Nonlinear Combination of Financial Forecast with Genetic Algorithm

Ozun, Alper and Cifter, Atilla (2007): Nonlinear Combination of Financial Forecast with Genetic Algorithm.

Abstract

Complexity in the financial markets requires intelligent forecasting models for return volatility. In this paper, historical simulation, GARCH, GARCH with skewed student-t distribution and asymmetric normal mixture GRJ-GARCH models are combined with Extreme Value Theory Hill by using artificial neural networks with genetic algorithm as the combination platform. By employing daily closing values of the Istanbul Stock Exchange from 01/10/1996 to 11/07/2006, Kupiec and Christoffersen tests as the back-testing mechanisms are performed for forecast comparison of the models. Empirical findings show that the fat-tails are more properly captured by the combination of GARCH with skewed student-t distribution and Extreme Value Theory Hill. Modeling return volatility in the emerging markets needs “intelligent” combinations of Value-at-Risk models to capture the extreme movements in the markets rather than individual model forecast.

• Item Type: MPRA Paper
• Institution: Marmara University
• Language: English
• Keywords: Forecast combination; Artificial neural networks; GARCH models; Extreme value theory; Christoffersen test
• Subjects: G - Financial Economics > G0 - General; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models

References

Alexander, C. and Lazar, E., (2005) “The Equity Index Skew, Market Crashes and Asymmetric Normal Mixture Garch,” ISMA Center, Mimeo

Alexander, C. and Lazar, E., (2006) “Normal Mixture GARCH(1,1):Applications to Exchange Rate Modeling,” Journal of Applied Econometrics 21(3), pp.307-336.

Baillie, R. T. and Bollerslev, T., (1989) “The Message in Daily Exchange Rates: A Conditional-Variance Tale,” Journal of Business and Economic Statistics, 7, pp.297-305

Bates, D. S., (1991) “The Crash of ’87: Was It Expected? The Evidence from Options Markets,” Journal of Finance, 46, pp.1009-1044

Bekaert, G., and Wu, G., (2000) “Asymmetric Volatility and Risk Equity Markets,” The Review of Financial Studies, 13(1), pp.1-42

Bollerslev, T., (1986) “Generalized Autoregressive Conditional Heteroskedasticity,” Journal of Econometrics, 31, pp.307–327.

Bollerslev, T. (1987) “A Conditional Heteroskedasticity Time Series Model for Speculative Prices and Rates of Return,” Review of Economic and Statistics. 69, pp.542-547

Bollerslev, T., Chou, R.Y. and Kroner, K.F., (1992) “ARCH Modeling in Finance: A Review of the Theory and Empirical Evidence,” Journal of Economics and Statistics, 69, pp.542-547

Bollerslev, T. and Woolridge, J. M. (1992) “Quasi-maximum Likelihood Estmation Inference in Dynamic Models with Time-varying Covariances,” Econometric Theory, 11, pp.143-172

Chang, Lo, Chen and Huang (2006) “Journal of Information & Optimization Sciences,” 27 (2006), No. 3, pp. 615–628

Christoffersen, P.F. (1998) “Evaluating Interval Forecasts,” International Economic Review, 39, pp.841-862.

Christoffersen, P. F., and Jacobs, K., (2004) “Which Garch Model for Option Valuation?,” Management Science, 50, pp.1204-1221

Christoffersen, P. F., Heston, S. and Jacobs, K. (2004) “Option Valuation with Conditional Skewness,” Forthcoming in The Journal of Econometrics.

Dickey, D. A., Fuller, W.A. (1981) “Likelihood ratio statistics for autoregressive time series with a unit root,” Econometrica, 49, pp.1057–1072.

Doornik, J.A. (1999) “An Object Oriented Programming Language,” Timberlake Consultant, Third Ed.

Engle, F., (1982) “Autoregressive Conditional Heteroscedasticity with Estimate of the Variance of United Kingdom Inflation,” Econometrica, 50, pp.987-1007

Fernandez, Carmen, and Mark Stell. (1998) “On Bayesian Modeling of fat tails and skewness,” Journal of the American Statistical Association, 93, pp.359-371

Glosten, L. R., Jagahannathan, R., and Runkle, D. E., (1993) “On the Relationship between the Expected Value and The Volatility of the Nominal Excess Return on Stocks,” Journal of Finance, 48, pp.1779-1801

Hecht-Nielsen.R (1990) Neurocomputing, Wokingham, England: Addison-Wesley Publishing Company Ltd.

