# Neural Network - Multi Step Ahead Prediction

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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);

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

##### 2 Comments

Constantine
on 21 Nov 2014

with respect to the accepted answer by Lucas Garcia, I find the predicted data only agrees with the actual data as well as his every once in a while.

1. It's important, before running the fit, to clear the variables, eg. 'clear all.' Re-running without clearing the variables leads to much worse fits.

2. much better fits result from using a bigger delay, like 5, instead of the delay of 2 in his example. Or by adding additional training data, such as the time derivative or 2nd time derivatives of the training data. Of course, doing this makes the fit considerably slower.

### Accepted Answer

Lucas García
on 7 Sep 2011

Edited: Lucas García
on 3 Sep 2015

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')

##### 24 Comments

Chris P
on 2 Aug 2020

### More Answers (5)

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);

##### 4 Comments

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

Greg Heath
on 25 Mar 2014

##### 1 Comment

Mario Viola
on 26 Feb 2021

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?

Murat Akdag
on 28 Mar 2015

##### 4 Comments

hugo kuribayashi
on 15 Apr 2015

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

##### 1 Comment

Greg Heath
on 11 Jul 2017

Edited: Greg Heath
on 12 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

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