Time Series Analysis Methods Applied to the Super-Kamiokande I Data

TL;DR

This paper compares traditional Lomb-Scargle periodogram analysis with a new likelihood-based approach for detecting modulations in noisy time series, applied specifically to Super-Kamiokande I neutrino flux data, highlighting the advantages and relationships of both methods.

Contribution

It introduces an analytical likelihood methodology for time series analysis, demonstrating its application and advantages over Lomb-Scargle in neutrino data analysis.

Findings

Likelihood method effectively detects signals in noisy data.

Comparison shows likelihood approach has advantages over Lomb-Scargle.

Analytical assessment of signal significance enhances analysis robustness.

Abstract

The need to unravel modulations hidden in noisy time series of experimental data is a well known problem, traditionally attacked through a variety of methods, among which a popular tool is the so called Lomb-Scargle periodogram. Recently, for a class of problems in the solar neutrino field, it has been proposed an alternative maximum likelihood based approach, intended to overcome some intrinsic limitations affecting the Lomb-Scargle implementation. This work is focused to highlight the features of the likelihood methodology, introducing in particular an analytical approach to assess the quantitative significance of the potential modulation signals. As an example, the proposed method is applied to the time series of the measured values of the 8B neutrino flux released by the Super-Kamiokande collaboration, and the results compared with those of previous analysis performed on the same data sets. It is also examined in detail the comparison between the Lomb-Scargle and the likelihood methods, giving in the appendix the complete demonstration of their close relationship.