Uncovering delayed patterns in noisy and irregularly sampled time series: an astronomy application

TL;DR

This paper introduces an evolutionary algorithm-based method for estimating time delays in noisy, irregularly sampled time series, demonstrated on astronomical data with improved accuracy and stability over existing methods.

Contribution

We develop a novel evolutionary algorithm for hyperparameter estimation in kernel-based time delay analysis, specifically applied to gravitational lensing in astronomy.

Findings

More accurate time delay estimates for quasar Q0957+561

Enhanced stability of delay measurements compared to traditional methods

Applicable to various disciplines with irregular time series data

Abstract

We study the problem of estimating the time delay between two signals representing delayed, irregularly sampled and noisy versions of the same underlying pattern. We propose and demonstrate an evolutionary algorithm for the (hyper)parameter estimation of a kernel-based technique in the context of an astronomical problem, namely estimating the time delay between two gravitationally lensed signals from a distant quasar. Mixed types (integer and real) are used to represent variables within the evolutionary algorithm. We test the algorithm on several artificial data sets, and also on real astronomical observations of quasar Q0957+561. By carrying out a statistical analysis of the results we present a detailed comparison of our method with the most popular methods for time delay estimation in astrophysics. Our method yields more accurate and more stable time delay estimates: for Q0957+561, we obtain 419.6 days for the time delay between images A and B. Our methodology can be readily applied to current state-of-the-art optical monitoring data in astronomy, but can also be applied in other disciplines involving similar time series data.