Dimensionality analysis of time-series data: Nonlinear methods

The field of nonlinear dynamics has resulted in the development of several techniques aimed at determining the dimensionality of strange attractors underlying time series outputs from chaotic systems. Knowledge of the system dimension allows estimation of the number of independent variables governing it. The techniques also allow one to distinguish between data sets produced through either random (i.e. high dimension) or deterministic processes (i.e. low dimension). Unlike physics and geophysics where data strings may be large ( n ∼ 1000s) those in geology are generally short ( n ∼ 100s), and there is associated noise. A new algorithm modeled after that of Sugihara and May is presented which in comparison to the correlation function technique works on short and discontinuous data strings.