An application of Saddlepoint Approximation for period detection of stellar light observations

TL;DR

This paper introduces a saddlepoint approximation method for detecting periodic signals in irregular stellar light curve data, providing faster and more accurate period estimation with quantifiable uncertainty.

Contribution

It develops a novel saddlepoint approximation approach for period detection in irregular time series, extending to non-parametric and correlated noise models.

Findings

The method improves speed and accuracy over simulation-based techniques.

Application to real stellar data demonstrates effective period detection.

Quantifiable uncertainty enhances confidence in identified periods.

Abstract

One of the main features of interest in analysing the light curves of stars is the underlying periodic behaviour. The corresponding observations are a complex type of time series with unequally spaced time points and are sometimes accompanied by varying measures of accuracy. The main tools for analysing these type of data rely on the periodogram-like functions, constructed with a desired feature so that the peaks indicate the presence of a potential period. In this paper, we explore a particular periodogram for the irregularly observed time series data, similar to Thieler et. al. (2013). We identify the potential periods at the appropriate peaks and more importantly with a quantifiable uncertainty. Our approach is shown to easily generalise to non-parametric methods including a weighted Gaussian process regression periodogram. We also extend this approach to correlated background noise. The proposed method for period detection relies on a test based on quadratic forms with normally distributed components. We implement the saddlepoint approximation, as a faster and more accurate alternative to the simulation-based methods that are currently used. The power analysis of the testing methodology is reported together with applications using light curves from the Hunting Outbursting Young Stars citizen science project.