%% Default Diffuse Prior Model
% Consider the 3-D VAR(4) model for the US inflation (INFL), unemployment (UNRATE), and federal funds (FEDFUNDS) rates.
% \left[ {\begin{array}{*{20}{l}}
% {\texttt{INFL}_t}\\
% {\texttt{UNRATE}_t}\\
% {\texttt{FEDFUNDS}_t}
% \end{array}} \right] = c + \sum\limits_{j = 1}^4 {{\Phi _j}\left[ {\begin{array}{*{20}{l}}
% {\texttt{INFL}_{t-j}\\
% {\texttt{UNRATE}_{t-j}\\
% {\texttt{FEDFUNDS}_{t-j}
% \end{array}} \right]} + \left[ {\begin{array}{*{20}{c}}
% {{\varepsilon _{1,t}}}\\
% {{\varepsilon _{2,t}}}\\
% {{\varepsilon _{3,t}}}
% \end{array}} \right].
% For all t, \varepsilon_t is a series of independent 3-D normal innovations with a mean of 0 and variance \Sigma.
% Suppose that the AR coefficient matrices \Phi_1 ,\ldotp \ldotp \ldotp ,\Phi_4, model constant c, and innovations covariance matrix \Sigma are random variables, and their prior distributions are unknown. In this case, use the noninformative diffuse prior: the joint prior distribution \left(\Phi_1 ,\ldotp \ldotp \ldotp ,\Phi_4 ,c,\Sigma \right)is proportional to {\left| \Sigma  \right|^{ - 2}}.
% Create a diffuse prior model for the 3-D VAR(4) model parameters, which is the default prior model type.

numseries = 3;
numlags = 4;
PriorMdl = bayesvarm(numseries,numlags)

% PriorMdl is a diffusevarm Bayesian VAR model object representing the prior distribution of the AR coefficient matrices, model constant vector, and innovations covariance matrix. bayesvarm displays a summary of the prior distributions at the command line.
% AR — Prior means of the AR coefficient matrices.
% Constant — Prior means of the model constant vector.
% Trend and Beta — Prior means of the linear time trend vector and exogenous regression coefficient matrix, respectively.  Because the values are empty arrays, the corresponding parameters are not in the model.
% Covariance — Prior mean of the innovations covariance matrix.
% If you have data, then you can estimate characteristics of the posterior distribution by passing PriorMdl and the data to estimate.
% Copyright 2020 The MathWorks, Inc.
%