Multivariate Continuous-Time Autoregressive Moving Average Processes for Astronomical Multiband Time Series

Abstract

Large-scale astronomical surveys provide unprecedented volumes of multivariate time-series observations obtained through multiple optical filters. We develop a structured multivariate continuous-time autoregressive moving average (MCARMA) framework for multi-band time series with irregular sampling, heteroscedastic measurement errors, and partially observed bands. The framework allows band-specific stochastic dynamics while modeling cross-band dependence through correlated Brownian driving processes, with state-space and spectral representations enabling likelihood-based inference and interpretation of the fitted stochastic dynamics. We develop a two-stage estimation procedure in which a numerically stabilized preliminary fit initializes subsequent maximum likelihood estimation. Simulations show that higher-order stochastic structure can be recovered when its characteristic features are adequately resolved, but can become weakly identifiable because of limited temporal resolution or near pole--zero cancellation. Joint multivariate estimation improves parameter recovery in 23 of 27 settings and spectral recovery in 26 of 27 settings relative to separate single-band fits. Three Sloan Digital Sky Survey Stripe 82 quasars, respectively favoring MCARMA(1,0), MCARMA(2,0), and MCARMA(2,1), illustrate how joint multiband modeling uses cross-band dependence to inform marginal dynamics and can yield different model-order and spectral inference. The methodology is implemented in the Python package mcarma.