具有Cholesky随机波动率的大型VAR模型的贝叶斯推断、在线预测与模型选择
Bayesian inference, on-line forecasting and model choice for large VAR models with Cholesky stochastic volatility
- CREST, ENSAE（CREST，ENSAE）
- ESSEC Business School（ESSEC高等商学院）
- CREST, CNRS, École Polytechnique, ENSAE（CREST，CNRS，巴黎综合理工学院，ENSAE）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种改进的MCMC核和SMC²采样器，用于Cholesky-SV BVAR模型，实现高效后验推断、在线预测和模型选择，显著提升有效样本量。
AI中文摘要：
我们考虑K维贝叶斯向量自回归（BVAR）模型，其创新协方差矩阵是K个独立单变量随机波动率（SV）过程的下三角线性变换，即Cholesky随机波动率（SV）结构。此类模型在实证宏观经济学中被广泛用于捕捉时变不确定性并提高预测精度，但后验模拟的成本成为系统规模的制约因素，也是实证工作的主要瓶颈。我们引入一种马尔可夫链蒙特卡洛（MCMC）核，在相同计算复杂度下比现有采样器具有更好的混合性能。该核基于一种重新参数化，使得K条波动率轨迹条件独立，并利用粒子吉布斯（Particle Gibbs）更新每条轨迹。该核针对精确后验而非其近似，在K=15的应用中，相对于基准修正三角算法，它将每秒平均有效样本量提高了约14倍（针对VAR系数）和3.4倍（针对波动率）。我们还引入了一种序贯蒙特卡洛平方（SMC²）采样器，该采样器以我们的MCMC核为构建块，并在每个时间t提供一步前向预测密度和截至t的数据的边际似然，从而实现在线预测和模型选择。据我们所知，这是第一个为具有静态同期系数和非共轭先验的Cholesky-SV BVAR模型提供序贯边际似然的算法。我们使用美国月度宏观经济数据对两者进行说明，其中K=15用于后验推断，K=6用于序贯采样器和模型选择。
英文摘要：
We consider $K$-dimensional Bayesian vector autoregressions (BVARs) with Cholesky stochastic volatility (SV), in which the innovation covariance matrix is a lower-triangular linear transform of $K$ independent univariate SV processes. Such models are widely used in empirical macroeconomics to capture time-varying uncertainty and improve forecast accuracy, but the cost of posterior simulation is the binding constraint on the size of the system, and a major bottleneck for empirical work. We introduce a Markov chain Monte Carlo (MCMC) kernel that mixes better than existing samplers at the same computational complexity. It rests on a reparametrisation that makes the $K$ volatility trajectories conditionally independent, and on Particle Gibbs to update each trajectory. The kernel targets the exact posterior, rather than an approximation of it, and in an application with $K = 15$ it raises the mean effective sample size per second, relative to the benchmark corrected triangular algorithm, by a factor of approximately $14$ for the VAR coefficients and $3.4$ for the volatilities. We also introduce a a Sequential Monte Carlo squared (\smcsq{}) sampler, which used our MCMC kernel as a building block, and which delivers at every $t$ the one-step-ahead predictive density and the marginal likelihood of the data up to $t$, and hence on-line forecasting and model choice. To our knowledge, this is the first algorithm that delivers sequential marginal likelihoods for Cholesky-SV BVARs with static contemporaneous coefficients and a non-conjugate prior. We illustrate both on US monthly macroeconomic data, with $K=15$ for posterior inference and $K=6$ for the sequential sampler and model choice.
