function  LogLikelihood = no_kalman(hx,gx,SigX,Y,ny,T);
%LogLikelihood = no_kalman(hx,gx,SigX,Y,ny,T);
%Computes the log-likelihood function of a linearized model of the form:
%x_{t+1} = hx * x_t + eta *epsilon_{t+1}
%y_t = gx * x_t 
%where epsilon_t distributes N(0,I)
%Inputs: 
%hx and gx  (as described above)
%SigX the unconditional variance/covariance matrix 
%of x_t (i.e., SigX satisfies SigX = hx*SigX*hx' + eta*eta'. 
%Y is a vector of stacked observations. There are ny time series each of length T, so Y is of length ny*T. 
%Specifically, if DATA is an ny-by-T matrix containing the data, then Y=DATA(:).
%ny is the number of observables
%T length of each time series
%For details see the background paper ``Evaluating the Sample Likelihood of Linearized DSGE Models Without the Use of the Kalman Filter,'' by Stephanie Schmitt-Grohe and Martin Uribe, manuscript, Duke University, September 2007.
%(This paper also explains how the program can easily accomodate measurement errors without modificaitons.)
%(c) Stephanie Schmitt-Grohe and Martin Uribe, September 2007.












HX = SigX*gx';
A=gx*HX/2;

for i=1:T
L((i-1)*ny+1:i*ny,1:size(A,2))= A;
HX = hx*HX;
A = [gx*HX A];
end

OM_inverse = inv(L+L');

LogLikelihood = - ny*T/2 * log(2*pi) + 1/2 * log(det(OM_inverse)) - 1/2 * Y' * OM_inverse * Y