2.3 Testing for chaotic dynamics in observed time series

The third and final step in resolving the question of whether the observed dynamics are chaotic or not, is taken by applying statistical inference to the largest Lyapunov exponent. For example, observational noise may be present in the observed timeseries

in eq. (2.2).

Moreover, the time series may contain dynamic noise, i.e. the unknown system may be a stochastic dynamical system.

Therefore, a distributional theory which provides a framework for statistical inference is needed. Recently, Bailey (1996) and Whang and Linton (1997) have derived analytically the asymptotic distributions of estimators of the Lyapunov exponents for stochastic time series. Bailey (1996) deals with local Lyapunov exponents whereas Whang and Linton (1997) deal with global exponents.

Prof. Mikael Bask