高维时变参数模型的综合旋转高斯近似贝叶斯推断
Bayesian Inference in High-Dimensional Time-varying Parameter Models using Integrated Rotated Gaussian Approximations
摘要：
研究者们越来越希望对包含大量解释变量的时变参数回归进行估计。包括先验信息，以减轻过度参数化的问题，导致许多使用贝叶斯方法。然而，贝叶斯马尔可夫链蒙特卡罗（MCMC）方法在计算上要求很高。在本文中，我们开发了计算效率高的贝叶斯方法估计TVP模型使用集成旋转高斯近似（IRGA）。这利用了这样一个事实，即回归变量的常系数通常很重要，而大多数TVP通常不重要。由于高斯分布对旋转是不变的，我们可以将后验分为两部分：一部分涉及常数系数，另一部分涉及TVP。对后者使用近似方法，在此条件下，前者使用MCMC方法进行精确估计。在涉及人工数据和大型宏观经济数据集的实证练习中，我们展示了IRGA方法的准确性和计算优势。
英文摘要：
Researchers increasingly wish to estimate time-varying parameter (TVP) regressions which involve a large number of explanatory variables. Including prior information to mitigate over-parameterization concerns has led to many using Bayesian methods. However, Bayesian Markov Chain Monte Carlo (MCMC) methods can be very computationally demanding. In this paper, we develop computationally efficient Bayesian methods for estimating TVP models using an integrated rotated Gaussian approximation (IRGA). This exploits the fact that whereas constant coefficients on regressors are often important, most of the TVPs are often unimportant. Since Gaussian distributions are invariant to rotations we can split the the posterior into two parts: one involving the constant coefficients, the other involving the TVPs. Approximate methods are used on the latter and, conditional on these, the former are estimated with precision using MCMC methods. In empirical exercises involving artificial data and a large macroeconomic data set, we show the accuracy and computational benefits of IRGA methods.
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