Delay Estimation from noisy time series

We propose here a method to estimate a delay from a time series taking advantage of analysis of random walks with delay. This method is applicable to a time series coming out of a system which is or can be approximated as a linear feedback system with delay and noise. We successfully test the method with a time series generated by discrete Langevin equation with delay.Comment: Tentatively scheduled to appear as a Rapid Communication in Phys. Rev. E., March 199

Delay Estimation From Noisy Time Series

We propose here a method to estimate a delay from a time series taking advantage of analysis of random walks with delay. This method is applicable to a time series coming out of a system which is or can be approximated as a linear feedback system with delay and noise. We successfully test the method with a time series generated by discrete Langevin equation with delay. Estimation of delay from a noisy time series has attracted much attention. Especially, when the time series is chaotic, estimation of delay has a practical motivation: time--delayed coordinates are typically used to estimate fractal dimensions and Lyapunov exponents. There are series of works considering the subject from this viewpoint [1, 2, 3, 4]. Another viewpoint is to consider that a noisy time series consists of underlying deterministic dynamics with past influence and a noise term. Some statisticians have taken this stand and devised methods of analysis, for example, using the generalized Langevin equation [5, 6]..