The Properties of Volatility of Returns in Different Scales

Many empirical studies on the properties of different volatility models dedicate to find the best way to measure the volatility. In this paper, we specify and estimate volatility models for the jointed dynamics of different scales of returns by intra-daily high frequency data. As absolute return and high-low return are non-negative series, we adopt a multiplicative error model jointed with expanded GARCH model. For Shanghai composite index, both absolute return and high-low return are affected by asymmetric variables but with different extent. The results show that the inclusion of different scales of returns in estimating models will enhance the explanatory power in final estimation. Furthermore, we adopt ARFIMA process to model the long memory in volatility, the results show the existence of long memory in volatility of returns in Chinese stock market.