Research on financial signals' fractal characteristics based on wavelet theory and correlated dimension model

Efficient market theory is always the cornerstone to establish and study modern financial theory. But its explanatory power for financial markets is weakening with the appearing of financial crisis. Rapid development of nonlinear science such as wavelet analysis and fractal theory provides new theoretical tools for groping financial market. Taking intraday closing price of soybean futures on Dalian Commodity Exchange in 2008 for example, the paper uses wavelet analysis to decompose financial signals into low-frequency and high-frequency parts, and then uses fractal dimension theory to calculate fractal correlated dimensions of low-frequency and high-frequency signals respectively. Results show that structures of signals´ low-frequency and high-frequency parts are different, and the long-term memory abilities are different either. Thus, to establish models for low-frequency part and high-frequency part respectively can improve the model´s precision when modeling with financial signals.