Hi there, I am using a Narnet for multi-step ahead prediction of a non-linear time series. I read some posts on the newsgroup and wrote a script to train the neural network.
1. About the problem:
* The length of the series is about 1.3M points (i.e. 1 month);
* The sampling time of the series is 2 second and
* The prediction horizon is 30 steps (i.e. 1 minute);
* Only the first 2 hours (3600 points) are used to train the networks.
* d=300 and H =3 are chosen after checking the autocorr
2. MSE:
* The MSE of the open-loop net, nMSEo, is 2.8211e-04
* the MSE of the closed-loop net, nMSEc, is 1.4814
* the MSE of the re-trained close-loop net, nMSEcr, is 0.8838
3. My questions are:
* Is there any errors/misuses on the code/toolbox functions.
* Is that normal to have such a huge degradation (>3000times) on the network performance after closing the loop?
* Is closed-loop network the only way to make multi-step-ahead-prediction with NARNET.
* I am thinking to re-sample the series with a range of sampling rate i.e. 4, 6, 8, ...
* since the past data don't have much influence on the current value, should we use the new coming data to re-train the networks on every time interval to update the networks.
4. code:
filename=sprintf('data/%d %d.xlsx', month, year);
[num,txt,~] = xlsread(filename,sheetname);
nStep=size(num,1)-1;
nDay=size(txt,2);
nDay=1;
timestamp=num(:,1);
data=num(:,(1:nDay)+1);
date=txt(1:nDay);
signal.date = gadd(timestamp(1:end-1,1),datenum(date,'dd/mm/yyyy')');
signal.date = reshape(signal.date,[nDay*nStep,1]);
signal.data = reshape(data(1:end-1,1:end),[nDay*nStep,1]);
y=signal';
y=signal.data(1:2*length(signal)/24)';
Y=num2cell(y);
N = length(y);
d = 300; FD = 1:d; H = 3;
Horizon = 30;
neto = narnet( FD, H );
neto.divideFcn = 'divideblock';
neto.trainParam.showWindow = false;
[ Xo, Xoi, Aoi, To ] = preparets( neto, {}, {}, Y );
to = cell2mat( To ); zto = zscore(to,1);
rng( 'default' )
[ neto, tro, Yo, Eo, Aof, Xof ] = train( neto, Xo, To, Xoi, Aoi );
[ Yo, Xof, Aof ] = neto( Xo, Xoi, Aoi );
Eo = gsubtract( To, Yo );
perform(neto, To, Yo);
NMSEo = mse( Eo ) / var(to,1)
yo = cell2mat( Yo );
plt = plt+1; figure(plt), hold on
plot( d+1:N, to);
plot( d+1:N, yo, 'r--');
axis( [ 0 N+d -1 1 ] );
legend( 'TARGET', 'OUTPUT' );
title( 'OPENLOOP NARNET RESULTS' );
[ netc Xci Aci ] = closeloop( neto, Xoi, Aoi );
[ Xc, Xci, Aci, Tc ] = preparets( netc, {}, {}, Y );
if isequal( Tc, To )
tc = to ;
else
tc = cell2mat( Tc );
end
[ Yc Xcf Acf ] = netc( Xc, Xci, Aci );
Ec = gsubtract( Tc, Yc );
yc = cell2mat( Yc );
NMSEc = mse(Ec) /var(tc,1)
plt = plt+1; figure(plt), hold on
plot( d+1:N, tc )
plot( d+1:N, yc, 'r--' )
legend('TARGET', 'OUTPUT')
title('CLOSELOOP NARNET RESULTS');
[netc, trc, Ycr, Ecr, Acrf, Xcrf] = train(netc, Xc, Tc, Xci, Aci);
[Ycr, Xcrf, Acrf] = netc(Xc, Xci, Aci);
Ecr = gsubtract( Tc, Ycr );
perform(netc, Tc, Ycr);
ycr = cell2mat(Ycr);
NMSEcr = mse(Ecr) /var(tc,1)
Xc2 = cell(1,Horizon);
[ Yc2 Xcrf Acrf2 ] = netc( Xc2, Xcrf, Acrf );
yc2 = cell2mat(Yc2);
plt = plt + 1;
figure(plt), hold on
plot(d+1:N, tc, 'b')
plot(d+1:N, ycr, 'g--')
plot( N+1:N+Horizon, yc2, 'ro', 'LineWidth', 2 )
plot( N+1:N+Horizon, yc2, 'r', 'LineWidth', 2 )
legend('TARGET', 'OUTPUT', 'TARGETLESS PREDICTION')
title('TRAINED CLOSELOOP NARNET RESULTS');
