Independent component analysis for financial time series

The recent work in the author's research group on using independent component analysis (ICA) for the analysis and prediction of financial time series is reviewed. ICA belongs to the group of linear transform methods, with the goal to make a transform from the observed signals into a signal space in which the signals are statistically independent. Sometimes independence can be attained, especially in blind source separation in which the observed signals are assumed to be linear mixtures of independent source components. 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 produces useful component signals whose dependence is reduced, and that are nonGaussian with a density allowing sparse coding. The ICA transformation is also related to the temporal structure of the found signals as measured by Kolmogorov complexity or its approximations. The signals are structured and hence may be easier to interpret and predict. After discussing the ICA criterion within the context of linear signal transforms, the FastICA algorithm is reviewed. It is a computationally efficient method for finding a subset or all of the component signals. Then, two financial applications are covered: decomposition of parallel financial time series of weekly sales into basic factors, and prediction of mixture time series by linear combinations of predictions on the ICA components.