Space partitioning via Hilbert transform for symbolic time series analysis

Symbol sequence generation is a crucial step in symbolic time series analysis of dynamical systems, which requires phase-space partitioning. This letter presents analytic signal space partitioning (ASSP) that relies on Hilbert transform of the observed real-valued data sequence into the corresponding complex-valued analytic signal. ASSP yields comparable performance as other partitioning methods, such as symbolic false nearest neighbor partitioning (SFNNP) and wavelet-space partitioning (WSP). The execution time of ASSP is several orders of magnitude smaller than that of SFNNP. Compared to WSP, the ASSP algorithm is analytically more rigorous and is approximately five times faster.