MATLAB: Problem with NARX open-loop training – Correlated with a shift – How to improve NARX training / testing

annclose loopdelaynarxnarxnetneural networkopen looptime seriestrain

Hello everybody
I am new to statistics and ANN. I am using NARX (open-loop) to train a set of data (a time series as input X and a time series as target T, with more than 4000 data points). In the data, most of the time, X and T are constant, but sometimes X increases suddenly and after a short period of time T also increases, then X decreases to the constant value and T also decreases to its constant value. Please see the attached figure which shows a small part of the data.(in the figure, the green lines show the start of increase in X). After training the data I want to use the model to predict T at one-step ahead. But I have problem in training the data.
I use the following commands to create the net, train it, and then test it.
net = narxnet(inputDelays,feedbackDelays,hiddenLayerSize);
[inputs,inputStates,layerStates,targets] = ...
    preparets(net,inputSeries(train_period),{},targetSeries(train_period));
[net,tr] = train(net,inputs,targets,inputStates,layerStates);
outputs = net(inputs,inputStates,layerStates);
The output Y correlates to the target T, but, as can be seen in the figure, with a shift of about one step size!. In the lower plot, blue line is the target and red line shows the output. This is only a short part of the data, and this problem is seen in the whole data (even more serious when the bump in T is lower). My question is that why is there a shift of one step size between target T and output Y? How can I improve the model to have a good correlation between those two? I use 10 hidden layers, 3 input and feedback delays, and "divideint" for dividing the data. I also used other values for these parameters but no success.
I tried to use this trained model to predict one-step ahead of T, but as the output is shifted one step ahead in training, it also has a similar shift in the testing. Therefore, the result is not useful because when we are at time = n, the model gives the value of T at the same time as the output at time = n+1.
Any advice would be much appreciated. After solving this problem, I am going to use closed-loop to make multi-step ahead predictions.
Thank you!

Best Answer

 1. Openloop(OL) NAR and NARX configurations are NOT DEPLOYABLE! 
 2. They cannot estimate outputs when only inputs are known. 
 3. They are only stages in the design of deployable closeloop (CL) 
    configurations where past output signal estimates are fed back 
    to the input.
 4. Therefore, if you need a NAR or NARX timeseries net to estimate 
    unknown outputs from known inputs, you have to use a deployable 
    CL configuration.
 5. BOTTOM LINE: OL configurations are only useful for designing 
    deployable CL configurations!
Hope this helps.
Thank you for formally accepting my answer
Greg
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