Noise reduction by recycling dynamically coupled time series.

We say that several scalar time series are dynamically coupled if they record the values of measurements of the state variables of the same smooth dynamical system. We show that much of the information lost due to measurement noise in a target time series can be recovered with a noise reduction algorithm by crossing the time series with another time series with which it is dynamically coupled. The method is particularly useful for reduction of measurement noise in short length time series with high uncertainties.

Reduction of noise of large amplitude through adaptive neighborhoods.

We propose a noise reduction algorithm based on adaptive neighborhood selection that is able to obtain high levels of noise reduction for chaotic vector time series corrupted by observational noises with a noise-to-signal ratio of up to 300%.

Geometric noise reduction for multivariate time series.

We propose an algorithm for the reduction of observational noise in chaotic multivariate time series. The algorithm is based on a maximum likelihood criterion, and its goal is to reduce the mean distance of the points of the cleaned time series to the attractor. We give evidence of the convergence of the empirical measure associated with the cleaned time series to the underlying invariant measure, implying the possibility to predict the long run behavior of the true dynamics.