Independent Component Analysis For Industry Index Of China

Traditional researches focus on the characters of the time series itself which are used to interpret and predict. In this paper, we want to analysis the time series with a different angle by through independent component analysis. We analysis the factors affecting in order to explore, interpret and predict the time series. Independent component analysis (ICA) or blind source separation is a modern signal processing technique to multivariate financial time series such as a portfolio of stocks. The key idea of ICA is to map the observed multivariate time series into a new space of statistically independent components (ICs). Sometimes independence can be attained, Then the goal of ICA is to invert the unknown mixing operation. Even when independence is not possible, as is often the case in financial time series, the ICA transformation tries to produce useful component signals whose dependence is reduced. The signals are structured and hence may be easier to interpret and predict.The FastICA algorithm is a computationally efficient method for finding a subset or all of the component signals. We apply FastICA to four years of daily returns of the 5 largest Chinese industry indexes. The results indicate that the estimated ICs fall into two categories, (l) sudden and large shocks responsible for the major changes in the stock prices. (2) mild smaller fluctuations (contributing little to the overall level of the stock indexes),such as CPI, periodicity cur and so on. We show that the overall stock indexes can be re-constructed surprisingly well by using some thresholded weighted ICs.We try to predict the each IC separately by first going to the ICA space, doing the prediction there, and then transforming back to the original time series. In contrast, AR model is used to predict the original time series directly. Then the results are compared.