Assessing statistical significance of periodogram peaks

TL;DR

This paper improves methods for evaluating the statistical significance of peaks in periodograms, crucial for detecting true periodic signals in astronomical data, by providing more accurate false alarm probability estimates based on extreme value theory.

Contribution

It introduces enhanced analytic estimations of false alarm probabilities for periodogram peaks, including upper bounds, grounded in extreme value theory, and tests their practical applicability.

Findings

New analytic formulas for false alarm probabilities

Validated estimations through numerical testing

Applicable to various astronomical observational data

Abstract

The least-squares (or Lomb-Scargle) periodogram is a powerful tool which is used routinely in many branches of astronomy to search for periodicities in observational data. The problem of assessing statistical significance of candidate periodicities for different periodograms is considered. Based on results in extreme value theory, improved analytic estimations of false alarm probabilities are given. They include an upper limit to the false alarm probability (or a lower limit to the significance). These estimations are tested numerically in order to establish regions of their practical applicability.