Forecast of Stock Index Volatility Using Grey GARCH-Type Models

ABSTRACT

This paper integrated the genetic algorithm (GA) and grey forecasting (GM(1,1)) model into three GARCH-type models and proposed the GAGM-GARCH-type models. The 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 in parameters estimation of GM (1,1) model, the 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 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.

Keywords:

Genetic algorithm, Grey GARCH-type models, Volatility forecasting, ARCH model, GM-GARCH-Type Models, Optimal grey parameters.