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Forecasting volatility and the risk-return tradeoff: an application on the Fama-French benchmark market return. (English) Zbl 1462.62739

Summary: The paper uses the daily stock market index returns of Fama-French to attempt a comparative forecasting analysis of different volatility models. The comparison naturally pre-requests the specification of the competing volatility frameworks and therefore the paper among other issues deals with dilemmas about whether volatility-return relations hold. As expected the analysis focuses on FIEGARCH-M models that extend the basic long memory volatility framework of T. Bollerslev and H. O. Mikkelsen [J. Econom. 73, No. 1, 151–184 (1996; Zbl 0960.62560)] with the introduction of a volatility in mean effect. Taking also into consideration the work of B. J. Christensen and M. Ø. Nielsen [“The effect of long memory in volatility of stock market fluctuations”, Rev. Econ. Stat. 89, No. 4, 684–700 (2007; doi:10.1162/rest.89.4.684)] for the existence of spillover effects when conditional in mean equations hold a stationary and a long memory component the analysis estimates the filter long memory volatility models FIEGARCH-MG and FIEGARCH-MH presented in [B. J. Christensen et al., “Long memory in stock market volatility and the volatility-in-mean effect: the FIEGARCH-M Model”, J. Empirical Finance 17, No. 3, 460–470 (2010; doi:10.1016/j.jempfin.2009.09.008)] in order to test whether such filter adjustments can improve volatility forecasting. Although there is no particular reason to assume that the stationary inputs in the return equations will necessarily follow the normal distribution that [Christensen et al., loc. cit.] assume, the paper follows this path but nevertheless enriches this aspect of the analysis by introducing alternative distributional assumptions. The results indicate the existence of a statistically significant mean effect when both filter models are estimated under the assumption of t-student distribution, although as far as volatility forecasting is concerned both filtered models cannot outperform in terms of forecasting criteria the parsimonious FIEGARCH version that dominates filter and non-filter volatility models under various forecasting horizons.

MSC:

62P20 Applications of statistics to economics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M20 Inference from stochastic processes and prediction

Citations:

Zbl 0960.62560

Software:

G@RCH
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Full Text: DOI

References:

