Delay Estimation from noisy time series

TL;DR

This paper introduces a method to estimate delays in noisy time series by analyzing random walks, applicable to linear feedback systems with delay and noise, validated through Langevin equation simulations.

Contribution

The paper presents a novel delay estimation technique based on random walk analysis for noisy linear feedback systems.

Findings

Effective delay estimation in simulated Langevin systems.

Applicable to systems approximated as linear feedback with delay.

Validated through successful tests on generated time series.

Abstract

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.