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In several disciplines it is common to find time series measured at irregularobservational times. In particular, in astronomy there are a large number ofsurveys that gather information over irregular time gaps and in more than onepassband. Some examples are Pan-STARRS, ZTF and also the LSST. However, currentcommonly used time series models that estimate the time dependency inastronomical light curves consider the information of each band separately(e.g, CIAR, IAR and CARMA models) disregarding the dependency that might existbetween different passbands. In this paper we propose a novel bivariate modelfor irregularly sampled time series, called the bivariate irregularautoregressive (BIAR) model. The BIAR model assumes an autoregressive structureon each time series, it is stationary, and it allows to estimate theautocorrelation, the cross-correlation and the contemporary correlation betweentwo unequally spaced time series. We implemented the BIAR model on lightcurves, in the g and r bands, obtained from the ZTF alerts processed by theALeRCE broker. We show that if the light curves of the two bands are highlycorrelated, the model has more accurate forecast and prediction using thebivariate model than a similar method that uses only univariate information.Further, the estimated parameters of the BIAR are useful to characterizeLongPeriod Variable Stars and to distinguish between classes of stochasticobjects, providing promising features that can be used for classificationpurposes

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