Asked by Jack
on 2 Sep 2011

Hi all, please I need your help !

I've read all the posts here about Time Series Forecasting but still can't figure it out ! I'm drained.. *:-(*

I've a NARX neural network with 10 hidden neurons and 2 delays. As input I have a 510x5 (called Inputx) and as output I have a 510x1 (called Target).

I want to forecast 10 days ahead but it's really not working...

I tried the following code but I'm stuck now. *:-(*

Would you mind to help me ? *Some code will be awesome. :-(*

***////////////////////////////////////////////******** ***/////////////////////////////////////////// ******

inputSeries = tonndata(Inputx,false,false);

targetSeries = tonndata(Target,false,false);

netc = closeloop(net);

netc.name = [net.name ' - Closed Loop'];

[xc,xic,aic,tc] = preparets(netc,inputSeries,{},targetSeries);

yc = netc(xc,xic,aic);

***////////////////////////////////////////////******** ***/////////////////////////////////////////// ******

Answer by Lucas García
on 7 Sep 2011

Edited by Lucas García
on 3 Sep 2015

Accepted Answer

Hi Jack,

When using narxnet, the network performs only a one-step ahead prediction after it has been trained. Therefore, you need to use closeloop to perform a multi-step-ahead prediction and turn the network into parallel configuration.

Take a look at this example for a multi-step-ahead prediction, N steps. This uses the dataset magdata.mat which is available in the Neural Network Toolbox. Also, some of the inputs will be used for performing the multi-step-ahead prediction, and results validated with the original data. I hope the comments help to understand.

Edited in September 2015 to simplify step 5

%% 1. Importing data

S = load('magdata');

X = con2seq(S.u);

T = con2seq(S.y);

%% 2. Data preparation

N = 300; % Multi-step ahead prediction

% Input and target series are divided in two groups of data:

% 1st group: used to train the network

inputSeries = X(1:end-N);

targetSeries = T(1:end-N);

% 2nd group: this is the new data used for simulation. inputSeriesVal will

% be used for predicting new targets. targetSeriesVal will be used for

% network validation after prediction

inputSeriesVal = X(end-N+1:end);

targetSeriesVal = T(end-N+1:end); % This is generally not available

%% 3. Network Architecture

delay = 2;

neuronsHiddenLayer = 10;

% Network Creation

net = narxnet(1:delay,1:delay,neuronsHiddenLayer);

%% 4. Training the network

[Xs,Xi,Ai,Ts] = preparets(net,inputSeries,{},targetSeries);

net = train(net,Xs,Ts,Xi,Ai);

view(net)

Y = net(Xs,Xi,Ai);

% Performance for the series-parallel implementation, only

% one-step-ahead prediction

perf = perform(net,Ts,Y);

%% 5. Multi-step ahead prediction

[Xs1,Xio,Aio] = preparets(net,inputSeries(1:end-delay),{},targetSeries(1:end-delay));

[Y1,Xfo,Afo] = net(Xs1,Xio,Aio);

[netc,Xic,Aic] = closeloop(net,Xfo,Afo);

[yPred,Xfc,Afc] = netc(inputSeriesVal,Xic,Aic);

multiStepPerformance = perform(net,yPred,targetSeriesVal);

view(netc)

figure;

plot([cell2mat(targetSeries),nan(1,N);

nan(1,length(targetSeries)),cell2mat(yPred);

nan(1,length(targetSeries)),cell2mat(targetSeriesVal)]')

legend('Original Targets','Network Predictions','Expected Outputs')

Kelvin Wellington
on 5 Dec 2016

Do this, before you put the variables in the preparets:

inputSeries = con2seq(inputSeries); targetSeries = con2seq(targetSeries);

rabi darji
on 16 May 2017

after running the above code i am getting Error using closeloop Too many input arguments.

Error in magdata (line 35) [netc,Xic,Aic] = closeloop(net,Xfo,Afo);

rabi darji
on 16 May 2017

after running the above code i am getting Error using closeloop Too many input arguments.

Error in magdata (line 35) [netc,Xic,Aic] = closeloop(net,Xfo,Afo);

Sign in to comment.

Answer by Mark Hudson Beale
on 9 Sep 2011

Here is an example that may help. A NARX network is trained on series inputs X and targets T, then the simulation is picked up at the end of X using continuation input data X2 with a closed loop network. The final states after open loop simulation with X are used as the initial states for closed loop simulation with X2.

% DESIGN NETWORK

[x,t] = simplenarx_dataset;

net = narxnet;

[X,Xi,Ai,T] = preparets(net,x,{},t);

net = train(net,X,T,Xi,Ai);

view(net)

% SIMULATE NETWORK FOR ORIGINAL SERIES

[Y,Xf,Af] = sim(net,X,Xi,Ai);

% CONTINUE SIMULATION FROM FINAL STATES XF & AF WITH ADDITIONAL

% INPUT DATA USING CLOSED LOOP NETWORK.

% Closed Loop Network

netc = closeloop(net);

view(netc)

% 10 More Steps for the first (now only) input

X2 = num2cell(rand(1,10));

% Initial input states for closed loop continuation will be the

% first input's final states.

