|Tytuł||Multivariate cumulants in features selection and outlier detection for financial data analysis|
|Słowa kluczowe||Financial crisis detection, Financial data analysis, Multivariate cumulants, Mutual information, Non-Gaussian joint distributions, t-Student copula|
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 non-Gaussian distributes and a crisis finally occurs. For this reason, we use the decomposition higher order cumulants tensors to perform features selection and outlier detection on multivariate data. A target data subset is non-Gaussian, while ordinary data are multivariate Gaussian. Such target subset is assumed to have higher order dependencies, modelled by the t-Student copula. These higher order dependencies introduce an extra term to the Kullback-Leibler divergence, that measures the mutual information of data. Through experiment we show the advantage of our outlier detection method over the well known Reed-Xiaoli (RX) Detector, both on artificial and financial data, while detecting non-Gaussian distributed increments of shares prices during a crisis.