Extensions of ICA for Causality Discovery in the Hong Kong Stock Market

Recently independent component analysis (ICA) has been proposed for discovery of linear, non-Gaussian, and acyclic causal models (LiNGAM). As in practice the LiNGAM assumption usually does not exactly hold, in this paper we propose some methods to perform causality discovery even when LiNGAM is violated. The first method is ICA with a sparse separation matrix. By incorporating a suitable penalty term, the separation matrix produced by this method tends to satisfy the LiNGAM assumption. The other two methods are proposed to tackle nonlinearity in the data generation procedure, which violates the LiNGAM assumption. In the second method, the post-nonlinear mixing ICA model is exploited to do causality discovery when the nonlinearity is component-wise. The third method is proposed for the case where the nonlinear distortion in data generation is of arbitrary form, but smooth and weak. The separation system for such data is a linear transformation coupled with a nonlinear one, and the nonlinear one is as weak as possible such that it can be neglected when performing causality discovery. The linear causal relations in the data are then revealed. The proposed methods are applied to discover the causal relations in the Hong Kong stock market, and the last method works very well. The resulting causal diagram shows some interesting information in the stock market.