Xi2 = Xf(1,:);

% Initial 2nd layer states for closed loop contination will be the

% processed second input's final states. Initial 1st layer states

% will be zeros, as they have no delays associated with them.

Ai2 = cell2mat(Xf(2,:));

for i=1:length(net.inputs{1}.processFcns)

fcn = net.inputs{i}.processFcns{i};

settings = net.inputs{i}.processSettings{i};

Ai2 = feval(fcn,'apply',Ai2,settings);

end

Ai2 = mat2cell([zeros(10,2); Ai2],[10 1],ones(1,2));

% Closed loop simulation on X2 continues from open loop state after X.

Y2 = sim(netc,X2,Xi2,Ai2);

Elma
on 18 Feb 2014

I have tried this code, and it is great, but when I try to apply it for my problem, I get really bad results. I tried with changing input and feedback delays, as well as number of hidden neurons, but the results are always bad (figure) (green line is multi step predistion)

The code is given below:

% DESIGN NETWORK

ID=1:2;

HL=6

FD=1:2;

net = narxnet(ID,FD,HL);

[X,Xi,Ai,T] = preparets(net,x,{},WS);

net.divideFcn = 'divideblock';

net = train(net,X,T,Xi,Ai);

% SIMULATE NETWORK FOR ORIGINAL SERIES

[Y,Xf,Af] = sim(net,X,Xi,Ai);

% CONTINUE SIMULATION FROM FINAL STATES XF & AF WITH ADDITIONAL

% INPUT DATA USING CLOSED LOOP NETWORK.

% Closed Loop Network

netc = closeloop(net);

Xi2 = Xf(1,:);

Ai2 = cell2mat(Xf(2,:));

for i=1:length(net.inputs{1}.processFcns)

fcn = net.inputs{i}.processFcns{i};

settings = net.inputs{i}.processSettings{i};

Ai2 = feval(fcn,'apply',Ai2,settings);

end

Ai2 = mat2cell([zeros(10,2); Ai2],[10 1],ones(1,2));

Y2 = sim(netc,X2,Xi2,Ai2);

plot(1:length(WS),cell2mat(WS))

hold on

plot(1:length(Y),cell2mat(Y),'r')

plot(length(WS):length(WS)+length(Y2)-1,cell2mat(Y2),'g')

legend('Input data - target series','One-step ahead prediction','Multi-step prediction beyond target series');

WT
on 1 Mar 2015

May I know what this "Ai2 = mat2cell([zeros(10,2); Ai2],[10 1],ones(1,2));" means?

Thank You

IOANNIS4
on 5 Aug 2015

Please can someone exlpain little bit more this part

% Xi2 = Xf(1,:); Ai2 = cell2mat(Xf(2,:)); for i=1:length(net.inputs{1}.processFcns) fcn = net.inputs{i}.processFcns{i}; settings = net.inputs{i}.processSettings{i}; Ai2 = feval(fcn,'apply',Ai2,settings); end Ai2 = mat2cell([zeros(10,2); Ai2],[10 1],ones(1,2)); Y2 = sim(netc,X2,Xi2,Ai2);

Please you would really help us, Kind regards, Ioannis

Sign in to comment.

Answer by Greg Heath
on 25 Mar 2014

Sign in to comment.

Answer by mladen
on 25 Oct 2013

Be aware that predicting outputs this way (similar to cascade relaization of linear system) has great sensitivity to parametar estimation errors because they propagate in the process Mark Hudson Beale mentioned. This is highlighted in hard, multiple steps ahead problems.

Parallel realizations (simoltanoius output estimation...for instance 10 outputs of neural network for next 10 time steps) tend to be less sensitive to this errors. I have implemented this with my code which is alway prone to error :) So my subquestion is:

Is there some specific way to prepare my data for training with some matlab function?

Sign in to comment.

Answer by Murat Akdag
on 28 Mar 2015

Charles
on 10 Jul 2017

Greg Heath
on 11 Jul 2017

epochs are the number of loops the training goes through to trying to minimize the objective function ...

but you knew that already because you have GOOGLE & WIKIPEDIA

RIGHT?

Did you find this

https://www.quora.com/What-is-epochs-in-machine-learning

?

Charles
on 12 Jul 2017

Sign in to comment.

Answer by hugo kuribayashi
on 15 Apr 2015

Considering all this examples.. How can i calculate MAPE error instead MSE?

Greg Heath
on 11 Jul 2017

You mean "in addition to" ?

1. Learn with MSE or MSEREG

2. Report your findings with whatever floats your boat.

3. I prefer NMSE [0 1] for regression and time series

and

PCTERR [ 0 1 ]

for classification and pattern recognition

(;>)

Greg

P.S. Be aware of the shortcomings of MAPE and it's attempted modifications

https://en.wikipedia.org/wiki/Mean_absolute_percentage_error

Hope this helps.

Greg

Sign in to comment.

Opportunities for recent engineering grads.

Apply Today
## 2 Comments

## Oleg Komarov (view profile)

## Direct link to this comment

https://uk.mathworks.com/matlabcentral/answers/14970-neural-network-multi-step-ahead-prediction#comment_33198

## Constantine (view profile)

## Direct link to this comment

https://uk.mathworks.com/matlabcentral/answers/14970-neural-network-multi-step-ahead-prediction#comment_250932

Sign in to comment.