Nonlinear Time Series Clustering Based on Kolmogorov-Smirnov 2D Statistic

Time series clustering is to assign a set of time series into groups that share certain similarity. It has become an attractive analytic tool as many applications require such classifications. Clustering may also result in more accurate parameter estimates when a group of time series are assumed to share common models and parameters, especially for short panel time series. Many existing time series clustering methods are based on the assumption that the time series are linear. However, linearity assumptions often fail to hold. In this paper we consider the problem of clustering nonlinear time series. We propose the use of a two dimensional Kolmogorov-Smirnov statistic as a distance measure of two time series by measuring the affinity of nonlinear serial dependence structures. It is nonparametric in nature hence no model assumption are needed. The approach is illustrated with simulation studies as well as real data examples.