New insights into time series analysis

Abstract

Context. Statistical parameters are used to draw conclusions in a vast number of fields such as finance, weather, industrial, and science. These parameters are also used to identify variability patterns on photometric data to select non-stochastic variations that are indicative of astrophysical effects. New, more efficient, selection methods are mandatory to analyze the huge amount of astronomical data. Aims. We seek to improve the current methods used to select non-stochastic variations on non-correlated data. Methods. We used standard and new data-mining parameters to analyze non-correlated data to find the best way to discriminate between stochastic and non-stochastic variations. A new approach that includes a modified Strateva function was performed to select non-stochastic variations. Monte Carlo simulations and public time-domain data were used to estimate its accuracy and performance. Results. We introduce 16 modified statistical parameters covering different features of statistical distribution such as average, dispersion, and shape parameters. Many dispersion and shape parameters are unbound parameters, i.e. equations that do not require the calculation of average. Unbound parameters are computed with single loop and hence decreasing running time. Moreover, the majority of these parameters have lower errors than previous parameters, which is mainly observed for distributions with few measurements. A set of non-correlated variability indices, sample size corrections, and a new noise model along with tests of different apertures and cut-offs on the data (BAS approach) are introduced. The number of mis-selections are 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 I. The mis-selection 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. Conclusions. The selection of non-stochastic variations is improved by non-correlated indices. The even-averages provide a better estimation of mean and median for almost all statistical distributions analyzed. The correlated variability indices, which are 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 improvement on the efficiency of selection of variable stars, is now complete. Many of these techniques may be useful for a large number of fields. Next, we will commence a new step of this project regarding the analysis of period search methods.

VaST: A variability search toolkit

“…• Sensitive to both smoothness and scatter (Stetson's J index), maybe also taking into account the shape of the measured brightness distribution (e.g. L index Stetson 1996, Ferreira Lopes andCross 2016).…”

VVV survey near-infrared colour catalogue of known variable stars

“…The VIVA catalogue (Ferreira Lopes et al 2020) is based on a variability analysis of the VVV-DR4 Data Release that is the same as we used here. It was compiled following a series of recommendations in the New Insight into Time Series Analysis (NITSA -Ferreira Lopes & Cross 2016b, 2017bFerreira Lopes et al 2018). These criteria provide a good prescription for select-Herpich et al: VVV survey near-infrared colour catalogue of known variable stars Fig.…”

New type II Cepheids from VVV data towards the Galactic center

“…Ferreira Lopes & Cross (2017) presented new dispersion and shape parameters for distributions with an even number of items in order to decipher whether or not the input distribution -which must be an array of observed magnitudes -could be representative of the light curve of a PVS. We note that only the measured magnitudes are taken into account, and not the epochs of observation.…”