New Frontiers in Bayesian Econometrics and Forecasting

Vector autoregression (VAR) models are crucial for forecasting and analyzing macroeconomic variables, serving as a fundamental tool for applied macroeconomists. Recent literature has explored nonparametric approaches, such as Bayesian additive regression trees (BART), which allow for flexibility without strong parametric assumptions; however, existing frameworks like that proposed by (Huber and Rossini, 2022) do not adequately accommodate high-dimensional data or time dependency in the prior construction. This study enhances the literature by extending previous work to enable high-dimensional data analysis and variable selection through a sparsity-inducing Dirichlet hyperprior, as in Linero (2018) on the regression tree's splitting probabilities, while also proposing a prior that decrease the probability of splitting on variables that are have higher lags than smaller lags, similar to the approach taken by the Minnesota Prior. Empirical results show improvement compared to the baseline BART prior structure and a BVAR.  

Large datasets of matrix-valued time-series are increasingly common in
economics and finance, but they are typically subjected to complex missing
data patterns, such as unbalanced panels and mixed-frequency settings.
We develop a data augmentation scheme that can handle a large number
of missing values and complex cross-sectional and temporal correlation
structures. We illustrate the methodology by producing model-based
estimates of US state-level quarterly GDP from 1988 using a large dataset
of over 400 time-series. These include state-level quarterly GDP data from
2005, state-level annual GDP data from 1997, as well as a wide range of
state-level macroeconomic variables from 1988. 

Multivariate time series (MTS) data often include a heterogeneous mix of non-Gaussian distributional features (asymmetry, multimodality, heavy tails) and data types (continuous and discrete variables). Traditional MTS methods based on convenient parametric distributions are typically ill-equipped to model this heterogeneity. Copula models provide an appealing alternative, but present significant obstacles for fully Bayesian inference and probabilistic forecasting. To overcome these challenges, we propose a novel and general strategy for posterior approximation in MTS copula models and apply it to a Gaussian copula built from a dynamic factor model. This framework provides scalable, fully Bayesian inference for cross-sectional and serial dependencies and nonparametrically learns heterogeneous marginal distributions. We validate this approach by establishing posterior consistency and confirm excellent finite-sample performance even under model misspecification using simulated data. We apply our method to crime count and macroeconomic MTS data and find superior probabilistic forecasting performance compared to popular MTS models. These results demonstrate that the proposed method is a versatile, general-purpose utility for probabilistic forecasting of MTS that works well across of range of applications with minimal user input.

Paper: https://arxiv.org/abs/2502.16874 

In cases where simulation-based models lack a tractable likelihood, Bayesian inference traditionally relies on Approximate Bayesian Computation (ABC). More recently, generative models have been used to approximate the posterior distribution directly. However, the computational cost of generating enough simulated samples to resemble the observed dataset typically grows exponentially with the dimensionality of the parameter space. To address this scalability issue, we propose an optimization-driven approach to inference. We also provide theoretical analysis demonstrating how our approach scales more efficiently with the dimensionality of the parameter space, offering a more practical solution for high-dimensional simulator models.