The flux variability of Active Galactic Nuclei (AGNs) is commonly modeled using the damped random walk (DRW), but increasingly rich multiband time-domain surveys motivate more flexible stochastic models that characterize variability beyond a single timescale and exploit dependence across bands. Multivariate continuous-time autoregressive moving average (MCARMA) processes extend the multivariate DRW to higher-order stochastic dynamics and provide a matrix-valued power spectral density for characterizing marginal variability and cross-band dependence. In a carefully selected Sloan Digital Sky Survey (SDSS) Stripe~82 sample, higher-order models are selected for 109 of 134 AGNs (81.3\%), with substantial rather than marginal support in most objects; convergence diagnostics indicate that this fraction is conservative. The fitted models also reveal strong cross-band dependence that generally decreases with wavelength separation. Motivated by this richer structure, we investigate its recoverability under Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) observing conditions. Model-order recovery depends strongly on the underlying stochastic behavior as well as source brightness and observing cadence. Recovery is high across many of the simulated settings, but deteriorates when the characteristic features of higher-order variability become difficult to distinguish from the multivariate DRW. Additional simulations show that this loss of distinguishability can persist over a range of underlying variability behaviors. These results show that stochastic structure beyond the multivariate DRW is prevalent in our selected SDSS sample, while its recoverability with LSST depends on both observational conditions and the form of the underlying stochastic variability. The methodology is implemented in the Python package mcarma.

翻译：暂无翻译