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Elorrieta, F., Eyheramendy, S., & Palma, W. (2019). Discrete-time autoregressive model for unequally spaced time-series observations. Astron. Astrophys., 627, 11 pp.
Abstract: Most time-series 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 continuous-time 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 discrete-time process. We show that the model is weakly stationary and that it can be represented as a state-space 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.
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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 Pan-STARRS, 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 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 long-period variable stars and to distinguish between classes of stochastic objects, providing promising features that can be used for classification purposes.
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Forster, F., Cabrera-Vives, G., Castillo-Navarrete, E., Estevez, P. A., Sanchez-Saez, 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 self-consistent 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 Chilean-led broker run by an interdisciplinary team of astronomers and engineers working to become intermediaries between survey and follow-up facilities. ALeRCE uses a pipeline that includes the real-time ingestion, aggregation, cross-matching, machine-learning (ML) classification, and visualization of the ZTF alert stream. We use two classifiers: a stamp-based classifier, designed for rapid classification, and a light curve-based 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 real-time 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 real-time processing of 1.5 x 10(8) alerts, the stamp classification of 3.4 x 10(7) objects, the light-curve classification of 1.1 x 10(6) objects, the report of 6162 supernova candidates, and different experiments using LSST-like 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.
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Palma, W., Bondon, P., & Tapia, J. (2008). Assessing influence in Gaussian long-memory models. Comput. Stat. Data Anal., 52(9), 4487–4501.
Abstract: A statistical methodology for detecting influential observations in long-memory models is proposed. The identification of these influential points is carried out by case-deletion techniques. In particular, a Kullback-Leibler divergence is considered to measure the effect of a subset of observations on predictors and smoothers. These techniques are illustrated with an analysis of the River Nile data where the proposed methods are compared to other well-known approaches such as the Cook and the Mahalanobis distances. (c) 2008 Elsevier B.V. All rights reserved.
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