# NARX closed loop performance for multi-step prediction

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EanX on 27 Jun 2014
Edited: Greg Heath on 27 Jun 2014
I'm analyzing Matlab NARX example for multi-step prediction using maglev dataset but I'm not sure on how calculate closed loop performance.
Below my code:
%%Example NARX
[X,T] = maglev_dataset; % dataset containing 4001 records
% I want to investigate how number of samples affect NARX training
% so I use only a fraction, N samples, of entire dataset
N=60;
delay=2;
X1=X(1:N+delay);
T1=T(1:N+delay);
net = narxnet(1:delay,1:delay,10);
net.divideMode='value';
% dividerand should destroy inputs autocorrelation so
% I should set 'divideblock' ?
net.divideFcn='dividerand';
net.divideParam.trainRatio=0.60;
net.divideParam.testRatio=0.10;
net.divideParam.valRatio=0.20;
[x,xi,ai,t] = preparets(net,X1,{},T1);
net = train(net,x,t,xi,ai);
y = net(x,xi,ai);
perf=perform(net,t,y);
fprintf('Performance open looop :%d\n',perf);
%%now change to closeloop
pred_horizon=20;
% number of samples necessary to set initial state
% I want to test NARX prediction capability starting
% not where training end but after some samples
x1 = X(118:120);
t1 = T(118:120);
% this is correct? I have some perplexity on how define t2 (usually not available)
t2=T(121:121+pred_horizon-1);
x2 = X(121:121+pred_horizon-1);
[x,xi,ai,t] = preparets(net,x1,{},t1);
[y1,xf,af] = net(x,xi,ai);
% is better to train again network after changing to
% closeloop with same data utilized in openloop?
[netc,xi,ai] = closeloop(net,xf,af);
[y2,xf,af] = netc(x2,xi,ai);
perfc=perform(netc,t2,y2);
fprintf('Performance closed looop :%d\n',perfc);
err=gsubtract(t2,y2);
fprintf('MSE :%f\n',mse(cell2mat(err))); % same as perfc
subplot(2,1,1);
plot([cell2mat(y2)' cell2mat(t2)']);
legend('NARX output','Real Values');
subplot(2,1,2);
plot(cell2mat(err));
figure;
% does plotting regression chart make any sense ? I obtain weird results
plotregression(t2,y2);

Greg Heath on 27 Jun 2014
Edited: Greg Heath on 27 Jun 2014
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I like this one:
Hope this helps.
Thank you for formally accepting my answer
Greg

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