximation. Nonetheless, this assumption may not be met in the finite samples and there may be a need to normalize the financial series. Based on the empirical indices S&P500 and DAX, this paper examines the performance of the linear volatility model pre-treated with normalization compared to its existing counterpart. The empirical results show that by including normalization as a pre-treatment procedure, the forecast performance outperforms the existing model in terms of statistical and economic evaluations.

Keywords: Long-memory, Gaussian process, Whittle estimator, normalization, volatility, value-at-risk.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 970


[1] S. J. Koopman, B. Jungbacker, and E. Hol, “Forecasting daily variability of the S&P100 stock index using historical, realised and implied volatility measurements,” J. Empir. Financ., vol. 12, pp. 445–475, 2005.
[2] M. Martens, D. Dijk, and M. Pooter, “Forecasting S&P 500 volatility: long memory, level shifts, leverage effects, day of the week seasonality and macroeconomic announcements,” Int. J. Forecast., vol. 25, pp. 282–303, 2009.
[3] M. Martens, “Measuring and forecasting S&P 500 index-futures volatility using high-frequency data,” J. Futur. Mark., vol. 22, pp. 497–518, 2002.
[4] T. G. Andersen, T. Bollerslev, F. X. Diebold, and H. Ebens, “The distribution of realized stock returns volatility,” J. financ. econ., vol. 6, pp. 43–76, 2001.
[5] T. G. Andersen, T. Bollerslev, F. X. Diebold, and P. Labys, “Modeling and forecasting realized volatility,” Econometrica, vol. 71, no. 2, pp. 579–625, 2003.
[6] P. Brockwell and R. Davis, Time Series: Theory and Methods, 2nd ed. Berlin: Springer, 1996.
[7] J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput., vol. 19, pp. 297–301, 1965.
[8] E. J. Hannan, “Central limit theorems for time series regression,” Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 26, pp. 157–170, 1973.
[9] N. H. Chan and W. Palma, “Estimation of long-memory time series models: A survey of different likelihood-based methods,” Econom. Anal. Financ. Econ. Time Ser. B, vol. 20, pp. 89–121, 2006.
[10] M. Narukawa, “Semiparametric Whittle estimation of a cyclical long-memory time series based on generalised exponential models,” J. Nonparametr. Stat., vol. 28, no. 2, pp. 272–295, 2016.
[11] S. Bivona, G. Bonanno, R. Burlon, D. Gurrera, and C. Leone, “Stochastic models for wind speed forecasting,” Energy Convers. Manag., vol. 52, pp. 1157–1165, 2011.
[12] P. R. Hansen, “A test for superior predictive ability,” J. Bus. Econ. Stat., vol. 23, no. 4, pp. 365–380, 2005.
[13] J. Barunik and T. Krehlik, “Combining high frequency data with non-linear models for forecasting energy market volatility,” Expert Syst. with Appl., vol. 55, pp. 222–242, 2016.
[14] P. Giot and S. Laurent, “Modeling daily value-at-risk using realized volatility and ARCH type models,” J. Empir. Financ., vol. 11, pp. 379–398, 2004.
[15] D. P. Louzis, S. Xanthopoulos-Sisinis, and A. P. Refenes, “Realized volatility models and alternative Value-at-risk prediction strategies,” Econ. Model., vol. 40, pp. 101–116, 2014.
[16] R. Dahlhaus, “Efficient parameter estimation for self-similar processes,” Ann. Stat., vol. 17, pp. 1749–1766, 1989.
[17] R. Fox and M. S. Taqqu, “Large sample propertiew of parameter estimates for strongly dependent stationary Gaussian time series,” Ann. Stat., vol. 14, pp. 517–532, 1986.
[18] N. Demiris, D. Lunn, and L. D. Sharples, “Survival extrapolation using the poly-Weibull model,” Stat. Methods Med. Res., vol. 24, no. 2, pp. 287–301, 2015.
[19] S. H. Feizjavadian and R. Hashemi, “Analysis of dependent competing risks in the presence of progressive hybrid censoring using Marshall-Olkin bivariate Weibull distribution,” Comput. Stat. Data Anal., vol. 82, pp. 19–34, 2015.
[20] N. Balakrishnan and M. H. Ling, “Best Constant-Stress Accelerated Life-Test Plans With Multiple Stress Factors for One-Shot Device Testing Under a Weibull Distribution,” IEEE Trans. Reliab., vol. 63, no. 4, pp. 944–952, 2014.
[21] P. Abad, S. B. Muela, and C. L. Martin, “The role of the loss function in value-at-risk comparisons,” J. Risk Model Valid., vol. 9, no. 1, pp. 1–19, 2015.
[22] D. N. Politis and J. P. Romano, “The stationary bootstrap,” J. Am. Stat. Assoc., vol. 89, no. 428, pp. 1303–1313, 1994.