Novel bivariate autoregressive model for predicting and forecasting irregularly observed time series

TL;DR

This paper introduces the BIAR model, a novel bivariate autoregressive approach for irregularly observed time series, particularly in astronomy, enabling better forecasting and classification by capturing inter-band dependencies.

Contribution

The paper proposes the BIAR model, a new bivariate autoregressive method that accounts for cross-correlation in irregular time series, improving forecasting and classification in astronomical data.

Findings

BIAR model outperforms univariate models in highly correlated light curves.

Estimated parameters aid in classifying variable stars.

Model effectively captures dependencies between different observational bands.

Abstract

In several disciplines it is common to find time series measured at irregular observational times. In particular, in astronomy there are a large number of surveys that gather information over irregular time gaps and in more than one passband. Some examples are Pan-STARRS, ZTF and also the LSST. However, current commonly used time series models that estimate the time dependency in astronomical light curves consider the information of each band separately (e.g, CIAR, IAR and CARMA models) disregarding the dependency that might exist between different passbands. In this paper we propose a novel bivariate model for irregularly sampled time series, called the bivariate irregular autoregressive (BIAR) model. The BIAR model assumes an autoregressive structure on each time series, it is stationary, and it allows to estimate the autocorrelation, the cross-correlation and the contemporary correlation between two unequally spaced time series. We implemented the BIAR model on light curves, in the g and r bands, obtained from the ZTF alerts processed by the ALeRCE broker. We show that if the light curves of the two bands are highly correlated, the model has more accurate forecast and prediction using the bivariate model than a similar method that uses only univariate information. Further, the estimated parameters of the BIAR are useful to characterize LongPeriod Variable Stars and to distinguish between classes of stochastic objects, providing promising features that can be used for classification purposes