  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
