Hi everyone,
I am trying to estimate a Vector Autoregression (VAR) model with two endogenous variables and one lag using maximum likelihood (ML). My idea is to use "fminsearch" in order to minimise the (-1)*(log-likelihood), equivalently maximise the log-likelihood. However, I make a mistake and I do not see where. In particular the code seems to get stuck at the initial conditions, no matter which they are. The log-likelihood function is:
LLF = -(T*n/2)*log(2*pi) + (T/2)*log(determinant(inverse(omega))) -0.5*sum(over t) [ (y(t) - A*x(t))'*inverse(omega)*(y(t) - A*x(t))]
where n is the number of endogenous variables, my case 2 T is the sample size y(t) is a 2*1 vector of endogenous variables x(t) are the regressors. since I assume one lag, these are lagged values of y omega is the variance-covariance matrix.
My code is below, I actually create the y and x series myself. It can be run by giving the initial conditions and then executing the function as follows:
x0 = [0.5 ; 0.36 ; 0.8 ; 0.2]; [x, fval, exitflag, output] = fminsearch(@likelihood_ist, x0) ;
Does anyone have any ideas? Thanks a lot!!
******** THE CODE
function F = likelihood_ist(x)
err1 = randn(100,1); err2 = randn(100,1);
v1=zeros(90,1); v2=zeros(90,1);
for i=2:91 v1(i)= 0.8*v1(i-1) + 0.56*v2(i-1) + err1(i); v2(i)= 0.6*v2(i-1) + 0.24*v1(i-1) + err2(i); end
v1(1) = [] ; v2(1) = [] ;
SampleSize = length(v1); nvars = 2 ;
c1 = x(1) ; c2 = x(2) ; c3 = x(3) ; c4 = x(4) ; A = [c1 c2 ; c3 c4] ; omega = cov(err1, err2);
y = [v1 v2] ; for i = 2:length(y) y1 = zeros(nvars, 1); xx= zeros(nvars,1) ; y1(1) = y(i,1) ; y1(2) = y(i,2) ; xx(1) = y(i-1, 1) ; xx(2) = y(i-1, 2) ; summing(i-1) = (y1-A*xx)'*(inv(omega))*(y1-A*xx); end
allsum = sum(summing) ; F = (-1)* ((-SampleSize*nvars/2)*log(2*pi)+(SampleSize/2)*log(det(inv(omega))) - 0.5*allsum) ;
