Wavelet Methods For Financial Time Series Analysis

Wavelet analysis theory is one of the topics widely discussed and studied in the communities of science and engineering currently. It not only includes rich knowledge in mathematics, but also has wide latent applications. Based on the Fourier analysis, wavelet analysis is the great achievement of harmonic analysis in the past half century. Its basis idea is to express a general function by the linear combination of an orthonormal wavelet base. Wavelet analysis with the core of wavelet transformation has become an important tool in many engineering subjects because the favorable local properties of wavelet transformation in time-domain and frequency-domain can adjust the time-frequency window automatically to satisfy the needs of analysis in practice.In this thesis, the basic theory in wavelet analysis and financial time series is systemically discussed firstly. Then based on wavelet decomposition and the application of wavelet to the elimination of signal noise, combined with time series model for prediction, one prediction model with the reduced signal noise is presented, and compared with the original prediction model. The results say that prediction with the data which has been reduced noise from leads to a smaller relative error and a higher precision than that does directly with the original data. Then wavelet transforms and multiresolution analysis are employed to detect the singular point in financial time series with the real data of 100 stocks. And the reasonable explanation of that singular point is given with the incorporation of background in practice.Finally the theory that wavelet can recognize the useful signal from that with noise is applied to forecast the development of financial time series in a short time. And the real stock data is used to do simulations. The results show that this method is efficient.