Florian Huber, Gary Koop, Massimiliano Marcellino, Tobias Scheckel
{"title":"Bayesian modelling of VAR precision matrices using stochastic block networks","authors":"Florian Huber, Gary Koop, Massimiliano Marcellino, Tobias Scheckel","doi":"arxiv-2407.16349","DOIUrl":null,"url":null,"abstract":"Commonly used priors for Vector Autoregressions (VARs) induce shrinkage on\nthe autoregressive coefficients. Introducing shrinkage on the error covariance\nmatrix is sometimes done but, in the vast majority of cases, without\nconsidering the network structure of the shocks and by placing the prior on the\nlower Cholesky factor of the precision matrix. In this paper, we propose a\nprior on the VAR error precision matrix directly. Our prior, which resembles a\nstandard spike and slab prior, models variable inclusion probabilities through\na stochastic block model that clusters shocks into groups. Within groups, the\nprobability of having relations across group members is higher (inducing less\nsparsity) whereas relations across groups imply a lower probability that\nmembers of each group are conditionally related. We show in simulations that\nour approach recovers the true network structure well. Using a US macroeconomic\ndata set, we illustrate how our approach can be used to cluster shocks together\nand that this feature leads to improved density forecasts.","PeriodicalId":501293,"journal":{"name":"arXiv - ECON - Econometrics","volume":"306 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - ECON - Econometrics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.16349","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Commonly used priors for Vector Autoregressions (VARs) induce shrinkage on
the autoregressive coefficients. Introducing shrinkage on the error covariance
matrix is sometimes done but, in the vast majority of cases, without
considering the network structure of the shocks and by placing the prior on the
lower Cholesky factor of the precision matrix. In this paper, we propose a
prior on the VAR error precision matrix directly. Our prior, which resembles a
standard spike and slab prior, models variable inclusion probabilities through
a stochastic block model that clusters shocks into groups. Within groups, the
probability of having relations across group members is higher (inducing less
sparsity) whereas relations across groups imply a lower probability that
members of each group are conditionally related. We show in simulations that
our approach recovers the true network structure well. Using a US macroeconomic
data set, we illustrate how our approach can be used to cluster shocks together
and that this feature leads to improved density forecasts.
矢量自回归(VAR)常用的先验值会引起自回归系数的收缩。有时也会在误差协方差矩阵上引入收缩,但在绝大多数情况下,都没有考虑冲击的网络结构,而是将先验值置于精度矩阵的较低 Cholesky 因子上。在本文中,我们直接提出了 VAR 误差精度矩阵的先验值。我们的先验类似于标准的尖峰先验和板块先验,通过随机块模型对变量包含概率进行建模,将冲击聚类成组。在组内,组内成员之间存在关系的概率较高(导致较低的稀疏性),而组间关系则意味着每个组的成员之间存在条件关系的概率较低。我们的模拟结果表明,我们的方法很好地还原了真实的网络结构。通过使用美国宏观经济数据集,我们说明了如何使用我们的方法将冲击聚集在一起,并说明这一特征可以改善密度预测。