How to forecast with Neural Network?

I'm using MATLAB R2011a. I'm trying to predict next 100 points of time-serie X by means of neural net. Firstly, I create input time series Xtra and feedback time series Ytra:

lag = 50;
Xu = windowize(X,1:lag+1);  %Re-arrange the data points into a Hankel matrix
Xtra = Xu(:,1:lag);         %input time series
Ytra = Xu(:,end);           %feedback time series

Then I train neural net with this code:

inputSeries = tonndata(Xtra,false,false);
targetSeries = tonndata(Ytra,false,false);

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

% Prepare the Data for Training and Simulation
[inputs,inputStates,layerStates,targets] = preparets(net,inputSeries,{},targetSeries);

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

% Train the Network
[net,tr] = train(net,inputs,targets,inputStates,layerStates);

% Test the Network
outputs = net(inputs,inputStates,layerStates);
errors = gsubtract(targets,outputs);
performance = perform(net,targets,outputs)

And then I would like to predict next 100 points of my initial time-serie X, what should I do?

Thanks in advance for your answers.

Answer 1

[Greg Heath]

0. Incorrect use of the word 'lag'

1. It is rare that the default input parameters (ID,FD,H) are sufficient. They can be improved by using a subset of significant lags determined from the auto and cross-correlation functions and then searching over a range of H values. The smallest acceptable value of H should be used.

2. The default 'dividerand' should be overwritten (e.g., 'divideblock') to optimize the effectiveness of the significant correlation lags found in 1.

3. Train using the syntax

 [net tr Ys Es Xf Af ] = train(net,Xs,Ts,Xi,Ai);

to use Xf and Af as intial conditions for continuation data

4. After closing the loop, test the CL net on the original data. If performance is not good compared to the OL performance, train the CL net beginning with the weights obtained with the OL training.

5. Since you only have 1 series, you should have used NARNET. To continue beyond the original data

Xnew = net(NaN(1,100),Xf,Af);

Hope this helps

Greg

[Eric]

Hello, Greg! Regarding the above answer from you...

Please, can you write the syntax for Preparets as you did in (3) for train?

I want use NARNET for predict USD price beyond original data.

Like to try your method: Xnew = net(NaN(1,100),Xf,Af);

Thanks!

Answer 2

[Mark Hudson Beale]

You can convert the NARXNET from open-loop to closed-loop form to predict ahead any number of timesteps for which you have data for your input time series.

If you want to predict N steps ahead then:

% define N+2 timesteps of inputs
Xtra_predict = { ... };

% define N+2 feedback values, but ONLY first 2 need to be
% defined, the rest can be NaN (i.e. unknown) values.  The N unknown
% values will be the N predictions the network will make.  You could
% use the last 2 values of Ytra if you want to make the prediction directly
% after your training data sereies.
Ttra_predict = { ... } 

netCL = closeloop(net);
[X,Xi,Ai,T] = preparets(net,Xtra_predict,{},Ttra_predict);
y = sim(net,X,Xi,Ai)

After this code is run, y will now have N preditions based on the input series Xtra_predict and the initial two steps of Ttra_predict.

Answer 3

[Jack]

Hi All,

I have the same problem and looked everwhere to find an answer ... :-((

How would you define N+2 timestemps of inputs here ? What the code would look like ?

Xtra_predict = ?????????

Ttra_predict = ??????????

Thank you very much !

Answer 4

[Justin]

It doesn't seem that this can be done, I've been looking into it for a few weeks now, and although there seems to be a few interesting responses, in application, they always run into errors pertaining to the number of inputs into the network.

Answer 5

[Cristhiano Moreno]

How can i do it with a NAR Network ? I have a temporal serie with 99 values, and i want to predict the 100 value. And finally plot this 2 series y the same figure.

Somebody can help me ?

Answer 6

[Vito]

Let's play game. We throw a coin and we try to guess what side it has fallen. Certainly we don't know, and mathematical expectation = 0.5.

But after 10 throws we can count real mathematical expectation for this game. In due course, we will get used to this coin and we can guess to (predict).

At a network the same principle. Its principal advantage that she can remember all games. Therefore we can receive dependence of expected value from actual, on some time interval.

Let's create the elementary linear network.

delays = [0 1 2 3 4 5];
pi = {1 2 3 4 5};
net = newlin ([0 1], 1, delays);

Random variable.

GamVar = randsample ([0,1], 1, true, [.7,.3]); % one random variable

Also we will play 100 batches on 10 throws.

delays = [0 1 2 3 4 5 ];
pi ={1 2 3 4 5 };
net = newlin([0 1],1,delays);

S=[];
s=1;
t=1;
Me=[];
time=1;
step =1;
GamVar = randsample([0,1],1,true,[.7,.3]);% one random variable
T = con2seq([GamVar]);
P = T;
TM = con2seq(median(cat(2,T{:})));

%
Prize=0;
for mm=1:100

%---------
hold on
c=0;
y=[];

if mm ==1
T={mean(cat(2,T{:}))};
Me=T;
P=T;

TM=T;
PM=TM;

else % accamulate mean

T={mean([cat(2,T{:}) Me{:}])};
Me=T;
P=T;
TM = T;
PM=TM;    

end

GamVar = (randsample([0,1],10,true,[.7,.3]));% one random variable
for i = 1:10

GamVarT{i}=GamVar(i);
T{i} = GamVar(i);
P = T;

if i>1
TM ={T{1:i-1} mean(cat(2,TM{1:i-1}))};
else
TM{i}=mean(cat(2,TM{:}));    
end
PM=TM;

y= sim(net,PM,pi);
% correction
if  any([(round(cat(2,y{1:i})))~=cat(2,GamVarT{1:i})])

TM = T;

% in input - the mean, in output - real value
[net,y,e]=adapt(net,PM,TM,pi);

plot(i,round(double(y{i})),'or','LineWidth',2,'MarkerSize',10);
c=c+1;
end

time=time+1;

plot(1:size(PM,2),round(double(cat(2,y{:}))),'o--',1:size(P,2),cat(2,T{:}),'-*');
xlabel('Time');

axis([0 i -4 4]);
drawnow

if ~strcmp(get(get(0,'CurrentFigure'),'SelectionType'),'normal')
    disp('stop')
    break
  end
end

disp('Count error predaction')
c
disp('Relation error predaction / All samples')
(c/i)*100

S(s)=(c/i)*100;
s=s+1;
mean(S)

if ~strcmp(get(get(0,'CurrentFigure'),'SelectionType'),'normal')
    disp('stop')
    break
end

close all

disp('Prize')    
Prize= Prize+(10-c)-c

step=step+10;
end

We have benefited! If we will play once again the scoring will increase.

This very simple example shows that it is possible to predict on very wide intervals of time. Other network and other adjustments allow to achieve much the best results. Good luck. The code for version 7.2.

[Cristhiano Moreno]

Great.

But how using NAR NN ?

[Muhammad Hasnat]

I fail to understand any relation with what was being asked and this game.

Answer 7

[Vito]

Thank. :) Has only shown the general principle. Or one of variants. Creation neurosystems, on former art. Also leans against the creative approach. Before accurate formalization it is still far. Probably you offer the decision.

Therefore such subjects - an exchange of ideas, are always interesting and extremely useful.

Best regards.