Hill, B. M. (1975) “A simple general approach to inference about the tail of a distribution,” Annals of Statistics, 3, 1163-1174.

Holland, J. (1965) “Universal spaces: A basis for studies of adaptation,” In Automata Theory. Caianiello, E. R. (ed.) Academic Press. 218-30.

Hsieh, D. A. (1989) “Modeling Heteroskedasticity in Daily Foreign Exchange Rates,” Journal of Business and Economic Statistics, 7, pp.307-317

Kupiec, P. H. (1995) “Techniques for Verifying the Accuracy of Risk Measurement Models,” Journal of Derivatives, winter, pp. 73-84

Liu (2005) “Value-at-Risk Model Combination Using Artificial Neural Networks,” Emory University Working Paper Series.

Maasoumi, E., A. Khotanzad, and A. Abaye (1994) “Artificial Neural Networks for Some Macroeconomic Series : A First Report,” Econometric Reviews, 13, No. 1.

McNeil, A. J., (1996) "Estimating The Tails of Loss Severity Distributions Using Extreme Value Theory, Mimeo. ETH Zentrum, Zürich.

McNeil A. J. and Frey, R. (2000) “Estimation of tail-related risk measures for Heteroscedastic Financial time series: An extreme value approach,” Journal of Empirical Finance, 7, 271-300.

Neftci, S., (2000) “Value at Risk Calculations, Extreme Events, and Tail Estimation,” The Journal of Derivatives, Spring 2000.

Ozun, A., (2006) Theoretical Importance of Artificial Neural Networks For The Efficiency of Financial Markets, Proceedings of 5th International Finance Symposium: Integration in the Financial Markets, Vienna University&Marmara University with Cooperation of Istanbul Stock Exchange, 25-26 May, 2006, Istanbul

Palit, AK and Popovic, D. (2000) “Nonlinear Combination of Forecasts Using Artificial Neural Networks, Fuzzy Logic and Neuro-Fuzzy Approach,” FUZZ-IEEE, Vol. 2, pp. 566-571, 2000.

Pagan, A., (1996) “The Econometrics of Financial Markets,” Journal of Empirical Finance, 3, pp.15-102.

Palm, F., (1996) “Garch Models of Volatility”, in Handbook of Statistics, ed. By G.Maddala, and C.Rao, pp.209-240, Elsevier Science, Amsterdam.

Palm, F. and Vlaar, P. JG., (1997) “Simple Diagnostics Procedures for Modeling Financial Time Series,” Allgemeines Statistisches Archiv, 81, pp.85-101

Peters, JP., (2001) Estimating and Forecasting Volatility of Stock Indices Using Asymmetric Garch Models and (Skewed) Student-t Densities, Mimeo, Ecole d’Admin. des Affaires, Unv.of Li`ege.

Rumelhart, D.E. & McClelland, J.L. (1986) “PDP Models and General Issues in Cognitive Science”. In D.E. Rumelhart & J.L. McClelland (Eds.), Parallel Distributed Processing. Vol. 1. Cambridge, MA: MIT Press/Bradford Books.

Saltoğlu, B. (2003) A High Frequency Analysis of Financial Risk and Crisis: An Empirical Study on Turkish Financial Market, Yaylım Publishing, Istanbul

Sarma, M., Thomas, S. and Shah, A. (2001) Selection of Value-at-Risk Models, Mimeo

Shanming Shi, Li D Xu, Bao Liu. (1996) “Application of artificical neural networks to the nonlinear combinmation of forecasts,” Expert Systems,1996,13(3):195-201

Tang, T.L. and Shieh, S. J., (2006) “Long-Memory in Stock Index Futures Markets: A Value-at-Risk Approach,” Phsica A, Vol.366, pp.437-448

White, H. (1994) “Neural Networks,” Econometric Reviews, Vol.13, No.1.

Wu, G., (2001) “The Determinants of Asymmetric Volatility,” The Review of Financial Studies. 14(3), pp.837-859