# Bayesian Vector Autoregression Models

Posterior estimation and simulation using a variety of prior models for VARX model coefficients and innovations covariance matrix

A Bayesian vector autoregression (VAR) model assumes a prior probability distribution on all model coefficients (AR coefficient matrices, model constant vector, linear time trend vector, and exogenous regression coefficient matrix) and the innovations covariance matrix. When combined with data to form a posterior distribution, this framework can lead to a more flexible model and intuitive inferences.

To start a Bayesian VAR analysis, create the prior model object that best describes your prior assumptions on the joint distribution of the coefficients and innovations covariance matrix. `bayesvarm` creates Bayesian VAR models with a Minnesota prior regularization structure. Then, using the prior model and data, estimate characteristics of the posterior distributions, simulate from the posterior distributions, or forecast responses using the predictive posterior distribution.

## Objects

 `normalbvarm` Bayesian vector autoregression (VAR) model with normal conjugate prior and fixed covariance for data likelihood (Since R2020a) `conjugatebvarm` Bayesian vector autoregression (VAR) model with conjugate prior for data likelihood (Since R2020a) `semiconjugatebvarm` Bayesian vector autoregression (VAR) model with semiconjugate prior for data likelihood (Since R2020a) `diffusebvarm` Bayesian vector autoregression (VAR) model with diffuse prior for data likelihood (Since R2020a) `empiricalbvarm` Bayesian vector autoregression (VAR) model with samples from prior or posterior distribution (Since R2020a)

## Functions

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 `bayesvarm` Create prior Bayesian vector autoregression (VAR) model object (Since R2020a)
 `estimate` Estimate posterior distribution of Bayesian vector autoregression (VAR) model parameters (Since R2020a) `summarize` Distribution summary statistics of Bayesian vector autoregression (VAR) model (Since R2020a)
 `simsmooth` Simulation smoother of Bayesian vector autoregression (VAR) model (Since R2020a) `simulate` Simulate coefficients and innovations covariance matrix of Bayesian vector autoregression (VAR) model (Since R2020a)
 `forecast` Forecast responses from Bayesian vector autoregression (VAR) model (Since R2020a)