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面向二元、删失与计数变量的大型贝叶斯VARAI 解读

We extend the vector autoregression (VAR) to model binary, censored, count and unrestricted variables jointly, treating missing observations of any type in the same way. Each restricted observation is linked to a latent Gaussian variable, so that the standard machinery for VARs, such as shrinkage priors, stochastic volatility and outlier components, applies directly to the VAR for the latent variables. The latent variables have a truncated normal conditional distribution…

非高斯状态空间模型的精确拒绝采样AI 解读

Rejection sampling requires a proposal that dominates the target by a known constant, generally unavailable for non-Gaussian state space models. We construct such a proposal for the latent state path, yielding independent exact smoothing draws and an unbiased likelihood estimator whose relative variance is at most $1/p-1$ per draw at acceptance probability $p$. The method covers scalar states with affine Gaussian dynamics and log-concave observation densities, including…

高维矩阵值时间序列的贝叶斯动态因子模型AI 解读

We introduce a class of Bayesian dynamic factor models for matrix-valued time series, with autoregressive factor dynamics and idiosyncratic components that allow stochastic volatility, outliers, and a Kronecker-structured covariance capturing cross-row and cross-column correlation. Exploiting the matrix structure, we make these richly parameterized models tractable in high dimensions and develop an efficient Gibbs sampler for estimation. For model comparison, we propose a…

具有随机波动率的大型贝叶斯张量 VARAI 解读

We consider Bayesian tensor vector autoregressions (TVARs) in which the VAR coefficients are arranged as a three-dimensional array or tensor, and this coefficient tensor is parameterized using a low-rank CP decomposition. We develop a family of TVARs using a general stochastic volatility specification, which includes a wide variety of commonly-used multivariate stochastic volatility and COVID-19 outlier-augmented models. In a forecasting exercise involving 40 US quarterly…

多重等式与不等式约束下大型贝叶斯 VAR 的条件预测AI 解读

Conditional forecasts, i.e. projections of a set of variables of interest on the future paths of some other variables, are used routinely by empirical macroeconomists in a number of applied settings. In spite of this, the existing algorithms used to generate conditional forecasts tend to be very computationally intensive, especially when working with large Vector Autoregressions or when multiple linear equality and inequality constraints are imposed at once. We introduce a…

线性不等式约束下未观测成分模型的参数估计AI 解读

We propose a new \textit{quadratic programming-based} method of approximating a nonstandard density using a multivariate Gaussian density. Such nonstandard densities usually arise while developing posterior samplers for unobserved components models involving inequality constraints on the parameters. For instance, Chan et al. (2016) provided a new model of trend inflation with linear inequality constraints on the stochastic trend. We implemented the proposed quadratic…

含缺失数据的高维条件高斯状态空间模型AI 解读

We develop an efficient sampling approach for handling complex missing data patterns and a large number of missing observations in conditionally Gaussian state space models. Two important examples are dynamic factor models with unbalanced datasets and large Bayesian VARs with variables in multiple frequencies. A key insight underlying the proposed approach is that the joint distribution of the missing data conditional on the observed data is Gaussian. Moreover, the inverse…

大型贝叶斯 VAR 的随机波动率设定比较AI 解读

Large Bayesian vector autoregressions with various forms of stochastic volatility have become increasingly popular in empirical macroeconomics. One main difficulty for practitioners is to choose the most suitable stochastic volatility specification for their particular application. We develop Bayesian model comparison methods -- based on marginal likelihood estimators that combine conditional Monte Carlo and adaptive importance sampling -- to choose among a variety of…

大型随机波动贝叶斯 VAR 的快速精确变分推断AI 解读

We propose a new variational approximation of the joint posterior distribution of the log-volatility in the context of large Bayesian VARs. In contrast to existing approaches that are based on local approximations, the new proposal provides a global approximation that takes into account the entire support of the joint distribution. In a Monte Carlo study we show that the new global approximation is over an order of magnitude more accurate than existing alternatives. We…

大型混合时变参数 VAR 模型AI 解读

Time-varying parameter VARs with stochastic volatility are routinely used for structural analysis and forecasting in settings involving a few endogenous variables. Applying these models to high-dimensional datasets has proved to be challenging due to intensive computations and over-parameterization concerns. We develop an efficient Bayesian sparsification method for a class of models we call hybrid TVP-VARs--VARs with time-varying parameters in some equations but constant…

状态空间混频 VAR 的高效估计：基于精度矩阵的方法AI 解读

State-space mixed-frequency vector autoregressions are now widely used for nowcasting. Despite their popularity, estimating such models can be computationally intensive, especially for large systems with stochastic volatility. To tackle the computational challenges, we propose two novel precision-based samplers to draw the missing observations of the low-frequency variables in these models, building on recent advances in the band and sparse matrix algorithms for state-space…

具有随机波动率的大型排序不变贝叶斯 VARAI 解读

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 Cholesky decomposition for 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 Cholesky decomposition. We show that the presence of multivariate…

大型贝叶斯 VAR 的非对称共轭先验AI 解读

Large Bayesian VARs are now widely used in empirical macroeconomics. One popular shrinkage prior in this setting is the natural conjugate prior as it facilitates posterior simulation and leads to a range of useful analytical results. This is, however, at the expense of modeling flexibility, as it rules out cross-variable shrinkage -- i.e., shrinking coefficients on lags of other variables more aggressively than those on own lags. We develop a prior that has the best of both…