% Drifting Coefficients VAR for cattle cycle
%
% Based on T.Cogley and T.J. Sargent, "Evolving Post-World War II 
% U.S. Inflation Dynamics". NBER Macroeconomics Annual.
% 

%----------------------------------------------------------------
% 0. Housekeeping
%----------------------------------------------------------------

clear all
tic

%----------------------------------------------------------------
% 1. Reading the data
%----------------------------------------------------------------

% first column # of beef, second column # slaughtered beef, third column is the index

load data


%----------------------------------------------------------------
% 2. Priors
%----------------------------------------------------------------

n_variables=3;
n_lags=1;

% theta 1|0 definition

theta = zeros(12,1);

theta(2,1) = 1;

theta(7,1) = 1;

theta(12,1) = 1;

%P 1|0 definition

p=1000*eye(12);

c = zeros(12,3);

r=10*eye(3);
q = ((0.01)^2)*p;
v = [r, c';c q];

%----------------------------------------------------------------

% 3. Likelihood

%----------------------------------------------------------------

% Given theta 1|0, P 1|0 and V, we can calculate the likelihood function....

logl = kalmanforward(y,theta,p,v)

save output_drifting_coefficients