|Tytuł||Multivariate cumulants in features selection and outlier detection for financial data analysis|
Analogies of financial models with complex physical systems yield two stage models where either financial data variation is limited or an analogy to the phase transition occurs. In second case variation of financial data is large and a crisis finally occurs. This scenario appears in real life financial data processing, where the Central Limit Theorem roughly holds in general but breaks for unusual events such as crises. In this paper, we use the High Order Singular Value Decomposition (HOSVD) of higher order cumulant tensors to perform features selection and outlier detection on multivariate data. A target data subset are non-Gaussian, and ordinary data are modelled by a Gaussian multivariate distribution. The non-Gaussian target subset is assumed to have higher order dependencies, modelled by the t-Student copula. We collect information about higher order dependencies by means of the 4th cumulant's tensor. Such approach is more general in comparison to recently introduced approach that uses 3rd cumulant's tensor. Moreover, through experiment we show the advantage of our outlier detection method over the well known Reed-Xiaoli (RX) Detector. We demonstrate finally, that our method has an advantage for detecting outliers being non-Gaussian distributed increments of shares prices during a crisis. Hence, due to these non-Gaussian outliers, we acknowledge the two stage model of multivariate financial data inspired by the analogy between financial models and complex physical systems.