Journal of Finance and Economics
ISSN (Print): 2328-7284 ISSN (Online): 2328-7276 Website: http://www.sciepub.com/journal/jfe Editor-in-chief: Suman Banerjee
Open Access
Journal Browser
Go
Journal of Finance and Economics. 2016, 4(2), 54-62
DOI: 10.12691/jfe-4-2-3
Open AccessArticle

Forecasting Financial Assets Volatility Using Integrated GARCH-Type Models: International Evidence

Samir Mabrouk1,

1Faculty of Management and Economic Sciences of Sousse, Sousse University, Tunisia

Pub. Date: April 21, 2016

Cite this paper:
Samir Mabrouk. Forecasting Financial Assets Volatility Using Integrated GARCH-Type Models: International Evidence. Journal of Finance and Economics. 2016; 4(2):54-62. doi: 10.12691/jfe-4-2-3

Abstract

In this article we compare the forecasting ability of two symmetric integrated GARCH models (FIGARCH & HYGARCH) with an asymmetric model (FIAPARCH) based on a skewed Student distribution. Each model is used for forecasting the daily conditional variance of 10 financial assets, for a sample period of about 18 years. This exercise is done for seven stock indexes (Dow Jones, NASDAQ, S&P500, DAX30, FTSE100, CAC40 and Nikkei 225) and three exchange rates vis-a-vis the US dollar (the GBP- USD, YEN-USD and Euro-USD). Results indicate that the skewed Student AR (1) FIAPARCH (1.d.1) relatively outperforms the other models in out-of-sample forecasts for one, five and fifteen day forecast horizons. Results indicate also, no difference for the AR (1) FIGARCH (1.d.1) and AR (1) HYGARCH (1.d.1) models since they have the same forecasting ability.

Keywords:
forecasting volatility skewed Student distribution Long-range memory

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  Andersen, T.G., T. Bollerslev, F.X. Diebold and P. Labys, 2003, Modeling and forecasting realized volatility, Econometrica, 71, 2, 529-626.
 
[2]  Andersen, T., and T. Bollerslev (1998) Answering the skeptics: Yes, standard volatility models do provide accurate forecasts, International Economic Review, 39, 4, 885-905.
 
[3]  Angelidis, T., A. Benos, and S. Degiannakis (2004). The use of GARCH models in VaR estimation. Statistical Methodology 1-2, 105-128.
 
[4]  Baillie, R.T., T. Bollerslev and H.O. Mikkelsen (1996) Fractionally integrated generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 74, 1, 3-30.
 
[5]  Baillie, R.T., and T. Bollerslev (1989) The message in daily exchange rates: a conditional variance, Journal of Business and Economic Statistics, 7, 3, 297-305.
 
[6]  Baillie, R.T., T. Bollerslev and H.O. Mikkelsen (1996) Fractionally integrated generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 74, 1, 3-30.
 
[7]  Bali, T.G. (2000) Testing the empirical performance of stochastic volatility models of the short-term interest rate, Journal of Financial and Quantitative Analysis, 35, 2, 191-215.
 
[8]  Bera, A. and M. Higgins (1993). ARCH models: Properties, estimation and testing. Journal of Economic Surveys 7, 305-362.
 
[9]  Bollerslev, T. (1987) A conditionally heteroskedastic time series model for speculative prices and rates of return, Review of Economics and Statistics, 69, 3, 542-547.
 
[10]  Bollerslev, T., R.F. Engle and D.B. Nelson (1994) ARCH models, in: Engle, R.F., and D.L. McFadden (eds), Handbook of Econemetrics, Vol. IV, North Holland, Amsterdam, pp. 2959-3038.
 
[11]  Bollerslev, T., R.Y. Chou and K.P. Kroner (1992) ARCH modeling in finance: A Review of the theory and empirical evidence, Journal of Econometrics, 52, 5-59.
 
[12]  Bollerslev, T. (1990) Modelling the coherence in short-run nominal exchange rates: A multivariate generalized ARCH model, Review of Economics and Statistics, 72,498-505.
 
[13]  Cao, C.Q., and R.S. Tsay (1992) Nonlinear time-series analysis of stock volatilities, Journal of Applied Econometrics, December, Supplement, 1, S165-S185.
 
[14]  Chin Wen Cheong. (2009), “Modeling and forecasting crude oil markets using ARCH-type models”. Energy Policy 37-2346-2355.
 
[15]  Davidson, J. (2004). Forecasting Markov–switching dynamic, conditionally heteroskedastic processes. Statistics & Probability Letters 68, 137-147.
 
[16]  Diebold, F. X. and R. S. Mariano (1995). Comparing predictive accuracy. Journal of Business and Economic Statistics 13, 253-263.
 
[17]  Diebold, F. X. and J. A. Lopez (1995). Modeling volatility dynamics. In K. V. Hoover (Ed.), Macroeconometrics: Developments, Tensions and Prospects, pp. 427-472. Boston / Dordrecht / London: Kluwer Academic Press.
 
[18]  Ding, Z., C. W. Granger, and R. F. Engle (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance 1, 83-106.
 
[19]  Dickey, D., Fuller, W., 1979. Distribution of the estimators for autoregressive time series with unit root. Journal of American Statistic Association 74, 427-431.
 
[20]  Engle, R. F. (1982a). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987-1007.
 
[21]  Engle, R. F. (1990). Stock volatility and the crash of ’87: Discussion. Review of Financial Studies 3, 103-106.
 
[22]  Fan, J., Y. Li, and K. Yu (2010). Vast volatility matrix estimation using high frequency data for portfolio selection. Technical report, Princeton University.
 
