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.
KeywordsStock Market Independent Component Analysis Independent Component Analysis Blind Source Separation Nonlinear Distortion
Unable to display preview. Download preview PDF.
- 4.Granovetter, M.: Business groups. In: Handbook of Economic Sociology, ch. 18, Princeton University Press, Princeton (1994)Google Scholar
- 5.Ho, R.Y., Strange, R., Piesse, J.: The structural and institutional features of the Hong Kong stock market: Implications for asset pricing. Research Paper 027, The Management Centre Research Papers, King’s College London (2004)Google Scholar
- 7.Jutten, C., Karhunen, J.: Advances in nonlinear blind source separation. In: Proc. ICA 2003, pp. 245–256 (2003); Invited paper in the special session on nonlinear ICA and BSS Google Scholar
- 8.Khanna, T., Rivkin, J.W.: Interorganizational ties and business group boundaries: Evidence from an emerging economy. Organization Science (forthcoming, 2006)Google Scholar
- 11.Shimizu, S., Hoyer, P.O., Hyvärinen, A., Kerminen, A.J.: A linear non-Gaussian acyclic model for causal discovery. Journal of Machine Learning Research (submitted, 2006)Google Scholar
- 15.Zhang, K., Chan, L.W.: Nonlinear ICA with limited nonlinearity. Technical report, The Chinese Univerity of Hong Kong (2006) (to be available soon)Google Scholar