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A Hybrid Fuzzy GJR-GARCH Modeling Approach for Stock Market Volatility Forecasting

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Advances in Financial Risk Management

Abstract

Accurately measuring and forecasting stock market volatility plays a crucial role for asset and derivative pricing, hedge strategies, portfolio allocation and risk management. Since the 1987 stock market crash, academics, practitioners and regulators have investigated the development of financial time series models with changing variance over time in order to avoid huge investment losses due to their exposure to unexpected market movements (Allen and Morzuch, 2006, Carvalho et al., 2005, Lin et al., 2012). Indeed, volatility, as a measure of financial security prices fluctuation around its expected value, is one of the primary inputs in decision making processes under uncertainty, justifying its growing interest in the financial and economic literature (Kapetanios et al., 2006, Lux and Kaizoji, 2007).

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References

  • Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–23.

    Article  Google Scholar 

  • Allen, P. G. and Morzuch, B. J. (2006). Twenty-five years of progress, problems, and conflicting evidence in econometric forecasting. What about the next 25 years? International Journal of Forecasting, 22, 475–92.

    Article  Google Scholar 

  • Bildirici, M. and Ersin, Ö. O. (2009). Improving forecasts of GARCH family models with the artificial neural networks: an application to the daily returns in Istanbul Stock Market Exchange. Expert Systems with Applications, 36, 7355–62.

    Article  Google Scholar 

  • Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 31, 307–27.

    Article  Google Scholar 

  • Brailsford, T. J. and Faff, R. W. (1996). An evaluation of volatility forecasting techniques. Journal of Banking and Finance, 20, 419–38.

    Article  Google Scholar 

  • Caretta, P. S., de Barba, F. G., Vieira, K. M. and Casarin, F. (2011). Previsï£io da volatilidade intradiï£iria: Anï£ilise das distribuiï£iï£ies alternativas. Brazilian Review of Finance, 9, 209–26.

    Google Scholar 

  • Carvalho, M. C., Freire, M. A., Medeiros, M. C. and Souza, L. R. (2005). Modeling and forecasting the volatility of Brazilian asset returns: a realized variance approach. Brazilian Review of Finance, 4, 321–43.

    Google Scholar 

  • Chang, J., Wei, L. and Cheng, C. (2011). A hybrid ANFIS model based on AR and volatility for TAIEX forecasting. Applied Soft Computing, 11, 1388–95.

    Article  Google Scholar 

  • Chiu, S. L. (1994). Fuzzy model identification based on cluster estimation. Journal of Intelligent Fuzzy Systems, 2, 267–78.

    Google Scholar 

  • Clerc, M. and Kennedy, J. (2002). The particle swarm explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, 6, 58–73.

    Article  Google Scholar 

  • Coelho, L. S. and Santos, A. A. P. (2011). A RBF neural network model with GARCH errors: application to electricity price forecasting. Electric Power Systems Research, 81, 74–83.

    Article  Google Scholar 

  • Das, S., Abraham, A., Chakraborty, U. K. and Konar, A. (2009). Differential evolution using a neighborhood based mutation operator. IEEE Transactions on Evolutionary Computation, 13, 526–53

    Article  Google Scholar 

  • Das, S. and Suganthan, P. N. (2011). Differential evolution: a survey of the state-of-the-art. IEEE Transactions on Evolutionary Computation, 15, 4–31.

    Article  Google Scholar 

  • Diebold, F. X. and Mariano, R. S. (1995). Comparing predictive accuracy. Journal of Business and Economic Statistics, 13, 253–65.

    Google Scholar 

  • Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987–1007.

    Article  Google Scholar 

  • Fama, E. F. (1965). The behavior of stock market price. Journal of Business, 38, 34–105.

    Article  Google Scholar 

  • Fouque, J., Papanicolaou, G. and Sircar, R. (2000). Mean reverting stochastic volatility. International Journal of Theoretical and Applied Finance, 3 101–42.

    Article  Google Scholar 

  • Geng, L. and Ma, J. (2008). TSK fuzzy inference system based GARCH model for forecasting exchange rate volatility. Annals of the Fifth International Conference on Fuzzy Systems and Knowledge Discovery, 103–7, Shandong, China.

