多元连续时间自回归滑动平均过程用于天文多波段时间序列
Multivariate Continuous-Time Autoregressive Moving Average Processes for Astronomical Multiband Time Series
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中文总结 AI 辅助
本文提出MCARMA框架处理天文多波段不规则采样时间序列，通过两阶段估计和联合建模利用跨波段依赖，提升参数与谱恢复，并在SDSS类星体数据中验证。Python包mcarma实现。
中文摘要 AI 辅助
大规模天文巡天提供了通过多个光学滤光片获得的空前数量的多元时间序列观测。我们开发了一个结构化的多元连续时间自回归滑动平均（MCARMA）框架，用于具有不规则采样、异方差测量误差和部分观测波段的多波段时间序列。该框架允许特定波段的随机动力学，同时通过相关的布朗驱动过程建模跨波段依赖性，其状态空间和谱表示使得基于似然的推断和拟合随机动力学的解释成为可能。我们开发了一个两阶段估计程序，其中数值稳定的初步拟合初始化后续的最大似然估计。模拟表明，当高阶随机结构的特征特征被充分解析时，可以恢复该结构，但由于有限的时间分辨率或接近极点-零点抵消，其可识别性可能变弱。相对于单独的单波段拟合，联合多元估计在27个设置中的23个中改善了参数恢复，在27个设置中的26个中改善了谱恢复。三个斯隆数字巡天Stripe 82类星体，分别倾向于MCARMA(1,0)、MCARMA(2,0)和MCARMA(2,1)，说明了联合多波段建模如何利用跨波段依赖性来告知边际动力学，并可能产生不同的模型阶数和谱推断。该方法已在Python包mcarma中实现。
英文摘要
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.
发表机构
- Oregon State University（俄勒冈州立大学）
- Pennsylvania State University（宾夕法尼亚州立大学）
- Seoul National University（首尔国立大学）
机构由 AI 辅助整理，请以论文原文为准。
