Quasar variability, driven by multi-scale physical processing within a relativistic accretion disk, is commonly modelled with stochastic time series models. The simplest of these is the Damped Random Walk (DRW), also known as the Ornstein-Uhlenbeck (OU) process. Here, we demonstrate that, when fitting such a model to quasar light curve data, the mean of the light curve, $μ$, should not be fixed (which is the typical approach), as this leads to overconfident inferences about the variability timescale $τ$, with substantially underestimated uncertainties. However, the short term volatility parameter $η$ is typically very well constrained from short light curves. Through simulations, we compute information theoretic quantities such as the conditional entropy and the mutual information, confirming that light curves provide much more information about $η$ than about $τ$. As a result, we recommend that future quasar variability studies focus on $η$ rather than $τ$. To demonstrate this approach, we fit a hierarchical Bayesian regression model for $η$ as a function of bolometric luminosity and rest wavelength to a dataset of 570 light curves measured over decades. We perform the fit using a likelihood function that uses the light curves directly, rather than using intermediate $η$ values from individual light curve fits. We find that volatility decreases as a function of both bolometric luminosity and rest wavelength. The volatility also decreases more steeply with redshift than time dilation alone would suggest, pointing to an increase in intrinsic volatility as quasars evolve over cosmic time.

翻译：类星体变光现象由相对论性吸积盘内的多尺度物理过程驱动，通常采用随机时间序列模型进行建模。其中最简单的模型是阻尼随机游走（DRW），也称为奥恩斯坦-乌伦贝克（OU）过程。本文证明，在将此类模型拟合至类星体光变曲线数据时，不应固定光变均值μ（常规处理方法），否则会导致变时标τ的推断过于自信且不确定性被严重低估。然而，短期波动参数η通常能通过短光变曲线得到良好约束。通过模拟计算条件熵和互信息等信息论量，我们证实光变曲线提供的η信息远多于τ。因此建议未来类星体变光研究应聚焦η而非τ。为展示该方法，我们建立层次贝叶斯回归模型，以辐射光度与静止波长为函数对η进行建模，并应用于570条跨度数十年的光变曲线数据集。本工作采用直接利用光变曲线的似然函数进行拟合，而非使用单条光变曲线拟合得到的中间η值。研究发现波动性随辐射光度与静止波长增加而降低。同时波动性随红移的衰减斜率比单纯时间膨胀效应更为陡峭，表明类星体在宇宙时标演化过程中固有波动性呈增强趋势。