%% Prepare Prior for Exogenous Predictor Variables
% Consider the 2-D VARX(1) model for the US real GDP (RGDP) and investment (GCE) rates that treats the personal consumption (PCEC) rate as exogenous:
% \left[ {\begin{array}{*{20}{l}}
% {\texttt{RGDP}_t}\\
% {\texttt{GCE}_t}
% \end{array}} \right] = c + \Phi\left[ {\begin{array}{*{20}{l}}
% {\texttt{RGDP}_{t-1}\\
% {\texttt{GCE}_{t-1}
% \end{array}} \right] + \texttt{PCEC}_t\beta+\varepsilon_t.
% For all t, \varepsilon_t is a series of independent 2-D normal innovations with a mean of 0 and fixed covariance \Sigma = I. Assume that the prior distribution of the coefficients is \textrm{vec}\left({\left\lbrack \begin{array}{ccc}
% \Phi  & c & \beta
% \end{array}\right\rbrack }^{\prime } \right)\left|\Sigma \sim N_8 \left(\mu ,V\right)\right., where \mu is an 8-by-1 vector of means and V is the 4-by-4 covariance matrix.
% Create a normal conjugate prior model for the 2-D VARX(1) model parameters.

numseries = 2;
numlags = 1;
numpredictors = 1;
PriorMdl = normalbvarm(numseries,numlags,'NumPredictors',numpredictors)

% Display the prior mean of the coefficients Mu with the coefficient to which they correspond.

coeffnames = ["phi(11)"; "phi(12)"; "c(1)"; "beta(1)"; "phi(21)"; "phi(22)"; "c(2)"; "beta(2)"];
array2table(PriorMdl.Mu,'VariableNames',{'PriorMean'},'RowNames',coeffnames)

% Copyright 2019 The MathWorks, Inc.
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