Applications Of Fractal Methods In Financial Time Series Analysis

The volatility,change trend and risk measurement of financial markets have been paid extensive attention by scholars,investors and policymakers.Influenced by various factors,the fluctuation of a financial market usually presents nonlinear dynamic characteristics.It is hard to describe the complexity of a financial market for the traditional linear method.Fractal theory and methods can better reveal the features of financial time series.In this thesis,we firstly use fractal analysis theory and fractal interpolation method to establish a statistical prediction model,and to fit and predict the every 5-minute high frequency series of Shanghai Composite Index(SCI).Then we build a mixed model combined the fractal interpolation model with support vector machine algorithm to analyze and forecast the daily closing data of SCI.The empirical results show that the prediction model of this thesis is better than the other two forecasting models.The content of this paper is summarized as follows:Firstly,we introduce the related knowledge of fractal analysis theory and fractal interpolation method,mainly including fractal market theory,fractal dimension,rescaled range analysis(R/S),fractal interpolation and support vector machine algorithm.Secondly,this thesis proposes a new method of calculating vertical scaling factors of the fractal interpolation iterated function system,constructs an improved fractal interpolation model,the model is used to fit and forecast every 5-minute high frequency series of Shanghai Composite Index.The empirical results show good fitting and forecasting effect.In addition,comparing the improved model with other models,the improved model has higher accuracy.Finally,combining the support vector machine algorithm with the fractal interpolation model to establish a mixed forecasting model,the vertical scaling factors of fractal interpolation in mixed model are calculated by the new method,using mixed model to analyze and predict closing data of Shanghai Composite Index.Then compare the mixed model's prediction error with other models',the results show that the mixed model has less prediction error.