Forecasting with Bayesian Vector Autoregressions with Time Variation in the Mean

Abstract

We develop a vector autoregressive model with time variation in the mean and the variance. The unobserved time-varying mean is assumed to follow a random walk and we also link it to long-term Consensus forecasts, similar in spirit to so called democratic priors. The changes in variance are modelled via stochastic volatility. The proposed Gibbs sampler allows the researcher to use a large cross-sectional dimension in a feasible amount of computational time. The slowly changing mean can account for a number of secular developments such as changing inflation expectations, slowing productivity growth or demographics. We show the good forecasting performance of the model relative to popular alternatives, including standard Bayesian VARs with Minnesota priors, VARs with democratic priors and standard time-varying parameter VARs for the euro area, the United States and Japan. In particular, incorporating survey forecast information helps to reduce the uncertainty about the unconditional mean and along with the time variation improves the long-run forecasting performance of the VAR models.

Large mixed-frequency VARs with a parsimonious time-varying parameter structure

“… 4 A third related paper is the one by Bańbura and van Vlodrop ( 2018 ), although their time-varying VAR includes only a single frequency. As in our model, though, time variation is restricted to certain parameters.…”

“…While this complicates the estimation, it is typically easier to elicit informative priors for the unconditional mean. Bańbura and van Vlodrop ( 2018 ) even take one promising step further and link the unconditional mean to long-run Consensus forecasts.…”

An Overview of Dynamic Model Averaging Techniques in Time‐series Econometrics

“…Interestingly, in recent years a number of studies have tried to propose solutions to this problem. For instance, Banbura and van Vlodrop (2018) and Götz and Hauzenberger (2018) consider a large VAR with only time-varying intercepts, Chan (2019) suggests a large hybrid TVP-VAR model, Eisenstat et al (2020) model the time-varying regressison coefficients using a reduced-rank structure, and Huber et al (2020) develop a method that first shrinks the time-varying coefficients, followed by setting the small values to zero. Koop and Korobilis (2014) are the first to demonstrate that the DMA framework can be used to estimate large TVP-VAR models.…”

Bayesian VAR Forecasts, Survey Information and Structural Change in the Euro Area

“…Another related paper by Bańbura and van Vlodrop (2018) uses euro area Consensus Economics long-run forecasts to anchor a time-varying mean of a Bayesian VAR that captures low frequency movements of the variables. Different from our work, they focus on long-run forecasts from Consensus Economics, the survey information only affects the time-varying mean and the authors do not make use of survey density forecasts.…”