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1 function [ypred, ll, mse] = eval_AR_perf(coef, C, y, model)
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2 % Evaluate the performance of an AR model.
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3 %
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4 % Inputs
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5 % coef(:,:,k,m) - coef. matrix to use for k steps back, model m
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6 % C(:,:,m) - cov. matrix for model m
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7 % y(:,t) - observation at time t
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8 % model(t) - which model to use at time t (defaults to 1 if not specified)
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9 %
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10 % Outputs
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11 % ypred(:,t) - the predicted value of y at t based on the evidence thru t-1.
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12 % ll - log likelihood
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13 % mse - mean squared error = sum_t d_t . d_t, where d_t = pred(y_t) - y(t)
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14
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15 [s T] = size(y);
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16 k = size(coef, 3);
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17 M = size(coef, 4);
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18
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19 if nargin<4, model = ones(1, T); end
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20
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21 ypred = zeros(s, T);
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22 ypred(:, 1:k) = y(:, 1:k);
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23 mse = 0;
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24 ll = 0;
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25 for j=1:M
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26 c(j) = log(normal_coef(C(:,:,j)));
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27 invC(:,:,j) = inv(C(:,:,j));
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28 end
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29 coef = reshape(coef, [s s*k M]);
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30
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31 for t=k+1:T
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32 m = model(t-k);
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33 past = y(:,t-1:-1:t-k);
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34 ypred(:,t) = coef(:, :, m) * past(:);
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35 d = ypred(:,t) - y(:,t);
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36 mse = mse + d' * d;
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37 ll = ll + c(m) - 0.5*(d' * invC(:,:,m) * d);
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38 end
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39 mse = mse / (T-k+1);
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40
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