Delayed Outputs in NARX - Predicted Behavior Explained

As predicted delayed outputs settle in NarX

simran_k asked: 2021-07-20 matlab , narx , tutorial

Master NARX networks for time-series prediction Learn how delayed outputs are modeled and settle. Get a step-by-step guide to dynamic state transitions. Sta...

Expert Answer

Prashant Kumar answered . 2025-07-07 14:07:18

% 1. Selected ending semicolons can be removed to aid debugging

 [P, T ] = simplenarx_dataset;
 whos
 p= cell2mat(P);
 t = cell2mat(T);

 ID = 1:1
 FD = 1:1
 H = 5

 NID= length(ID)
 NFD=length(FD)
 Nw = (NID*I+NFD*O+1)*H+(H+1)*O

% 2. Use NID and NFD for Nw in case delays are not single

% 3. No need to use tonndata because the simplenarx_data set is instantly ready for preparets.

% 4. No need for (p1,t1) and (p2,t2). Delete both.

% 5. Input delays are suboptimal. Did you try to find the significant lags of the target/input cross-correlation function?

% 6. Feedback delays are suboptimal. Did you try to find the significant lags of the target autocorrelation function?

% 7. H is suboptimal. Was it chosen using the suboptimal delays? If so, please explain how.

 rng(0)
 net = narxnet(ID,FD,H);
 [inputs,inputStates,layerStates,targets] = preparets(net,P,{},T);
 whos P T inputs inputStates layerStates targets

%8. N=N-1: DELETE. NOT A GOOD IDEA TO USE A VARIABLE OR PARAMETER NAME ON BOTH SIDES OF AN EQUATION. BESIDES, PREPARETS OUTPUTS THE CORRECT DIMENSIONS

 [ I N ] = size(inputs)
 [ O N ] = size(targets)

% 9. No need for ttotal it should be the same as targets. % No need for Neq, MSE00,MSE00a and t4. Delete

 net.divideFcn='divideblock';
 [trainInd,valInd,testInd] = divideblock(N,0.7,0.15,0.15); 
 ttrn = targets(trainInd);
 tval = targets(valInd);
 ttest = targets(testInd);
 Ntst = length(ttrn) 
 Nval = length(valInd)
 Ntst = length(testInd)
 Ntrneq = prod(size(ttrn))     % Ntrn*O
 Ndof = Ntrneq-Nw

%Naive Constant Output Model

 ytrn00= mean(ttrn,2);     
 Nw00 = size(ytrn00,2)
 Ndof00 = Ntrneq-Nw00
 MSEtrn00 = sse(ttrn-ytn000)/Ntrneq
 MSEtrn00=mean(var(ttrn,1))
 MSEtrn00a = sse(ttrn-ytrn00)/Ndof00
 MSEtrn00a=mean(var(ttrn,0))

%9. MSEval00 and MSEtst00 should be obtained from the Naive constant output model output

 MSEval00 = mse(tval-ytrn00)
 MSEtst00 = mse(tttst-ytrn00)

 net.trainParam.goal = 0.01*Ndof*MSEtrn00a/Ntrneq;  % R2trna >= 0.99
 rng(0)
 [net,tr,Ys,Es,Xf,Af] = train(net,inputs,targets,inputStates,layerStates);

 outputs = net(inputs,inputStates,layerStates);

 errors = gsubtract(targets,outputs);

 MSE = perform(net,targets,outputs);

 MSEa=Neq*MSE/(Neq-Nw)

 R2=1-MSE/MSE00

 R2a=1-MSEa/MSE00a

% 10. The DOF "a"djustment is only applied to the training data

% 11. Can delete the last 6 equations that refer to all of the data instead of the trn/val/tst division.

 MSEtrn=tr.perf(end)
 MSEtrna = Ntrneq*MSEtrn/Ndof
 MSEval=tr.vperf(end)
 MSEtst=tr.tperf(end)

% 12.Using "end" is only valid if training converges because of tr.min_grad (not valstop ). Better to use "tr.best_epoch".

 R2trn=1-MSEtrn/MSEtrn00
 R2trna=1-MSEtrna/MSEtrn00a

%13 Original MSEtrna misprint.

 R2val=1-MSEval/MSEval00
 R2tst=1-MSEtst/MSEtst00

and my results are:

% 14. Unable to compare results because you did not intialize the RNG before the first call of the RNG in the net creation command net = ... where H =5 random weights were assigned to the input bias. I will use rng(0) before the net creation.