    Google Scholar 

  • Glosten, L. R., Jagannathan, R. and Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance, 48, 1779–801.

    Article  Google Scholar 

  • Hajizadeh, E., Seifi, A., Fazel Zarandi, M. H. and Turksen, B. (2012). A hybrid modeling approach for forecasting the volatility of S&P 500 index return. Expert Systems with Applications, 39, 431–6.

    Article  Google Scholar 

  • Hamid, S. A. and Iqbal, Z. (2004). Using neural networks for forecasting volatility of S&P 500. Journal of Business Research, 57, 1116–25.

    Article  Google Scholar 

  • Han, H. and Park, J. Y. (2008). Time series properties of ARCH processes with persistent covariates. Journal of Econometrics, 146, 275–92.

    Article  Google Scholar 

  • Hansen, P. R. and Lunde, A. (2006). Realized variance and market microstructure noise (with discussion). Journal of Business and Economic Statistics, 24, 127–61.

    Article  Google Scholar 

  • Haofei, Z., Guoping, X., Fangting, Y. and Han, Y. (2007). A neural network model based on the multi-stage optimization approach for short-term food pricing forecasting in China. Expert Systems with Applications, 33, 347–56.

    Article  Google Scholar 

  • Haykin, S. (2001). Adaptive Filter Theory, 4th edn. Prentice Hall, Englewood Cliffs, New Jersey, 989.

    Google Scholar 

  • Helin, T. and Koivisto, H. (2011). The GARCH-Fuzzy Density method for density forecasting. Applied Soft Computing, 11, 4212–25.

    Article  Google Scholar 

  • Hung, J. (2009a). A fuzzy asymmetric GARCH model applied to stock markets. Information Sciences, 179, 3930–43.

    Article  Google Scholar 

  • Hung, J. (2009b). A fuzzy GARCH model applied to stock market scenario using a genetic algorithm. Expert Systems with Applications, 36, 11710–17.

    Article  Google Scholar 

  • Hung, J. (2011a). Adaptive Fuzzy-GARCH model applied to forecasting the volatility of stock markets using particle swarm optimization. Information Sciences, 181, 4673–83.

    Article  Google Scholar 

  • Hung, J. (2011b). Applying a combined fuzzy systems and GARCH model to adaptively forecast stock market volatility. Applied Soft Computing, 11, 3938–45.

    Article  Google Scholar 

  • Ji, Y., Massanari, R. M., Ager, J., Yen, J., Miller, R. E. and Ying, H. (2007). A fuzzy logic-based computational recognition-primed decision model. Information Sciences, 177, 4338–53.

    Article  Google Scholar 

  • Kapetanios, G., Labhard, V. and Price, S. (2006). Forecasting using predictive likelihood model averaging. Economic Letters, 91, 373–9.

    Article  Google Scholar 

  • Lin, E. M. H., Chen, C. W. S. and Gerlach, R. (2012). Forecasting volatility with asymmetric smooth transition dynamic range models. International Journal of Forecasting, 28, 384–99.

    Article  Google Scholar 

  • Liu, H. and Hung, J. (2010). Forecasting S&P-100 stock index volatility: the role of volatility asymmetry and distributional assumption in GARCH models. Expert Systems with Applications, 37, 4928–34.

    Article  Google Scholar 

  • Luna, I. and Ballini, R. (2012). Adaptive fuzzy system to forecast financial time series volatility. Journal of Intelligent & Fuzzy Systems, 23, 27–38.

    Google Scholar 

  • Lux, T. and Kaizoji, T. (2007). Forecasting volatility and volume in the Tokyo stock market: long memory, fractality and regime switching. Journal of Economic Dynamics and Control, 31, 1808–43.

    Article  Google Scholar 

  • Martens, M., van Dijk, D. and de Potter, M. (2009). Forecasting S&P 500 volatility: long memory, level shifts, leverage effects, day-of-the-week seasonality, and macroeconomic announcements. International Journal of Forecasting, 25, 282–303.

    Article  Google Scholar 

  • Morgan, J. P. (1996) Risk Metrics: Technical Document, 4th edn. Morgan Guaranty Trust Company, New York, 74.

    Google Scholar 

  • Nelson, D. B. (1991). Conditional heteroscedasticity in asset returns: a new approach. Econometrica, 59, 347–70.

