We develop a Coordinate Ascent Variational Inference (CAVI) algorithm for Bayesian Mixed Data Sampling (MIDAS) regression with linear weight parameterizations. The model separates impact coeffcients from weighting function parameters through a normalization constraint, creating a bilinear structure that renders generic Hamiltonian Monte Carlo samplers unreliable while preserving conditional conjugacy exploitable by CAVI. Each variational update admits a closed-form solution: Gaussian for regression coefficients and weight parameters, Inverse-Gamma for the error variance. The algorithm propagates uncertainty across blocks through second moments, distinguishing it from naive plug-in approximations. In a Monte Carlo study spanning 21 data-generating configurations with up to 50 predictors, CAVI produces posterior means nearly identical to a block Gibbs sampler benchmark while achieving speedups of 107x to 1,772x (Table 9). Generic automatic differentiation VI (ADVI), by contrast, produces bias 714 times larger while being orders of magnitude slower, confirming the value of model-specific derivations. Weight function parameters maintain excellent calibration (coverage above 92%) across all configurations. Impact coefficient credible intervals exhibit the underdispersion characteristic of mean-field approximations, with coverage declining from 89% to 55% as the number of predictors grows a documented trade-off between speed and interval calibration that structured variational methods can address. An empirical application to realized volatility forecasting on S&P 500 daily returns cofirms that CAVI and Gibbs sampling yield virtually identical point forecasts, with CAVI completing each monthly estimation in under 10 milliseconds.

翻译：本文针对采用线性权重参数化的贝叶斯混合数据抽样（MIDAS）回归模型，开发了一种坐标上升变分推断（CAVI）算法。该模型通过归一化约束将影响系数与权重函数参数分离，形成双线性结构——这种结构虽使通用哈密顿蒙特卡洛采样器不可靠，却保留了CAVI可利用的条件共轭性。每个变分更新均存在闭式解：回归系数和权重参数服从高斯分布，误差方差服从逆伽马分布。该算法通过二阶矩在参数块间传递不确定性，从而区别于简单的插件近似法。在涵盖21种数据生成配置（最多包含50个预测变量）的蒙特卡洛研究中，CAVI产生的后验均值与分块吉布斯采样基准几乎完全相同，同时实现了107倍至1,772倍的加速（表9）。相比之下，通用自动微分变分推断（ADVI）产生的偏差增大了714倍，且速度慢数个数量级，这证实了模型特定推导的价值。权重函数参数在所有配置中均保持优异的校准性（覆盖率达到92%以上）。影响系数的可信区间表现出平均场近似特有的欠分散特征：随着预测变量数量增加，覆盖率从89%下降至55%——这是速度与区间校准之间已知的权衡关系，结构化变分方法可对此进行改进。在标准普尔500指数日收益率已实现波动率预测的实证应用中，CAVI与吉布斯采样产生了几乎完全相同的点预测结果，且CAVI每次月度估计可在10毫秒内完成。