Effect of data gaps on correlation dimension computed from light curves of variable stars

TL;DR

This paper examines how data gaps affect the calculation of correlation dimension in light curves of variable stars, proposing a method to assess reliability without interpolation and highlighting potential pitfalls of spline interpolation.

Contribution

It introduces a method to evaluate the impact of data gaps on correlation dimension estimates and demonstrates how to identify reliable values in astrophysical time series analysis.

Findings

Correlation dimension remains reliable for certain gap distributions.

Spline interpolation can falsely indicate chaos in non-chaotic data.

Careful binning can improve the reliability of correlation dimension estimates.

Abstract

Observational data, especially astrophysical data, is often limited by gaps in data that arises due to lack of observations for a variety of reasons. Such inadvertent gaps are usually smoothed over using interpolation techniques. However the smoothing techniques can introduce artificial effects, especially when non-linear analysis is undertaken. We investigate how gaps can affect the computed values of correlation dimension of the system, without using any interpolation. For this we introduce gaps artificially in synthetic data derived from standard chaotic systems, like the R{\"o}ssler and Lorenz, with frequency of occurrence and size of missing data drawn from two Gaussian distributions. Then we study the changes in correlation dimension with change in the distributions of position and size of gaps. We find that for a considerable range of mean gap frequency and size, the value of correlation dimension is not significantly affected, indicating that in such specific cases, the calculated values can still be reliable and acceptable. Thus our study introduces a method of checking the reliability of computed correlation dimension values by calculating the distribution of gaps with respect to its size and position. This is illustrated for the data from light curves of three variable stars, R Scuti, U Monocerotis and SU Tauri. We also demonstrate how a cubic spline interpolation can cause a time series of Gaussian noise with missing data to be misinterpreted as being chaotic in origin. This is demonstrated for the non chaotic light curve of variable star SS Cygni, which gives a saturated D$_{2}$ value, when interpolated using a cubic spline. In addition we also find that a careful choice of binning, in addition to reducing noise, can help in shifting the gap distribution to the reliable range for D$_2$ values.