Financial Time Series Multi-level Fractal Analysis In The Information-mining Applications

This thesis studies how to mine the implicit structural information such as multiple trend, cycles, seasonality, noise as well as patterns from financial time series based on multilevel fractal analysis.Firstly, three multilevel fractal decomposition methods, including Wavelet Multiresolution Analysis, Empirical Mode Decomposition (EMD) and Zig-Zag Decomposition, are introduced to decompose the original financial time series into multilevel fractal subsequences. By comparison it can be found that, Wavelet approach generates a collection of subsequences with multiple time scale feature; EMD yields specific number of subsequences, each of which contains only a single intrinsic swing mode and has a clear physical sense; Zig-Zag Decomposition is capable of capturing important inflexions in each subsequence.Afterwards, this thesis advances a realization approach of Multilevel Structural Time Series (MSTS) models to extract the structural information, i.e. multiple trends, cycles, seasonality and noises, from financial time series based on multilevel fractal decomposition and structural time series model. This realization takes three major steps: First, an original time series is decomposed into multilevel subsequences using Wavelet Multiresolution Analysis; then all the pieces of structural information on each level are extracted from the subsequence via EMD and formed into state-space models; finally, the variable parameters are estimated adaptively by Kalman filter. The empirical studies on the four international stock indices confirm the capabilities of MSTS models for extracting multilevel structural information of financial time series, as well as show the good out-of-sample forecasting performance.Lastly, this thesis proposes Multilevel Pattern Matching (MPM) model by combining the multilevel fractal decomposition and pattern matching to mine the similar patterns in sequence or between sequences. The MPM model uses Zig-Zag approach to decompose the original financial time series into multilevel fractal sequences, and then performs the pattern matching hierarchically. On each level, a rough matching base on trends similarity and a precise matching based on the Euclidean distance of price change rate will be executed orderly. The results of experiments indicate that the matched candidate from MPM model is quite similar with the sample both at long trend and short fluctuation, which is coincident with people's cognitive process.