Clustering Conditional Higher Moments with a Model-Based Fuzzy Procedure

A new time series clustering procedure is considered, which allows for heteroskedasticity, non-normality and models non-linearity with a fuzzy approach. Specifically, considering a Generalized Autoregressive Score model, we propose to cluster time series according to their estimated conditional moments via the Autocorrelation-based fuzzy C-means (A-FCMd) algorithm. The usefulness of the proposed procedure is illustrated using several empirical applications with financial time series assuming both linear and nonlinear models specification and under several assumptions about time series density function. In the end, we provide a discussion on the possible use of projection pursuit with the aim of improving clustering performance.