How alignment of data is treated by the neural network algorithms for one day ahead prediction

I am having trouble understanding how the alignment of data is treated by the neural network algorithms for one day ahead prediction.

Suppose we have a target T from times 1,2,3…t. Suppose we have inputs X from times 1,2,3,…t. Imagine each time step is one day.

We want to do one step ahead prediction for each day prospectively, day by day. This means we never want to use any future information. Also, we want to predict tomorrow’s target at the end of today. In other words, we want to use X(1:t) and T(1:t) to predict T(t+1); we do not have X(t+1) at our disposal for this purpose, because that information lies in the future.

If we create a narxnet network with X(1:t) and T(1:t) aligned in time, the default output is T(t) which is found using all of X, including X(t).

So instead we convert the network a step ahead network. At time t, this gives us T(t+1) using only data from days 1 through t.

Is this correct? The results I get seem too good to be true.

[Greg Heath]

How does your code differ from that in the documentation

 help narxnet

 doc narxnet

Greg

[Kevin Johnson]

% inputsnn - input time series. % targetnn - feedback time series.

% note: inputs and target are aligned in time

X = tonndata(inputsnn,false,false); T = tonndata(targetnn,false,false);

% Training Function trainFcn = 'trainbr';

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

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

% Setup Division of Data for Training, Validation, Testing netts.divideParam.trainRatio = 70/100; netts.divideParam.valRatio = 15/100; netts.divideParam.testRatio = 15/100;

% Train the Network [netts,tr] = train(netts,x,t,xi,ai);

% Test the Network y = netts(x,xi,ai); e = gsubtract(t,y);

% Step-Ahead Prediction Network netsa = removedelay(netts); netsa.name = [netts.name ' - Predict One Step Ahead']; [xs,xis,ais,ts] = preparets(netsa,X,{},T); ys = netsa(xs,xis,ais); resultnn=[NaN;cell2mat(ys)'];

[Kevin Johnson]

Trying to attach image of results here

Answer 1

[Greg Heath]

I don't understand your problem.

What fraction of the target variance did you want to achieve?

mse(error)/mean(var(target',1)) <= ?

Greg