Kalman filter question

Hello,

I am modeling the influence of systemic risk on a portfolio formed of equity indices. In the first case I am considering that stock returns are following a pure-diffusion process and every return is influenced by a marked-wide risk factor and k region-specific factors.(every international equity index belongs to a country and each country belongs to a region and there are k regions). In order to estimate the expected returns and sensitivities towards this risk I am performing a Kalman filter. This are the equations: x(t+1) = b+F*x(t) + e(t), e(t) ~ N(0,S); z(t) = a + A*x(t) + w(t), w(t)~ N(0,W) x k+1xT represents the matrix containing the brownian motion increments F-k+1xk+1; Z-nxT contains the observed returns of indices

I have tried to implement a code,but I only get 0 values or Nan for all arrays. Is definitely something wrong with the way I initialized the variables: function [xfilt, Vfilt, Vmfilt, loglik] = kalmanFilter( Z, A, W, F, S, a, b) T = size(Z,2); n = size(Z,1); k=3 xfilt = ones( k, T); Vfilt = zeros( k, k, T); Vmfilt = zeros( k, k, T); V=zeros(k,k,T) Vm=zeros(k,k,T) xhat=ones(k,T) xhatm=ones(k,T) if n~=size(A,1) error('Dimension error - A & Z must agree.'); end

if (n~=size(W,1) n~=size(W,2)) error('Dimension error - W is not valid covariance matrix.'); end

if (k~=size(F,2)) error('Dimension error - F not square.'); end

if (k~=size(A,2)) error('Dimension error - F & A do not agree.'); end

if (k~=size(S,1) k~=size(S,2)) error('Dimension error - S is not valid.'); end

if nargin < 6, a=0; else a=zeros(n,T); end if nargin < 7, b=0; else b= ones(k,T); end

% Initialize log-likelihood loglik = 0;

for i=1:T % Time update xhatm = F*xhat + b; Vm(:,:,i) = F*V(:,:,i)*F'+ S; end % Correction H = A*Vm(:,:,i)*A' + W; K = Vm(:,:,i) * A'*inv(H); xhat= xhatm+ K*(Z - a - A*xhatm); V= (eye(k) - K*A)*Vm(:,:,i)*(eye(k) - K*A)'; xfilt(:,i) = xhat(:,i); Vfilt = V; Vmfilt(:,:,i) = Vm(:,:,i); % Update log likelihood loglik = loglik -(n/2)*log(2*pi) - .5 * log( abs(det(H)) ) -.5*(( Z - a - A*xhatm )'*inv(H)*( Z - a - A*xhatm )); end

A call this funtion from another.m file: load DAT1.dat Z=DAT1 T = size(Z,2); n = size(Z,1); k = 3; xfilt = ones( k, T); Vfilt = zeros( k, k, T); Vmfilt = zeros( k, k, T); A=eye(n,k) W=zeros(n,n) F=zeros(k,k) S=zeros(k,k) a=zeros(n,T) b=ones(k,T); [xfilt, Vfilt, Vmfilt, loglik] = kalmanFilter( Z, A, W, F, S, a, b)

Could you please help me, any suggestions will be greatly appreciated?

Thank you in advance, Isabela