Significance Tests for Periodogram Peaks

TL;DR

This paper reviews current methods for assessing the significance of peaks in periodograms of time series and introduces a Monte Carlo simulation-based approach for more accurate, data-agnostic significance testing.

Contribution

It proposes a practical, Monte Carlo simulation-based method for estimating periodogram peak significance applicable to all types of time series.

Findings

The method provides tailored significance tests for astronomical data.

It accounts for data spacing and independence assumptions.

The approach improves accuracy over traditional methods.

Abstract

We discuss methods currently in use for determining the significance of peaks in the periodograms of time series. We discuss some general methods for constructing significance tests, false alarm probability functions, and the role played in these by independent random variables and by empirical and theoretical cumulative distribution functions. We also discuss the concept of "independent frequencies" in periodogram analysis. We propose a practical method for estimating the significance of periodogram peaks, applicable to all time series irrespective of the spacing of the data. This method, based on Monte Carlo simulations, produces significance tests that are tailor-made for any given astronomical time series.