Time-series prediction using another time series

I am working on a dynamic model for which I want to predict its time-series response when subjected to input time-series.

Let's say X1(t) is input vector and Y1(t) is corresponding output vector. After training, I want my model to predict the response of a completely new time-series input, say Y2(t) as response when it is given X2(t) as input vector. I have tried NARXnet. However, after making it close loop once training is done, it still requires a target data, which in my case is not available and that is what I want my model to predict using only input data i.e. X2(t).

Am i using the correct network i.e. NARXnet or not? If not, what else I should look for?

Code is shown below:

X = tonndata(X1,false,false); %input time-series
T = tonndata(Y1,false,false); %output time-series

trainFcn = 'trainbr';  % Bayesian Regularization backpropagation.

% Create a Nonlinear Autoregressive Network with External Input
inputDelays = 1:2;
feedbackDelays = 1:2;
hiddenLayerSize = 10;
net = narxnet(inputDelays,feedbackDelays,hiddenLayerSize,'open',trainFcn);

% Prepare the Data for Training and Simulation
[x,xi,ai,t] = preparets(net,X,{},T);

% Setup Division of Data for Training, Validation, Testing
net.divideFcn = 'dividerand';  % Divide data randomly
net.divideMode = 'time';  % Divide up every sample
net.divideParam.trainRatio = 70/100;
net.divideParam.valRatio = 15/100;
net.divideParam.testRatio = 15/100;

% Choose a Performance Function
net.performFcn = 'mse';  % Mean Squared Error
 
% Train the Network
[net,tr] = train(net,x,t,xi,ai);
 
% Test the Network
y = net(x,xi,ai);
e = gsubtract(t,y);
performance = perform(net,t,y)

% Closed Loop Network
netc = closeloop(net);
netc.name = [net.name ' - Closed Loop'];
view(netc)

X_new = tonndata(X2,false,false); %new time series for which i want to get output without having Y2
T_new = tonndata(Y2,false,false); %i don't have this response time-series. I want to predict this using X2 i.e. X_new
[xc,xic,aic,tc] = preparets(netc,X_new,{},T_new);

yc = netc(xc,xic,aic);

closedLoopPerformance = perform(netc,tc,yc)

Answer 1

[Srivardhan Gadila]

Refer to Shallow Neural Network Time-Series Prediction and Modeling and use Nonlinear Input-Output.