    Article  Google Scholar 

  • Ng, H. G. and McAleer, M. (2004). Recursive modeling of symmetric and asymmetric volatility in the presence of extreme observations. International Journal of Forecasting, 20, 115–29.

    Article  Google Scholar 

  • Popov, A. A. and Bykhanov, K. V. (2005). Modeling volatility of time series using fuzzy GARCH models. Annals of the 9th Russian-Korean International Symposium on Science and Technology, 687–92, Novosibirsk, Russia.

    Google Scholar 

  • Price, K. V. and Rönkkönen, J. T. (2006). Comparing the unimodal scaling performance of global and local selection in a mutationonly differential evolution algorithm. Annals of the IEEE Congress of Evolutionary Computation, 2034–41, Vancouver, Canada.

    Google Scholar 

  • Racine, J. (2001). On the nonlinear predictability of stock returns using financial and economic variables. Journal of Business and Economic Statistics, 19, 380–2.

    Article  Google Scholar 

  • Rahnamayan, S., Tizhoosh, H. R. and Salama, M. A. (2008). Opposition-based differential evolution. IEEE Transactions on Evolutionary Computation, 12, 64–79.

    Article  Google Scholar 

  • Savran, S. (2007). An adaptive recurrent fuzzy system for nonlinear identification. Applied Soft Computing, 7, 593–600.

    Article  Google Scholar 

  • Schwarz, G. (1978). Estimating the dimension of model. The Annuals of Statistics, 6, 461–4.

    Article  Google Scholar 

  • Storn, R. and Price, K. V. (1997). Differential evolution — a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11, 341–59.

    Article  Google Scholar 

  • Taylor, J. W. (2004). Volatility forecasting with smooth transition exponential smoothing. International Journal of Forecasting, 20, 273–86.

    Article  Google Scholar 

  • Thavaneswaran, A., Appadoo, S. S. and Paseka, A. (2009). Weighted possibilistic moments of fuzzy numbers with applications to GARCH modeling and option pricing. Mathematical and Computer Modeling, 49, 352–68.

    Article  Google Scholar 

  • Tino, P., Schittenkopf, C. and Dorffner, G. (2001). Financial volatility trading using recurrent neural networks. IEEE Transactions on Neural Networks, 12, 865–74.

    Article  Google Scholar 

  • Tseng, C., Cheng, S., Wang, Y. and Peng, J. (2008). Artificial neural network model of the hybrid EGARCH volatility of the Taiwan stock index option prices. Physica A: Statistical Mechanisms and Its Applications, 387, 3192–200.

    Article  Google Scholar 

  • Tung, W. L. and Quek, C. (2011). Financial volatility trading using a self-organising neural-fuzzy semantic network and option straddle-based approach. Expert Systems with Applications, 38, 4668–88.

    Article  Google Scholar 

  • Wang, C., Lin, S., Huang, H. and Wu, P. (2012). Using neural network for forecasting TXO price under different volatility models. Expert Systems with Applications, 39, 5025–32.

    Article  Google Scholar 

  • Wang, L. and Mendel, J. M. (1992). Fuzzy basis functions, universal approxima-tion, and orthogonal least-squares learning. IEEE Transactions on Neural Networks, 2, 807–14.

    Article  Google Scholar 

  • Wang, Y. (2009). Nonlinear neural network forecasting model for stock index option price: hybrid GJR-GARCH approach. Expert Systems with Applications, 36, 564–70.

    Article  Google Scholar 

  • Zadeh, L. (2005). Toward a generalized theory of uncertainty (GTU) — an outline. Information Sciences, 172, 1–40.

    Article  Google Scholar 

  • Zhang, J. and Sanderson, A. C. (2003). JADE: adaptive differential evolution with optional external archive. IEEE Transactions on Evolutionary Computation, 13, 945–58.

    Article  Google Scholar 

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© 2013 Leandro Maciel

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Maciel, L. (2013). A Hybrid Fuzzy GJR-GARCH Modeling Approach for Stock Market Volatility Forecasting. In: Batten, J.A., MacKay, P., Wagner, N. (eds) Advances in Financial Risk Management. Palgrave Macmillan, London. https://doi.org/10.1057/9781137025098_11

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