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.
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BibTeX
@misc{schmidlkofer2026multivariate,
title = {{Multivariate Continuous-Time Autoregressive Moving Average Processes for Astronomical Multiband Time Series}},
author = {Izak Schmidlkofer and Zhirui Hu and Lishan Shi and Weixiang Yu and Hyungsuk Tak},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28419},
eprint = {2609.28419},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28419},
}
RIS
TY - UNPB
TI - Multivariate Continuous-Time Autoregressive Moving Average Processes for Astronomical Multiband Time Series
AU - Izak Schmidlkofer
AU - Zhirui Hu
AU - Lishan Shi
AU - Weixiang Yu
AU - Hyungsuk Tak
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28419
UR - https://arxiv.org/abs/2609.28419
AB - 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.
ER -