1. The script obtained from nntool can be simplified by deleting all redundant statements that explicitly assign default values.
2. It is useful to use uppercase for cells and lowercase for doubles.
3. It is also useful to use the subscripts 'o' and 'c' for open and close loop, respectively.
The code you have posted calculates correctly. However, I see no plot command. That is where your mistake occurs. Remember that the outputs of preparets are shifted from the original variables.
Taking my advice into account yields
Understanding Simple Narx Example
% I am doing the narx neural network using the simplenarx_dataset. % Supposedly it is to predict y(t) based on y(t-1),x(t-1)... etc
No.
Although the feedback delays must be positive ( FD > 0) Input delays must be NONNEGATIVE ( ID >= 0)
Therefore, in general, it estimates y(t) based on x(t), x(t-1), y(t-1)... etc
% but after training open loop I find that output y(t) is two time steps % before the target data... so I think it is predicting y(t+2). see below % figure: blue - net output (y) red - target data (T)
It's all relative, i.e., whether YOU define t = 0 at the input or the output.
Changing notation and using implied defaults, your code can be simplified to
Lower case for doubles
Upper case for cells
Subscript "o" for "o"pen loop
Subscript "c" for "c"losed loop
close all, clear all, clc
[ X, T ] = simplenarx_dataset;
N = length(T)
neto = narxnet;
[ Xo, Xoi, Aoi, To ] = preparets( neto, X, {}, T );
to = cell2mat( To );
MSE00o = mean(var(to',1)) % Normalization Reference
rng('default') % Added for reproducibility
[ neto, tro, Yo, Eo, Xof, Aof ] = train( neto, Xo, To, Xoi, Aoi );
% [ Yo Xof Aof ] = net(Xo,Xoi,Aoi); Eo = gsubtract(To,Yo);
NMSEo = mse(Eo)/MSE00o
R2o = 1 - NMSEo % Rsquared (see Wikipedia )
yo = cell2mat(Yo);
figure(1), hold on
plot( 3:N, to, 'LineWidth', 2)
plot( 3:N, yo, 'ro', 'LineWidth', 2)
legend( ' TARGET ', ' OUTPUT ' )
title( ' NARXNET EXAMPLE ' )
Hope this helps.
Thank you for formally accepting my answer
Greg
