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One of the goals of time series analysis is to understand the underlying mechanisms that generate different dynamics for different time series. If a time series is not a product of random process, then we can assume that some kind of dynamics govern the time series. The question is what kinds of dynamics are controlling the time series. For nonlinear time series analysis, our focus is on nonlinear dynamics, and one of the goals is to characterize those dynamics by applying nonlinear tools. However, it is important to establish evidence of nonlinearity in a time series first in order to avoid obtaining possible spurious results by applying nonlinear tools to the system that does not contain nonlinearity. Second, nonlinearity is considered as one of the key features of time series that exhibit chaos, which has been shown to have a potential link with overall health of the biological system (Amato 1992; Buchman et al. 2001; Cavanaugh et al. 2010; Garfinkel et al. 1992; Goldstein et al. 1998; Orsucci 2006; Slutzky et al. 2001; Toweill and Goldstein 1998; Wagner et al. 1996). Therefore, in terms of detecting chaos in a time series, identifying the presence of nonlinearity in the system is essential.
Nonlinear Analyses of Human Movement
4. Myers, SA, Stergiou, N. Surrogation Analysis. (2015). In: Stergiou N. Nonlinear Analyses of Human Movement. Boca Raton, FL: CRC Press. https://www.routledge.com/Nonlinear-Analysis-for-Human-Movement-Variability/Stergiou/p/book/9781498703321
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