Forecast of Stock Index Volatility Using Grey GARCH-Type Models

This paper integrated genetic algorithm (GA) and grey forecasting (GM(1,1)) model into three GARCH- type models and proposed GAGM-GARCH-type models. GM(1,1) model was used to modify the error terms of the GARCH-type models to improve the volatility forecasting performance of the traditional GARCH-type models. Meanwhile, as for the shortcomings on parameters estimation of GM(1,1) model, GA was adopted to find the optimal grey parameters of GM(1,1) model. Using the stock data of China stock market, the paper compared the performance of the GAGAM-GARCH-type models in out-of-sample volatility forecasting with those of the GM-GARCH-type, RGM-GARCH-type, and GARCH-type models. It is indicated by the values of the evaluation criteria that the GAGM-GARCH-type models have better volatility forecasting performances relative to the other three types of GARCH-type models.

[1]  Daniel B. Nelson.  CONDITIONAL HETEROSKEDASTICITY IN ASSET RETURNS: A NEW APPROACH , 1991 .

[2]  Li-Chang Hsu,et al.  A genetic algorithm based nonlinear grey Bernoulli model for output forecasting in integrated circuit industry , 2010, Expert Syst. Appl..

[3]  Sheng-Tzong Cheng,et al.  Artificial neural network model of the hybrid EGARCH volatility of the Taiwan stock index option prices , 2008 .

[4]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[5]  L. Glosten,et al.  On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks , 1993 .

[6]  Sheng-Tzong Cheng,et al.  New hybrid methodology for stock volatility prediction , 2009, Expert Syst. Appl..

[7]  Yi-Hsien Wang,et al.  Nonlinear neural network forecasting model for stock index option price: Hybrid GJR-GARCH approach , 2009, Expert Syst. Appl..

[8]  Ping Xue-liang,et al.  Grey System Theory and Its Applications in Engineering , 2003 .

[9]  Vipul Jain,et al.  A grey approach for forecasting in a supply chain during intermittentdisruptions , 2013, Eng. Appl. Artif. Intell..

[10]  Niccolò Gordini,et al.  A genetic algorithm approach for SMEs bankruptcy prediction: Empirical evidence from Italy , 2014, Expert Syst. Appl..

[11]  Lee-Ing Tong,et al.  Forecasting nonlinear time series of energy consumption using a hybrid dynamic model , 2012 .

[12]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .