Large Order-Invariant Bayesian VARs with Stochastic Volatility
针对现有向量自回归模型因误差协方差矩阵下三角参数化导致的变量排序依赖问题，提出一种排序不变的规范，并开发了贝叶斯估计与预测的MCMC算法。在20变量宏观经济预测中，新方法优于传统方法，且变量排序选择不当会显著降低预测精度。
Many popular specifications for Vector Autoregressions (VARs) with multivariate stochastic volatility are not invariant to the way the variables are ordered due to the use of a lower triangular parameterization of the error covariance matrix. We show that the order invariance problem in existing approaches is likely to become more serious in large VARs. We propose the use of a specification which avoids the use of this lower triangular parameterization. We show that the presence of multivariate stochastic volatility allows for identification of the proposed model and prove that it is invariant to ordering. We develop a Markov chain Monte Carlo algorithm which allows for Bayesian estimation and prediction. In exercises involving artificial and real macroeconomic data, we demonstrate that the choice of variable ordering can have non-negligible effects on empirical results when using the nonorder invariant approach. In a macroeconomic forecasting exercise involving VARs with 20 variables we find that our order-invariant approach leads to the best forecasts and that some choices of variable ordering can lead to poor forecasts using a conventional, non-order invariant, approach.