New Insights into Time Series Analysis II -- No Correlated Observations

TL;DR

This paper introduces new statistical parameters and methods to improve the detection and classification of non-correlated and correlated variability in time series data, significantly reducing misclassification rates.

Contribution

It presents 16 modified statistical parameters, a new noise model, and an improved approach for variability detection that enhances efficiency over previous methods.

Findings

Misclassification reduced by up to 1200% using new indices.

New parameters have lower error, especially with few measurements.

Improved correlated indices using the even mean enhance classification accuracy.

Abstract

Statistical parameters are used in finance, weather, industrial, science, among other vast number of different fields to draw conclusions. New more efficient selection methods are mandatory to analyses the huge amount of astronomical data. The standard and new data-mining parameters to analyses non-correlated data are used to set the best way to discriminate stochastic and non-stochastic variations. We introduce 16 modified statistical parameters covering different features of statistical distribution, like; average, dispersion, and shape parameters. Many of dispersion and shape parameters are unbound parameters, i.e. equations which do not require the calculation of the average. Moreover, the majority of them have lower error than previous ones that is mainly observed for distributions having few measurements. A set of non-correlated variability indices, sample size corrections, and a new noise model as well as tests of different apertures and cutoffs on the data (BAS approach) are introduced. The number of misselections is reduced by about 520% using a single waveband and 1200% combining all wavebands. On the other hand, the even mean also improves the correlated indices introduced in Paper 1 Ferreira Lopes & Cross (2016). The misselection rate is reduced by about 18% if the even mean is used instead of the mean to compute the correlated indices in the WFCAM database. Even statistics allows us to improve the effectiveness of both correlated and non-correlated indices. The correlated variability indices, proposed in the first paper of this series, are also improved if the even mean is used. The even parameters will also be useful for classifying light curves in the last step of this project. We consider that the first step of this project, where we set new techniques and methods that provide a huge improve on the efficiency of selection of variable stars, is now complete.