Detecting Low-Dimensional Chaos of Non-stationary Time Series with Rescaled Range Analysis and Maximal Lyapunov Exponent

Abstract

Distinguishing low-dimensional chaos from noise time series is a very important topic in time series analysis. Among the several techniques proposed for this aim are the rescaled range analysis and maximal Lyapunov exponent, which quantifies the amount of a time series. These two nonlinear analysis techniques are applied to analyze the astronomical time series, which is non-stationary and nonlinear in nature. It is found that, (1) solar activity exhibits a complex and strongly chaotic behaviour and is governed by a low-dimensional chaotic attractor, (2) the predictability time of the chaotic motion in solar-activity indicator is up to 1.12 years. These results indicate that chaotic characteristics obviously exist in the solar time series, and thus techniques based on rescaled range analysis and maximal Lyapunov exponent can be used to analyze and predict solar activity. It should be pointed out that solar activity forecast should be done only for a short to medium term due to the initial value of the sensitive of the chaotic system.