function [A, C, Q, R, initx, initV] = ensure_AR(A, C, Q, R, initx, initV, k, obs, diagonal)%% Ensure that the system matrices have the right form for an autoregressive process.ss = length(A);if nargin<8, obs=ones(ss, 1); endif nargin<9, diagonal=0; end[coef, C] = SS_to_AR(A, Q, k, diagonal);[A, C, Q, R, initx, initV] = AR_to_SS(coef, C, obs);
function [ypred, ll, mse] = eval_AR_perf(coef, C, y, model)% Evaluate the performance of an AR model.% % Inputs% coef(:,:,k,m) - coef. matrix to use for k steps back, model m% C(:,:,m)      - cov. matrix for model m% y(:,t)        - observation at time t% model(t)      - which model to use at time t (defaults to 1 if not specified)%% Outputs% ypred(:,t)    - the predicted value of y at t based on the evidence thru t-1.% ll            - log likelihood% mse           - mean squared error = sum_t d_t . d_t, where d_t = pred(y_t) - y(t)[s T] = size(y);k = size(coef, 3);M = size(coef, 4);if nargin<4, model = ones(1, T); endypred = zeros(s, T);ypred(:, 1:k) = y(:, 1:k);mse = 0;ll = 0;for j=1:M  c(j) = log(normal_coef(C(:,:,j)));  invC(:,:,j) = inv(C(:,:,j));endcoef = reshape(coef, [s s*k M]);for t=k+1:T  m = model(t-k);  past = y(:,t-1:-1:t-k);  ypred(:,t) = coef(:, :, m) * past(:);  d = ypred(:,t) - y(:,t);  mse = mse + d' * d;  ll = ll + c(m) - 0.5*(d' * invC(:,:,m) * d);endmse = mse / (T-k+1);