The Volatility of Return, Trading Volume and Amount in Different Scales

In this paper, we use different scales to examine the volatility of return, volume and trading amount by intra-daily high frequency data. Besides the conventional measures of the volatility that make use of the unobserved variance or standard deviation of its return, another two different types of return - absolute return, high-low return are introduced. Two models are considered. One is an ARMA model which is applied to stationary series. The other is a MEM model called multiplicative error model jointed with expanded GARCH model. For Shanghai composite index, we find the relationship between these returns, and observe that both absolute return and high-low return are affected by asymmetric variables but with different extent. The estimation results of trading volume and amount show that their volatilities have significant cluster and persistence.