[1] Ang, A.; Hodrick, R. J.; Xing, Y.; Zhang, X., The Cross-Section of Volatility and Expected Returns, Journal of Finance, 61, 259-99 (2006); · doi:10.1111/j.1540-6261.2006.00836.x
[2] Baillie, R. T.; Bollerslev, T., The Message in Daily Exchange Rates: A Conditional -Variance Tale, Journal of Business and Economic Statistics, 7, 297-305 (1989);
[3] Baillie, R. T.; Bollerslev, T.; Mikkelsen, H., Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, 74, 3-30 (1996); · Zbl 0865.62085 · doi:10.1016/S0304-4076(95)01749-6
[4] Baillie, R. T.; Morana, C., Modelling Long Memory and Structural Breaks in Conditional Variances: An Adaptive FIGARCH Approach, Journal of Economic Dynamics and Control, 33, 8, 1577-92 (2009); · Zbl 1170.91483 · doi:10.1016/j.jedc.2009.02.009
[5] Barkoulas, J. T.; Baum, C. F., Long Term Dependence in Stock Returns, Economic Letters, 53, 253-59 (1996); · Zbl 0897.90037 · doi:10.1016/S0165-1765(96)00935-4
[6] Barkoulas, J. T.; Baum, C. F.; Travlos, N., Long Memory in the Greek Stock Market, Applied Financial Economics, 10, 177-84 (2000); · doi:10.1080/096031000331815
[7] Bauwens, L.; Laurent, S., A New Class of Multivariate Skew Densities, with Application to GARCH Models, Journal of Business and Economic Statistics, 23, 346-54 (2005); · doi:10.1198/073500104000000523
[8] Black, F.1976. “Studies of Stock Market Volatility Changes.” Proceedings of the American Statistical Association’, Business and Economic Statistics Section 177-181.;
[9] Bollerslev, T., A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return, Review of Economics and Statistics, 69, 542-47 (1987); · doi:10.2307/1925546
[10] Bollerslev, T.; Chou, R. Y.; Kroner, K. F., ARCH Modeling in Finance: A Review of the Theory and Empirical Evidence, Journal of Econometrics, 52, 5-59 (1992); · Zbl 0825.90057 · doi:10.1016/0304-4076(92)90064-X
[11] Bollerslev, T.; Mikkelsen, H. O., Modeling and Pricing Long Memory in Stock Market Volatility, Journal of Econometrics, 73, 151-84 (1996); · Zbl 0960.62560 · doi:10.1016/0304-4076(95)01736-4
[12] Βοllerslev, T.; Wooldridge, R. F., Quasi-Maximum Likelihood Estimation and Inference in Dynamic Models with Time Varying Covariance, Econometric Reviews, 11, 143-72 (1992); · Zbl 0850.62884 · doi:10.1080/07474939208800229
[13] Campbell, J. Y.; Hentschel, L., No News Is Good News: An Asymmetric Model of Changing Volatility in Stock Returns, Journal of Financial Economics, 31, 281-318 (1992); · doi:10.1016/0304-405X(92)90037-X
[14] Cheung, Y. W.; Lai, K., A Search for Long-Memory in International Stock Market Returns, Journal of International Money and Finance, 14, 597-615 (1995); · doi:10.1016/0261-5606(95)93616-U
[15] Christensen, B. J.; Nielsen, M. O.; Zhu, J., The Effect of Long Memory in Volatility of Stock Market Fluctuations, Review of Economics and Statistics, 89, 684-700 (2007); · doi:10.1162/rest.89.4.684
[16] Christensen, B. J.; Nielsen, M. Ǿ.; Zhu, J., Long Memory in Stock Market Volatility and the Volatility-in-Mean Effect: The FIEGARCH-M Model, Journal of Econometrics, 155, 170-87 (2010);
[17] Clements, M. P.; Hendry, D. F., On the Limitations of Comparing Mean Squared Forecast Errors, Journal of Forecasting, 12, 617-37 (1993); · doi:10.1002/for.3980120802
[18] Crato, N., Some International Evidence Regarding the Stochastic Behaviour of Stock Returns, Journal of International Money and Finance, 14, 597-615 (1994);
[19] Crato, N.; de Lima, P., Long-Range Dependence in the Conditional Variance of Stock Returns, Economic Letters, 45, 281-85 (1994); · Zbl 0800.62791 · doi:10.1016/0165-1765(94)90024-8
[20] Diebold, F. X.; Mariano, R. S., Comparing Predictive Accuracy, Journal of Business and Economic Statistics, 13, 253-63 (1995);
[21] Engle, R. F., Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, 50, 987-1006 (1982); · Zbl 0491.62099 · doi:10.2307/1912773
[22] Engle, R. F.; Ng, V. K., Measuring and Testing the Impact of News on Volatility, Journal of Finance, 48, 1749-78 (1993); · doi:10.1111/j.1540-6261.1993.tb05127.x
[23] Fernandez, C.; Steel, M., On Bayesian Modeling on Fat Tails and Skewness, Journal of American Statistical Association, 93, 359-71 (1998); · Zbl 0910.62024
[24] French, K.; Schwert, W.; Stambaugh, R., Expected Stock Returns and Volatility, Journal of Financial Economics, 19, 3-29 (1987); · doi:10.1016/0304-405X(87)90026-2
[25] Geweke, J.; Porter-Hudak, S., The Estimation and Application of Long Memory Time Series Models, Journal of Time Series Analysis, 4, 221-38 (1983); · Zbl 0534.62062 · doi:10.1111/j.1467-9892.1983.tb00371.x
[26] Gil-Alana, L. A., Fractional Integration in Daily Stock Market Returns, Review of Financial Economics, 15, 28-48 (2006); · doi:10.1016/j.rfe.2005.02.003
[27] Harris, R., and Sollis, R.. 2003. “Applied Time Series Modeling and Forecasting.” 213-38.;
[28] Harvey, D. I.; Leybourne, S. J.; Newbold, P., Testing the Equality of Prediction Mean Squared Error, International Journal of Forecasting, 13, 28-48 (1997); · doi:10.1016/S0169-2070(96)00719-4
[29] Henry, O. T., Long Memory in Stock Returns. Some International Evidence, Applied Financial Economics, 12, 725-29 (2002); · doi:10.1080/09603100010025733
[30] Hsieh, D. A., Modeling Heteroskedasticity in Daily Foreign Exchange Rates, Journal of Business and Economic Statistics, 7, 307-17 (1989);
[31] Lambert, P., and Laurent, S.. 2001. “Modeling Financial Time Series Using GARCH-Type Models and a Skewed Student Density.” Mimeo, Universite de Liege.;
[32] Laurent, S.; Peters, J. P., G@RCH 2.2: An OX Package for Estimating and Forecasting Various ARCH Models, Journal of Economic Surveys, 16, 447-85 (2002); · doi:10.1111/1467-6419.00174
[33] Lo, A.; Mackinlay, A. C., An Econometric Analysis of Nonsynchronous Trading, Journal of Econometrics, 40, 203-38 (1990); · Zbl 0712.62102 · doi:10.1016/0304-4076(89)90083-3
[34] Nelson, D. B., Conditional Heteroskedasticity in Asset Returns: A New Approach, Econometrica, 59, 347-70 (1991); · Zbl 0722.62069 · doi:10.2307/2938260
[35] Pagan, A., The Econometrics of Financial Markets, Journal of Empirical Finance, 3, 15-102 (1996); · doi:10.1016/0927-5398(95)00020-8
[36] Palm, F. C.; Maddala, G.; Rao, C., Handbook of Statistics, 209-40 (1996);
[37] Palm, F. C.; Vlaar, P. J. G., Simple Diagnostics Procedure for Modeling Financial Time Series, Allgemeines Statistisches Archiv, 81, 85-101 (1997);
[38] Robinson, P. M., Testing for Strong Serial Correlation and Dynamic Conditional Heteroskedasticity in Multiple Regressions, Journal of Econometrics, 47, 67-84 (1991); · Zbl 0734.62070 · doi:10.1016/0304-4076(91)90078-R
[39] Robinson, P. M., and Henry, M.. 1998. “Long and Short Memory Conditional Heteroscedasticity in Estimating the Memory Parameter of Levels.” Discussion paper STIDERG Econometrics EM/98/357, London School of Economics and Political Science.;
[40] Sadique, S.; Silvapulle, P., Long-Term Memory in Stock Market Returns. International Evidence, International Journal of Finance and Economics, 6, 59-67 (2001); · doi:10.1002/ijfe.143
[41] Scholes, M.; Williams, J., Estimating Betas from Nonsynchronous Data, Journal of Financial Economics, 5, 309-28 (1977); · doi:10.1016/0304-405X(77)90041-1
[42] Tolvi, J., Long Memory and Outliers in Stock Market Returns, Applied Financial Economics, 13, 495-502 (2003); · doi:10.1080/09603100210161983
[43] Weiss, A. A., Asymptotic Theory for ARCH Models: Estimation and Testing, Econometric Theory, 2, 107-31 (1986); · doi:10.1017/S0266466600011397
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