A new method of reconstruction of dynamical system of nonstationary time-series

The phase space reconstruction of nonstationary time-series is a bewildering problem since the conventional methods are all based on the assumption that the targeted time-series is stationary. In this paper, a new method of phase space reconstruction is proposed for the nonstationary time-series. The nonstationary time-series is firstly converted into its analytical form via the Hilbert transform, which retains both the nonstationarity and the nonlinear dynamics of the original time-series. The instantaneous phase angle θ is then extracted from the complex time-series. The 1^st and 2^nd-order derivatives θ, θ of phase angle θ are calculated. It is mathematically proved that the vector field [θ,θ,θ]is the phase space of the original time-series. The proposed method puts no constraint on the stationarity of the time-series, and it is available for both stationary and nonstationary time-series. The simulation tests show the proposed method is effective.