Time series clustering using copula-based higher order Markov process
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In model-based time series clustering, most models used only allow linear dependence. This could lead to unsatisfactory clustering results due to the limited use of information. We propose using the copula-based higher order Markov process (CHOMP) by Ibragimov (2009). The CHOMP can capture not only dependence strengths, but also different dependence structures (linear or non-linear). We further relax the stationarity condition in the original version of CHOMP by Ibragimov (2009) so that it can also capture the profile/shape information in non-stationary time series. Moreover, a non-parametric estimation for the CHOMP is proposed based on the two-step procedure of Chen and Fan (2006). Finally, a time series clustering algorithm based on CHOMP is proposed using agglomerative hierarchical clustering and finite mixture models. With more information extracted and used in clustering, our algorithm outperforms its competitors in an extensive simulation study and two real data analyses.