An Improvement to LMSV Parameter Estimation: Modelling and Forecasting Volatility and Value-at-risk

  • Grace Lee Ching Yap School of Applied Mathematics, Faculty of Engineering, (Malaysia Campus), 43500 Semenyih, Selangor, Malaysia
  • Wen Cheong Chin Faculty of Management, SIG Quantitative Economics and Finance, Multimedia University, 63100 Cyberjaya, Selangor, Malaysia
Keywords: long memory, volatility, normalization, value-at-risk.

Abstract

This paper proposes an improvement to the long memory stochastic volatility (LMSV) model to forecast volatility using high frequency data. To allow frequency domain quasi-maximum likelihood (FDQML) estimation, we suggest a parsimonious normalization procedure that avoids repetitive parameter estimation. This resultantly produces more efficient parameter estimation as less estimation error is involved. Besides, a de-trending procedure is proposed prior to the de-seasonalization procedure to improve the identification of seasonal patterns. We compare the performance of volatility forecasts by the proposed refined FDQML-LMSV model with the existing LMSV and the linear long memory model that fits to logarithms of realised volatility. The empirical results show that the proposed method outperforms the existing models statistically, and the output of the proposed method improves the accuracy and efficiency in value-at-risk forecasting.

References

[1] T. G. Andersen and T. Bollerslev, “Answering the skeptics: yes, standard volatility models do provide accurate forecasts,” Int. Rev. Econ., vol. 39, pp. 885–905, 1998.
[2] 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.
[3] O. E. Barndorff-Nielsen and N. Shephard, “Econometric analysis of realized volatility and its use in estimating stochastic volatility models,” R. Stat. Soc. Ser. B, vol. 64, pp. 253–280, 2002.
[4] M. Martens, “Measuring and forecasting S&P 500 index-futures volatility using high-frequency data,” J. Futur. Mark., vol. 22, pp. 497–518, 2002.
[5] 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.
[6] 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.
[7] 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.
[8] 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.
[9] 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.
[10] R. Deo, C. Hurvich, and Y. Lu, “Forecasting realized volatility using a long-memory stochastic volatility model: estimation, prediction and seasonal adjustment,” J. Econom., vol. 131, pp. 29–58, 2006.
[11] F. Corsi, “A simple approximate long-memory model of realized volatility,” J. Financ. Econom., vol. 7, no. 2, p. 174–196., 2009.
[12] 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.
[13] B. Cabdelon and L. A. Gil-Alana, “Fractional integration and business cycle features,” Empir. Econ., vol. 29, pp. 1–17, 2004.
[14] G. M. Caporale, J. Cunado, and L. A. Gil-Alana, “Modelling long-run trends and cycles in financial time series data,” J. Time Ser. Anal., vol. 34, pp. 405–421, 2013.
[15] 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.
[16] 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.
[17] 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.
[18] 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.
[19] F. M. Longin and B. Solnik, “Is the correlation in international equity returns constant,” J. Int. Money Financ., vol. 14, no. 1, pp. 3–26, 1995.
[20] M. C. Munnix, T. Shimada, R. Schafer, F. Leyvraz, T. H. Seligman, T. Guhr, and H. E. Stanley, “Identifying states of a financial market,” Sci. Rep., vol. 2, p. 644, 2012.
[21] T. A. Schmitt, R. Schafer, D. Wied, and T. Guhr, “Spatial dependence in stock returns: local normalization and VaR forecasts,” Empir. Econ., vol. 50, pp. 1091–1109, 2016.
[22] P. R. Hansen, “A test for superior predictive ability,” J. Bus. Econ. Stat., vol. 23, no. 4, pp. 365–380, 2005.
[23] D. N. Politis and J. P. Romano, “The stationary bootstrap,” J. Am. Stat. Assoc., vol. 89, no. 428, pp. 1303–1313, 1994.
[24] P. Lambert and S. Laurent, Modelling financial time series using GARCH-type models and a skewed Student density. Mimeo: University of Liege, 2001.
[25] P. Christoffersen, “Evaluating interval forecasts,” Int. Econ. Rev. (Philadelphia)., vol. 39, pp. 841–862, 1998.
[26] 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.
[27] R. Giacomini and I. Komunjer, “Evaluation and combination of conditional quantile forecasts,” J. Bus. Econ. Stat., vol. 23, no. 4, pp. 416–431, 2005.
Published
2017-01-19
Section
Articles