Heteroscedastic Proxy Vector Autoregressions

Bayesian Vector Autoregressions

This article provides an introduction to the burgeoning academic literature on Bayesian Vector Autoregressions, benchmark models for applied macroeconomic research. We first explain Bayes’ theorem and the derivation of the closed-form solution for the posterior distribution of the parameters of the model given data. We further consider parameter shrinkage, a distinguishing feature of the prior ...

Vector Autoregressions and Cointegration*

Prior Selection for Vector Autoregressions∗

Vector autoregressions (VARs) are flexible time series models that can capture complex dynamic interrelationships among macroeconomic variables. However, their dense parameterization leads to unstable inference and inaccurate out-ofsample forecasts, particularly for models with many variables. A potential solution to this problem is to use informative priors, in order to shrink the richly param...

Heteroscedastic Relevance Vector Machine

In this work we first propose a heteroscedastic generalization to RVM, a fast Bayesian framework for regression, based on some recent similar works. We use variational approximation and expectation propagation to tackle the problem. The work is still under progress and we are examining the results and comparing with the previous works.

Priors about Observables in Vector Autoregressions

Standard practice in Bayesian VARs is to formulate priors on the autoregressive parameters, but economists and policy makers actually have priors about the behavior of observable variables. We show how this kind of prior can be used in a VAR under strict probability theory principles. We state the inverse problem to be solved and we propose a numerical algorithm that works well in practical sit...