Modeling Stochastic Variability in Multi-Band Time Series Data
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In preparation for the era of the time-domain astronomy with upcoming large-scale surveys, we propose a state-space representation of a multivariate damped random walk process as a tool to analyze irregularly-spaced multi-filter 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^3n) 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 multi-band light curves in one vector with maximum O(k^3n^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 five-band light curves for a comparison with independent single-band fits; (ii) analyzing five-band light curves of a quasar obtained from the Sloan Digital Sky Survey (SDSS) Stripe 82 to estimate the short-term variability and timescale; (iii) analyzing gravitationally lensed g- and r-band light curves of Q0957+561 to infer the time delay. Two R packages, Rdrw and timedelay, are publicly available to fit the proposed models.
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