statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

and econometrics, Bayesian vector autoregression (BVAR) uses

Bayesian methods Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and e ...

to estimate a vector autoregression (VAR) model. BVAR differs with standard VAR models in that the model parameters are treated as

random variable A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...

s, with prior probabilities, rather than fixed values. Vector autoregressions are flexible statistical models that typically include many free parameters. Given the limited length of standar
macroeconomic datasets
relative to the vast number of parameters available, Bayesian methods have become an increasingly popular way of dealing with the problem of over-parameterization. As the ratio of variables to observations increases, the role of prior probabilities becomes increasingly important. The general idea is to use informative priors to shrink the unrestricted model towards a parsimonious naïve benchmark, thereby reducing parameter uncertainty and improving forecast accuracy. A typical example is the shrinkage prior, proposed by Robert Litterman (1979) and subsequently developed by other researchers at University of Minnesota, (i.e. Sims C, 1989), which is known in the BVAR literature as the "Minnesota prior". The informativeness of the prior can be set by treating it as an additional parameter based on a hierarchical interpretation of the model. In particular, the Minnesota prior assumes that each variable follows a random walk process, possibly with drift, and therefore consists of a normal prior on a set of parameters with fixed and known covariance matrix, which will be estimated with one of three techniques: Univariate AR, Diagonal VAR, or Full VAR. This type model can be estimated with Eviews,

Stata Stata (, , alternatively , occasionally stylized as STATA) is a general-purpose statistical software package developed by StataCorp for data manipulation, visualization, statistics, and automated reporting. It is used by researchers in many fie ...

, Python or R Statistical Packages. Recent research has shown that Bayesian vector autoregression is an appropriate tool for modelling large data sets.

See also

References

Further reading