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Ck = [ -y(t) -y(t-1) -y(t-10) -y(t-12) -y(t-22) -y(t-23) -y(t-24) h_et(t-1) h_et(t-12) h_et(t-13) h_et(t-22) h_et(t-23) h_et(t-24) ut(t-1) ]; % C_{t+1|t} yk = Ck*xt(:,t); % \hat{y}_{t+1|t} = C_{t+1|t} A x_{t|t} Ck2 = [ -yk -y(t) -y(t-9) -y(t-11) -y(t-21) -y(t-22) -y(t-23) h_et(t) h_et(t-11) h_et(t-12) h_et(t-21) h_et(t-22) h_et(t-23) ut(t) ]; % C_{t+1|t} yk2 = Ck2*xt(:,t); % \hat{y}_{t+1|t} = C_{t+1|t} A x_{t|t} % Note that the k-step predictions is formed using the k-1, k-2, ... % predictions, with the predicted future noises being set to zero. If % the ARMA has a higher order AR part, one needs to keep track of each % of the earlier predicted values. for k0=3:k Ck = [ -yk2 -yk -y(t-11+k0) -y(t-13+k0) -y(t-23+k0) -y(t-24+k0) -y(t-25+k0) h_et(t-2+k0) h_et(t-13+k0) h_et(t-14+k0) h_et(t-23+k0) h_et(t-24+k0) h_et(t-25+k0) ut(t-2+k0) ]; % C_{t+k|t} yk = Ck*A^k*xt(:,t); % \hat{y}_{t+k|t} = C_{t+k|t} A^k x_{t|t} end yhatk(t+k) = yk; % Note that this should be stored at t+k. %h_et_k(t+k) = y(t+k)-yhat(t+k); end
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