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Elorrieta, F., Eyheramendy, S., & Palma, W. (2019). Discretetime autoregressive model for unequally spaced timeseries observations. Astron. Astrophys., 627, 11 pp.
Abstract: Most timeseries models assume that the data come from observations that are equally spaced in time. However, this assumption does not hold in many diverse scientific fields, such as astronomy, finance, and climatology, among others. There are some techniques that fit unequally spaced time series, such as the continuoustime autoregressive moving average (CARMA) processes. These models are defined as the solution of a stochastic differential equation. It is not uncommon in astronomical time series, that the time gaps between observations are large. Therefore, an alternative suitable approach to modeling astronomical time series with large gaps between observations should be based on the solution of a difference equation of a discrete process. In this work we propose a novel model to fit irregular time series called the complex irregular autoregressive (CIAR) model that is represented directly as a discretetime process. We show that the model is weakly stationary and that it can be represented as a statespace system, allowing efficient maximum likelihood estimation based on the Kalman recursions. Furthermore, we show via Monte Carlo simulations that the finite sample performance of the parameter estimation is accurate. The proposed methodology is applied to light curves from periodic variable stars, illustrating how the model can be implemented to detect poor adjustment of the harmonic model. This can occur when the period has not been accurately estimated or when the variable stars are multiperiodic. Last, we show how the CIAR model, through its state space representation, allows unobserved measurements to be forecast.
Keywords: methods: statistical; methods: data analysis; stars: general

Elorrieta, F., Eyheramendy, S., Palma, W., & Ojeda, C. (2021). A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series. Mon. Not. Roy. Astron. Soc., 505(1), 1105–1116.
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 PanSTARRS, ZTF, and also the LSST. However, current commonly used time series models that estimate the time dependence in astronomical light curves consider the information of each band separately (e.g, CIAR, IAR, and CARMA models) disregarding the dependence 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 crosscorrelation 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.

SanchezSaez, P., Reyes, I., Valenzuela, C., Forster, F., Eyheramendy, S., Elorrieta, F., et al. (2021). Alert Classification for the ALeRCE Broker System: The Light Curve Classifier. Astron. J., 161(3), 141.
Abstract: We present the first version of the Automatic Learning for the Rapid Classification of Events (ALeRCE) broker light curve classifier. ALeRCE is currently processing the Zwicky Transient Facility (ZTF) alert stream, in preparation for the Vera C. Rubin Observatory. The ALeRCE light curve classifier uses variability features computed from the ZTF alert stream and colors obtained from AllWISE and ZTF photometry. We apply a balanced random forest algorithm with a twolevel scheme where the top level classifies each source as periodic, stochastic, or transient, and the bottom level further resolves each of these hierarchical classes among 15 total classes. This classifier corresponds to the first attempt to classify multiple classes of stochastic variables (including core and hostdominated active galactic nuclei, blazars, young stellar objects, and cataclysmic variables) in addition to different classes of periodic and transient sources, using real data. We created a labeled set using various public catalogs (such as the Catalina Surveys and Gaia DR2 variable stars catalogs, and the Million Quasars catalog), and we classify all objects with >= 6 gband or >= 6 rband detections in ZTF (868,371 sources as of 2020 June 9), providing updated classifications for sources with new alerts every day. For the top level we obtain macroaveraged precision and recall scores of 0.96 and 0.99, respectively, and for the bottom level we obtain macroaveraged precision and recall scores of 0.57 and 0.76, respectively. Updated classifications from the light curve classifier can be found at the ALeRCE Explorer website (http://alerce.online)..
Keywords: Active galaxies; Astronomy data analysis; Variable stars; Supernovae; Surveys

Forster, F., CabreraVives, G., CastilloNavarrete, E., Estevez, P. A., SanchezSaez, P., Arredondo, J., et al. (2021). The Automatic Learning for the Rapid Classification of Events (ALeRCE) Alert Broker. Astron. J., 161(5), 242.
Abstract: We introduce the Automatic Learning for the Rapid Classification of Events (ALeRCE) broker, an astronomical alert broker designed to provide a rapid and selfconsistent classification of large etendue telescope alert streams, such as that provided by the Zwicky Transient Facility (ZTF) and, in the future, the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). ALeRCE is a Chileanled broker run by an interdisciplinary team of astronomers and engineers working to become intermediaries between survey and followup facilities. ALeRCE uses a pipeline that includes the realtime ingestion, aggregation, crossmatching, machinelearning (ML) classification, and visualization of the ZTF alert stream. We use two classifiers: a stampbased classifier, designed for rapid classification, and a light curvebased classifier, which uses the multiband flux evolution to achieve a more refined classification. We describe in detail our pipeline, data products, tools, and services, which are made public for the community (see ). Since we began operating our realtime ML classification of the ZTF alert stream in early 2019, we have grown a large community of active users around the globe. We describe our results to date, including the realtime processing of 1.5 x 10(8) alerts, the stamp classification of 3.4 x 10(7) objects, the lightcurve classification of 1.1 x 10(6) objects, the report of 6162 supernova candidates, and different experiments using LSSTlike alert streams. Finally, we discuss the challenges ahead in going from a single stream of alerts such as ZTF to a multistream ecosystem dominated by LSST.
