Asymptotically valid Bayesian inference in the presence of distributional misspecification in VAR models
VAR 分布误设下渐近有效的贝叶斯推断AI 解读 ↓
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VAR 分布误设下渐近有效的贝叶斯推断
- 研究问题
- 研究 VAR 中错误施加高斯分布假设如何影响截距、波动矩阵及脉冲响应等后验推断，以及如何修正这些可信集合的渐近有效性。
- 方法与思路
- 作者利用 QML 估计量的渐近协方差构造闭式修正后验，收缩估计创新偏度和峰度，并结合核方法处理参数不稳定情形。
- 材料陈述的贡献
- 摘要称，方法无需指定扰动分布即可提供渐近正确的后验可信集合，并通过模拟检查覆盖率，实证展示高斯及同方差假设的局限。
- 阅读关注点
- 应核对所需矩条件与依赖条件、偏度峰度收缩估计的一致性，以及后验修正如何传递到脉冲响应、方差分解和密度预测。
- 阅读边界
- 所给出版社摘要未列出全部正则条件、覆盖率数值或参数不稳定的具体形式，不能把无需指定分布理解为无需任何扰动条件。
原文摘要
Inaccurately imposing Gaussian distributional assumptions in standard multivariate time series models does not affect inference on the autoregressive coefficients but distorts both classical and Bayesian inference on the volatility matrix whenever the true error distribution has excess kurtosis relative to the multivariate normal density. Inference on the intercept is also affected whenever the innovations are generated from a non-symmetric distribution. As a result of distributional misspecification, Bayesian methods lead to asymptotically invalid posterior inference for the intercept and the volatility matrix and, consequently, invalid posterior credible sets for quantities such as impulse responses, variance decompositions and density forecasts. We propose a robust and computationally fast Bayesian procedure which delivers asymptotically correct posterior credible sets without the need for distributional assumptions. The proposed corrected Bayesian posteriors for the volatility matrix and the intercept vector are based on the asymptotic covariance of the QML estimators and admit a closed form. Implementation of the procedure requires consistent estimation of the multivariate skewness and kurtosis of the innovations, and we propose novel shrinkage estimators designed to shrink these large dimensional objects towards the skewness and kurtosis of a Gaussian vector. We extend our robust Bayesian analysis to accommodate non-Gaussian disturbances in the presence of parameter instability, by combining the estimators of the current paper with semi-parametric kernel-type methods. We demonstrate that our estimators deliver correct posterior coverage rates in an extensive Monte Carlo exercise under a variety of distributional specifications. Finally, we present empirical evidence that imposing Gaussianity or homoskedasticity assumptions on financial and uncertainty shocks is not justified and may lead to misleading empirical conclusions.