Bayesian Vector Autoregression (BVAR) is a term which indicates that Bayesian methods

Bayesian inference

In statistics, Bayesian inference is a method of statistical inference. It is often used in science and engineering to determine model parameters, make predictions about unknown variables, and to perform model selection...

 are used to estimate a vector autoregression

Vector autoregression

Vector autoregression is a statistical model used to capture the linear interdependencies among multiple time series. VAR models generalize the univariate autoregression models. All the variables in a VAR are treated symmetrically; each variable has an equation explaining its evolution based on...

 (VAR). In that respect, the difference with standard VAR models lies on the fact that the model parameters are treated as random variables

Random variable

In probability and statistics, a random variable or stochastic variable is, roughly speaking, a variable whose value results from a measurement on some type of random process. Formally, it is a function from a probability space, typically to the real numbers, which is measurable functionmeasurable...

, and prior probabilities

Prior probability

In Bayesian statistical inference, a prior probability distribution, often called simply the prior, of an uncertain quantity p is the probability distribution that would express one's uncertainty about p before the "data"...

 are assigned to them.

The parameter space of VARs proliferates with the number of dependent variables and the number of lags. At the same time, (macro-) economic datasets involve monthly, quarterly or annual observations and, thus are only of moderate size. Bayesian methods have attracted attention because full and empirical Bayes estimators

Bayes estimator

In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function . Equivalently, it maximizes the posterior expectation of a utility function...

help provide shrinkage over unrestricted least squares estimates. A typical example is the shrinkage prior proposed by Robert Litterman , and subsequently developed by other researchers at University of Minnesota , which came to stay in the BVAR literature as the "Minnesota prior".

Recent research have shown that vector auto regression with Bayesian shrinkage is an appropriate tool for large scale dynamic models.