What's the difference between NARX open loop + remove delay and closed loop to forecast N steps ahead?

Question

Tarcisio Prest Bernabé 2018-9-17

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https://ww2.mathworks.cn/matlabcentral/answers/419410-what-s-the-difference-between-narx-open-loop-remove-delay-and-closed-loop-to-forecast-n-steps-ahea

回答： Greg Heath 2018-9-23

I'm trying to forecast one day ahead (N = 24 steps) of a time series. In a previous work, I solved this problem by using an open loop (OL) NARX and removedelay function to shift my output (predicted value) 24 steps forward.

%%3. OL NARX Approach
%%3. Network Architecture
fh = 24; %Forecast Horizon
delay = 24;
inputDelays = fh:fh+delay;
feedbackDelays = fh:fh+delay;
neuronsHiddenLayer = 10;
% Network Creation
net = narxnet(inputDelays,feedbackDelays,neuronsHiddenLayer);
net = removedelay(net,fh);
%%4. Training the network
[Xs,Xi,Ai,Ts] = preparets(net,inputSeries,{},targetSeries); 
net = train(net,Xs,Ts,Xi,Ai);
view(net)
% y(t+24)
Y = net(Xs,Xi,Ai); 
% Performance for the series-parallel implementation, only 
% one-step-ahead prediction
perf = perform(net,Ts,Y);

But now, by better searching the features of the toolbox, I noticed that people use NARX in closed loop (CL) to forecasting N steps ahead. More or less like the code below.

%%CL NARX Approach
%%2. Data Preparation
N = 24; % Multi-step ahead prediction
% Input and target series are divided in two groups of data:
% 1st group: used to train the network
inputSeries  = X(1:end-N);
targetSeries = T(1:end-N);
% 2nd group: this is the new data used for simulation. inputSeriesVal will 
% be used for predicting new targets. targetSeriesVal will be used for
% network validation after prediction
inputSeriesVal  = X(end-N+1:end);
targetSeriesVal = T(end-N+1:end);
%%3. Network Architecture
delay = 24;
neuronsHiddenLayer = 10;
% Network Creation
net = narxnet(1:delay,1:delay,neuronsHiddenLayer);
%%4. Training the network
[Xs,Xi,Ai,Ts] = preparets(net,inputSeries,{},targetSeries); 
net = train(net,Xs,Ts,Xi,Ai);
view(net)
Y = net(Xs,Xi,Ai); 
% Performance for the series-parallel implementation, only 
% one-step-ahead prediction
perf = perform(net,Ts,Y);
%%5. Multi-step ahead prediction
[Xs1,Xio,Aio] = preparets(net,inputSeries(1:end-delay),{},targetSeries(1:end-delay));
[Y1,Xfo,Afo] = net(Xs1,Xio,Aio);
[netc,Xic,Aic] = closeloop(net,Xfo,Afo);
[yPred,Xfc,Afc] = netc(inputSeriesVal,Xic,Aic);
multiStepPerformance = perform(net,yPred,targetSeriesVal);