Sparse Bayesian vector autoregressions in huge dimensions

We develop a Bayesian vector autoregressive (VAR) model with multivariate stochastic volatility that is capable of handling vast dimensional information sets. Three features are introduced to permit reliable estimation of the model. First, we assume that the reduced-form errors in the VAR feature a factor stochastic volatility structure, allowing for conditional equation-by-equation estimation. Second, we apply recently developed global-local shrinkage priors to the VAR coefficients to cure the curse of dimensionality. Third, we utilize recent innovations to efficiently sample from high-dimensional multivariate Gaussian distributions. This makes simulation-based fully Bayesian inference feasible when the dimensionality is large but the time series length is moderate. We demonstrate the merits of our approach in an extensive simulation study and apply the model to US macroeconomic data to evaluate its forecasting capabilities

Sophisticated and small versus simple and sizeable: When does it pay off to introduce drifting coefficients in Bayesian VARs?

We assess the relationship between model size and complexity in the time-varying parameter VAR framework via thorough predictive exercises for the Euro Area, the United Kingdom and the United States. It turns out that sophisticated dynamics through drifting coefficients are important in small data sets while simpler models tend to perform better in sizeable data sets. To combine best of both worlds, novel shrinkage priors help to mitigate the curse of dimensionality, resulting in competitive forecasts for all scenarios considered. Furthermore, we discuss dynamic model selection to improve upon the best performing individual model for each point in time

Introducing shrinkage in heavy-tailed state space models to predict equity excess returns

We forecast S&P 500 excess returns using a flexible Bayesian econometric state space model with non-Gaussian features at several levels. More precisely, we control for overparameterization via novel global-local shrinkage priors on the state innovation variances as well as the time-invariant part of the state space model. The shrinkage priors are complemented by heavy tailed state innovations that cater for potential large breaks in the latent states. Moreover, we allow for leptokurtic stochastic volatility in the observation equation. The empirical findings indicate that several variants of the proposed approach outperform typical competitors frequently used in the literature, both in terms of point and density forecasts

Density Forecasting using Bayesian Global Vector Autoregressions with Common Stochastic Volatility

This paper puts forward a Bayesian Global Vector Autoregressive Model with Common Stochastic Volatility (B-GVAR-CSV). We assume that Country specific volatility is driven by a single latent stochastic process, which simplifies the analysis and implies significant computational gains. Apart from computational advantages, this is also justified on the ground that the volatility of most macroeconomic quantities considered in our application tends to follow a similar pattern. Furthermore, Minnesota priors are used to introduce shrinkage to cure the curse of dimensionality. Finally, this model is then used to produce predictive densities for a set of macroeconomic aggregates. The dataset employed consists of quarterly data spanning from 1995:Q1 to 2012:Q4 and includes 45 economies plus the Euro Area. Our results indicate that stochastic volatility specifications influences accuracy along two dimensions: First, it helps to increase the overall predictive fit of our model. This result can be seen for some variables under scrutiny, most notably for real GDP and short-term interest rates. Second, it helps to make the model more resilient with respect to outliers and economic crises. This implies that when evaluated over time, the log predictive scores tend to show significantly less variation as compared to homoscedastic models. (author's abstract)Series: Department of Economics Working Paper Serie

Dealing with heterogeneity in panel VARs using sparse finite mixtures

In this paper, we provide a parsimonious means of estimating panel VARs with stochastic volatility. We assume that coefficients associated with domestic lagged endogenous variables arise from a finite mixture of Gaussian distribution. Shrinkage on the cluster size is introduced through suitable priors on the component weights and cluster-relevant quantities are identified through novel normal-gamma shrinkage priors. To assess whether dynamic interdependencies between units are needed, we moreover impose shrinkage priors on the coefficients related to other countries' endogenous variables. Finally, our model controls for static interdependencies by assuming that the reduced form shocks of the model feature a factor stochastic volatility structure. We assess the merits of the proposed approach by using synthetic data as well as a real data application. In the empirical application, we forecast Eurozone unemployment rates and show that our proposed approach works well in terms of predictions.Series: Department of Economics Working Paper Serie