Wavelet-based long memory study in american and chinese stock market

A long memory analysis based on wavelet transform of financial data is proposed. This method treats return series and volatility series in stock market as a fractional differenced noise process, and analyzes it by MODWT(maximal overlap discrete wavelet transform). The result shows there is a lineal relationship between wavelet variance logarithm and scale logarithm, so a long memory parameter can be obtained by using the relationship. This method is proved to be effective and feasible by analyzing the return series and volatility series of composite indexes of American and Chinese stock market.