Modeling Stochastic Variability in Multiband Timeseries Data
Abstract
In preparation for the era of timedomain astronomy with upcoming largescale surveys, we propose a statespace representation of a multivariate damped random walk process as a tool to analyze irregularlyspaced multifilter light curves with heteroscedastic measurement errors. We adopt a computationally efficient and scalable Kalman filtering approach to evaluate the likelihood function, leading to maximum $O({k}^{3}n)$ complexity, where k is the number of available bands and n is the number of unique observation times across the k bands. This is a significant computational advantage over a commonly used univariate Gaussian process that can stack up all multiband light curves in one vector with maximum $O({k}^{3}{n}^{3})$ complexity. Using such efficient likelihood computation, we provide both maximum likelihood estimates and Bayesian posterior samples of the model parameters. Three numerical illustrations are presented: (i) analyzing simulated fiveband light curves for a comparison with independent singleband fits; (ii) analyzing fiveband light curves of a quasar obtained from the Sloan Digital Sky Survey Stripe 82 to estimate shortterm variability and timescale; (iii) analyzing gravitationally lensed g and rband light curves of Q0957+561 to infer the time delay. Two R packages, Rdrw and timedelay, are publicly available to fit the proposed models.
 Publication:

The Astronomical Journal
 Pub Date:
 December 2020
 DOI:
 10.3847/15383881/abc1e2
 arXiv:
 arXiv:2005.08049
 Bibcode:
 2020AJ....160..265H
 Keywords:

 Astrostatistics;
 Interdisciplinary astronomy;
 Astrostatistics tools;
 1882;
 804;
 1887;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 Statistics  Methodology
 EPrint:
 doi:10.3847/15383881/abc1e2