New Insights into Time Series Analysis IV: Panchromatic and Flux Independent Period Finding Methods

TL;DR

This paper introduces new panchromatic and flux-independent period-finding methods for time series data, applicable across disciplines, validated through simulations and observational data, and comparable in efficiency to existing methods.

Contribution

It adapts panchromatic correlated indices to develop novel period-finding techniques suitable for single- and multi-band data, with analytical noise modeling and performance evaluation.

Findings

Methods perform similarly to String Length period method.

Effective in single and multiple wavebands sharing a fundamental frequency.

Analytical noise amplitude equation established for various false alarm probabilities.

Abstract

New time-series analysis tools are needed in disciplines as diverse as astronomy, economics and meteorology. In particular, the increasing rate of data collection at multiple wavelengths requires new approaches able to handle these data. The panchromatic correlated indices $K^{(s)}_{(fi)}$ and $L^{(s)}_{(pfc)}$ are adapted to quantify the smoothness of a phased light-curve resulting in new period-finding methods applicable to single- and multi-band data. Simulations and observational data are used to test our approach. The results were used to establish an analytical equation for the amplitude of the noise in the periodogram for different false alarm probability values, to determine the dependency on the signal-to-noise ratio, and to calculate the yield-rate for the different methods. The proposed method has similar efficiency to that found for the String Length period method. The effectiveness of the panchromatic and flux independent period finding methods in single waveband as well as multiple-wavebands that share a fundamental frequency is also demonstrated in real and simulated data.