Long-term Trend in Non-stationary Time Series with Nonlinear Analysis Techniques

Understanding, modeling, and forecasting the evolution of complex dynamic system is an important but hard task in many natural phenomena. In the present paper, three advanced analysis approaches, including the rescaled range analysis, empirical mode decomposition and cross-recurrence plot, have been proposed to analyze the long-term persistence and secular trend of nonlinear and non-stationary time series. The case study uses the chaotic time-series data of solar-activity indicators in the time interval from 1874 May to 2013 March. The analysis results indicate that the combination of these three techniques is an effective tool not only for capturing the long-range persistence of non-stationary processes, but also for determining the secular trend of a complex time-series.