Linear And Non-linear Prediction Of Time-series Based On ICA Method

As to the analysis and prediction of financial time series,the Auto-Regressive and Moving Average(ARMA)model and the Auto-Regressive Integrated Moving Average(ARIMA)model are widely used as classical methods up to now.Meanwhile,the Independent Component Analysis(ICA)method is able to recreate the original signals from a set of observed signals,and has been applied to many engineering areas,such as financial time series,wireless communication,signal procession and biological engineering etc.In this essay,the combination of the ICA method and the ARMA/TAR models being applied in the analysis and prediction of financial time series are seriously discussed and addressed,which are described in the following three parts:1.The basic theory of the ICA method and the ARMA/TAR models are systematically introduced.Some typical characteristics of ICA are analyzed.And several classical objective functions and optimization algorithms in independent component analysis are summarized.2.By proofing that ICA is able to extract and separate the self-correlation functions more precisely,the value of applying this method to ARMA/ARIMA models are demonstrated,because the accuracy of the predication is enhanced effectively by integrating these two algorithms.3.As some inevitable shortcomings and limitations in linear models,the Threshold Auto-Regressive(TAR)model is exploited by integrating it with the ICA method to invent a brand new model: ICA-TAR,aiming for promoting the prediction results.Moreover,ICA-ARTAR model is constructed to prove the whole effect further.Here the experiment has employed the real financial time series data in China: Shanghai(securities)Composite Index,Shenzhen(securities)Composite Index and the Growth Enterprise Market Index.As for the methods of simulation,both one-time mixed computation and step iteration are mainly used to predict the future values for related time series.In the end,the results of the linear and nonlinear configuration are displayed respectively and compared carefully.Some conclusions are therefore derived and discussed.Considering the fact that real financial index time series are normally non-stationary processes,the presumption of either linear/non-linear method or parameter/non-parameter models are hardly satisfied in the long run,which is the crucial handicap to the prediction.However in the short run and at some stage,these methods and models are truly effective.