Volatility Estimation Of Financial High Frequency Data Based On Wavelet Analysis

Estimation of high frequency volatility has been the hot research problem in the domain of data analysis. Integrated volatility of asset return is estimated by maximum overlap discrete wavelet transform. The different wavelet functions are chose to estimate integrated volatility of Shanghai and Shenzhen 300 index, and relative error statistics is calculated. The results show that integrated volatilities based on different wavelets have no significant difference. The estimated accuracy is improved with the increasing of sampling frequency. There is the obvious linear relationship between logarithmic scale and logarithmic volatilities. The volatility decreases little by little with the scale increasing.Integrated volatility of asset return is estimated by wavelet method. For comparing the influence of different sampling frequency to volatility estimation, the relative error statistic is constructed. Different wavelet functions are chosen to estimate integrated volatility for the data from different time intervals. The results demonstrate that the higher sampling frequency the estimation error is smaller.We analyse the relationship between the two different market revenue in the different scales by wavelet transform. The empirical study shows that large scale is greater than the small scale in the correlation. It could eliminate Calendar Effect of stock markets returns of Shanghai and Shenzhen using multi-resolution analysis. The research outcome indicated that the two sequence correlation is gradually decreased with the increase of the lag.