Detection of dynamical systems from noisy multivariate time series

Experimental observations of physical, social, or economical systems may often be reduced to multivariate time series. The observed time series may be investigated as random processes or realizations of stochastic dynamical systems. Studies of natural phenomena should consider that the time series are affected by a random noise such that some realizations of the underlying dynamical system are missed by the observer and some observations correspond to the realizations of a stochastic process associated to the method of measurement. Within this framework we consider discrete time series derived from mappings by the iterations of one observable, typically one of the system's coordinates. The time series were altered by several levels of noise and we show that a pattern detection algorithm was able to detect temporal patterns of events that repeated more frequently than expected by chance. These patterns were related to the generating attractors and were robust with respect to the appearance of spurious points due to the noise. On the basis of this result we propose a filtering procedure aimed at decreasing the amount of noisy events in time series.