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Working Paper
Large Vector Autoregressions with Stochastic Volatility and Flexible Priors
Recent research has shown that a reliable vector autoregressive model (VAR) for forecasting and structural analysis of macroeconomic data requires a large set of variables and modeling time variation in their volatilities. Yet, there are no papers jointly allowing for stochastic volatilities and large datasets, due to computational complexity. Moreover, homoskedastic VAR models for large datasets so far restrict substantially the allowed prior distributions on the parameters. In this paper we propose a new Bayesian estimation procedure for (possibly very large) VARs featuring time varying ...
Working Paper
Tail Forecasting with Multivariate Bayesian Additive Regression Trees
We develop multivariate time series models using Bayesian additive regression trees that posit nonlinearities among macroeconomic variables, their lags, and possibly their lagged errors. The error variances can be stable, feature stochastic volatility, or follow a nonparametric specification. We evaluate density and tail forecast performance for a set of US macroeconomic and financial indicators. Our results suggest that the proposed models improve forecast accuracy both overall and in the tails. Another finding is that when allowing for nonlinearities in the conditional mean, ...
Working Paper
Have Standard VARs Remained Stable since the Crisis?
Small or medium-scale VARs are commonly used in applied macroeconomics for forecasting and evaluating the shock transmission mechanism. This requires the VAR parameters to be stable over the evaluation and forecast sample, or to explicitly consider parameter time variation. The earlier literature focused on whether there were sizable parameter changes in the early 1980s, in either the conditional mean or variance parameters, and in the subsequent period till the beginning of the new century. In this paper we conduct a similar analysis but focus on the effects of the recent crisis. Using a ...
Working Paper
Capturing Macroeconomic Tail Risks with Bayesian Vector Autoregressions
A rapidly growing body of research has examined tail risks in macroeconomic outcomes. Most of this work has focused on the risks of significant declines in GDP, and has relied on quantile regression methods to estimate tail risks. In this paper we examine the ability of Bayesian VARs with stochastic volatility to capture tail risks in macroeconomic forecast distributions and outcomes. We consider both a conventional stochastic volatility specification and a specification featuring a common volatility factor that is a function of past financial conditions. Even though the conditional ...
Working Paper
Tail Forecasting with Multivariate Bayesian Additive Regression Trees
We develop novel multivariate time series models using Bayesian additive regression trees that posit nonlinear relationships among macroeconomic variables, their lags, and possibly the lags of the errors. The variance of the errors can be stable, driven by stochastic volatility (SV), or follow a novel nonparametric specification. Estimation is carried out using scalable Markov chain Monte Carlo estimation algorithms for each specification. We evaluate the real-time density and tail forecasting performance of the various models for a set of US macroeconomic and financial indicators. Our ...
Working Paper
Empirical simultaneous prediction regions for path-forecasts
This paper investigates the problem of constructing prediction regions for forecast trajectories 1 to H periods into the future - a path forecast. We take the more general view that the null model is only approximative and in some cases it may be altogether unavailable. As a consequence, one cannot derive the usual analytic expressions nor resample from the null model as is usually done when bootstrap methods are used. The paper derives methods to construct approximate rectangular regions for simultaneous probability coverage which correct for serial correlation. The techniques appear to work ...
Working Paper
Assessing International Commonality in Macroeconomic Uncertainty and Its Effects
This paper uses a large vector autoregression (VAR) to measure international macroeconomic uncertainty and its effects on major economies, using two datasets, one with GDP growth rates for 19 industrialized countries and the other with a larger set of macroeconomic indicators for the U.S., euro area, and U.K. Using basic factor model diagnostics, we first provide evidence of significant commonality in international macroeconomic volatility, with one common factor accounting for strong comovement across economies and variables. We then turn to measuring uncertainty and its effects with a large ...
Working Paper
Forecasting US Inflation Using Bayesian Nonparametric Models
The relationship between inflation and predictors such as unemployment is potentially nonlinear with a strength that varies over time, and prediction errors error may be subject to large, asymmetric shocks. Inspired by these concerns, we develop a model for inflation forecasting that is nonparametric both in the conditional mean and in the error using Gaussian and Dirichlet processes, respectively. We discuss how both these features may be important in producing accurate forecasts of inflation. In a forecasting exercise involving CPI inflation, we find that our approach has substantial ...
Working Paper
Common drifting volatility in large Bayesian VARs
The estimation of large vector autoregressions with stochastic volatility using standard methods is computationally very demanding. In this paper we propose to model conditional volatilities as driven by a single common unobserved factor.> This is justified by the observation that the pattern of estimated volatilities in empirical analyses is often very similar across variables. Using a combination of a standard natural conjugate prior for the VAR coefficients and an independent prior on a common stochastic volatility factor, we derive the posterior densities for the parameters of the ...
Working Paper
Measuring Uncertainty and Its Effects in the COVID-19 Era
We measure the effects of the COVID-19 outbreak on uncertainty, and we assess the consequences of the uncertainty for key economic variables. We use a large, heteroskedastic vector autoregression (VAR) in which the error volatilities share two common factors, interpreted as macro and financial uncertainty. Macro and financial uncertainty are allowed to contemporaneously affect the macroeconomy and financial conditions, with changes in the common component of the volatilities providing contemporaneous identifying information on uncertainty. The model includes additional latent volatility ...