[23]  Fernandez, C., J. Osiewalski, and M. F. Steel (1995). Modelling and inference with v–spherical distributions. Journal of the American Statistical Association 90, 1331-1340.
 
[24]  Figlewski, S. (1997) Forecasting volatility, Financial Markets, Institutions and Instruments (New York University Salomon Center), 6, 1, 1-88.
 
[25]  Geweke, J. and S. Porter-Hudak (1983). The estimation and application of long memory time series models. Journal of Time Series Analysis 4, 221-238.
 
[26]  Ghysels, E., A. Harvey, and E. Renault (1996). Stochastic volatility. In G. Maddala, and C. Rao (Eds.), Handbook of Statistics, pp. 119-191. Amsterdam: Elsevier Science.
 
[27]  Giot, P. and S. Laurent (2004). Modelling daily value–at–risk using realized volatility and ARCH type models. Journal of Empirical Finance 11, 379-398.
 
[28]  Heynen, R.C., and H.M. Kat (1994) Volatility prediction: A comparison of stochastic volatility, GARCH(1,1) and EGARCH(1,1) models, Journal of Derivatives, 2, 50-65.
 
[29]  Hamilton, J.D., and R. Susmel (1994) Autoregressive conditional heteroskedasticity and changes in regime, Journal of Econometrics, 64, 1-2, 307-333.
 
[30]  Hansen, P. R. and A. Lunde (2006a). Consistent ranking of volatility models. Journal of Econometrics 131, 97-121.
 
[31]  Jarque, C.M., A. K. Béra, 1980. Efficient tests for normality, homoscedasticity and serial independence of regression residuals. Economics Letters 6, 255-259.
 
[32]  Kang, S.H., S., M., Yoon, 2007. Value-at-risk analysis of the long memory volatility process: the case of individual stock returns, 101-130.
 
[33]  Kwiatkowski, D., Phillips P.C.W, Schmidt P. and Shin Y., 1992. Testing the null hypothesis of stationarity against the alternative of unit root. Journal of Econometrics 54, 159-178.
 
[34]  Lambert, P., and S. Laurent (2001): “Modelling Financial Time Series Using GARCH-Type Models and a Skewed Student Density,” Mimeo, Université de Liège.
 
[35]  Lee, K.Y. (1991) Are the GARCH models best in out-of-sample performance? Economics Letters, 37, 3, 305-308.
 
[36]  Li, K. (2002) Long-memory versus option-implied volatility prediction, Journal of Derivatives, 9, 3, 9-25.
 
[37]  Lo, A.W., 1991. Long term memory in stock market prices. Econometrica 59, 1279-1313.
 
[38]  Lopez, J. (2001). Evaluating the predictive accuracy of volatility models. Journal of Forecasting 20, 87-109.
 
[39]  Mabrouk. S., Aloui. C. “One-day-ahead value-at-risk estimations with dual long-memory models: evidence from the Tunisian stock market”, Int. J. Financial Services Management, Vol. 4, No. 2, 2010.
 
[40]  Mincer, J. and V. Zarnowitz (1969). The evaluation of economic forecasts. In J. Mincer (Ed.), Economic Forecasts and Expectations. New York: Columbia University Press.
 
[41]  Martens, M., and J. Zein (2004) Predicting financial volatility: High-frequency timeseries forecasts vis-`a-vis implied volatility, Journal of Futures Markets, 24, 11, 1005-1028.
 
[42]  Nelson, D. B. (1991b). Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59, 347-370.
 
[43]  Palm, F. (1996). GARCH models of volatility. In G. Maddala, and C. Rao (Eds.), Handbook of Statistics, pp. 209-240. Amsterdam: Elsevier Science.
 
[44]  Pagan, A. (1996). The econometrics of financial markets. Journal of Empirical Finance 3, 15-102.
 
[45]  Pagan, A.R., and G.W. Schwert (1990) Alternative models for conditional models for conditional stock volatility, Journal of Econometrics, 45, 1-2, 267-290.
 
[46]  Patton, A. J. (2011). Volatility forecast comparison using imperfect volatility proxies. Journal of Econometrics 160, 246-256.
 
[47]  Phillips, P.C.B., P. Perron, 1988. Testing for a unit root in time series regression. Biometrika 75, 335-346.
 
[48]  Pong, S., M.B. Shackleton, S.J. Taylor and X. Xu (2004) Forecasting Sterling/Dollar volatility: A comparison of implied volatilities and AR(FI)MA models, Journal of Banking and Finance, 28, 2541-2563.
 
[49]  Poon, S.-H., and C.W.J. Granger (2003) Forecasting financial market volatility: Areview, Journal of Economic Literature, 41, 2, 478-539.
 
[50]  Tang, T.L., S., J., Shieh, 2006. Long memory in stock index future markets: a value-at-risk approach. Physica A, 437-448.
 
[51]  Teverovsky, V., M. Taqqu, W. Willinger, 1999. A critical look at Lo’s modified R/S statistic. Journal of Statistical Planning and Inference 80, 211-227.
 
[52]  Taylor, J.W. (2004) Volatility forecasting with smooth transition exponential smoothing, International Journal of Forecasting, 20, 273-286.
 
[53]  Tse, Y.K. (1991) Stock return volatility in the Tokyo Stock Exchange, Japan and the World Economy, 3, 285-298.
 
[54]  Wu, P. T., S-J. Shieh, 2007. Value-at-risk analysis for long-term interest rate futures: fat-tail and long memory in return innovations. Journal of Empirical Finance 14, 248-259.
 
[55]  Xekalaki, E. and S. Degiannakis (2010). ARCH Models for Financial Applications. John Wiley & Sons.
 
[56]  Zumbach, G. (2002). Volatility processes and volatility forecast with long memory, Working paper, Olsen Associates.