MATLAB: Univariate time series prediction with neural network

narnarnetneural networksliding windowtime series predictions

hi all, I want to use neural network for predicting a univariate time series. I have a series of 1000 points, I want to use a sliding window (the size of my window is 35 points) to predict next 5 points. I am beginner in neural network so I dont know how to choose my inputs and outputs ( since I have to enter each 35 points for a response of 5 points over all my 1000 points I imagine! ). plz could you help me by giving a detailed programm? I looked at time delay neural network, but I dont know how to choose the number of delays and the number of hidden layers.

thanks

Best Answer

TIMEDELAYNET predicts future outputs from present and past inputs only

NARNET predicts future outputs from past outputs only

NARXNET predicts future outputs from past outputs in addition to present and past inputs.

Choose the delays from the significant values of the input/output crosscorrelation function at NONEGATIVE lags and output autocorrelation function at POSITIVE lags.

Choose the number of hidden nodes, H, by trial and error. The default is H = 10

[x,t] = simplenarx_dataset;

X = zscore(cell2mat(x));

T = zscore(cell2mat(t));

[ I N ] = size(X)

[ O N ] = size(T)

crosscorrXT = nncorr(X,T,N-1);

autocorrT = nncorr(T,T,N-1);

crosscorrXT(1:N-1) = []; % Delete negative delays

autocorrT(1:N-1) = [];

sigthresh95 = 0.21 % Significance threshold

sigcrossind = crosscorrXT( crosscorrXT >= sigthresh95 )

sigautoind = autocorrT( autocorrT >= sigthresh95 )

inputdelays = sigcrossind(sigcrossind <= 35)

feedbackdelays = sigautoind(sigautoind <= 35)

feedbackdelays(1)=[] % Delete zero delay

If your N = 1000 series is relatively stationary (i.e., the local means and variances are relatively constant) you should be able to reduce the window size below 35 (15?).

Hope this helps.

Thank you for formally accepting my answer.

Greg

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MATLAB: How to use neural network for multi step ahead prediction

Increase the number of feedback delays.

Hope this helps

Thank you for formally accepting my answer

Greg

MATLAB: NARXnet non-integer delays problem

% NARXnet non-integer delays problem

 % Asked by Olumide Oladoyin on 22 May 2015 at 13:09 
 % I have read quite a bit on the crosscorr and autocorr and nncorr
 % I just dont get what this statement means: Use the significant lags of
 % the target autocorrelation function and the target/input crosscorrelation
 % function to determine ID and FD. could you please explain further?

I am not a statistician. Therefore, if you need the explanation to be precise, find a statistics text or reference. For example, search using Wikipedia and/or Google using the term "significant correlations".

At certain lags the magnitude of the correlation between two time functions exceeds that expected from two uncorrelated functions.

To quantify the concept, estimate the cumulative probability of the absolute value of the correlation coefficient between two independent Gaussian noise samples of length N. Choose a significant probability level, e.g., 95%. and the corresponding correlation value sigthresh95. This threshold value depends on N.

The absolute value of the correlation coefficient, at lag m, between two time functions of length N ls considered significant if it is greater or equal to sigthresh95. The lag values for which this occurrs are called significant lags.

For time-series prediction I just use trial and error to choose a subset of the smaller significant lags. However, there are more exact selection methods using "partial correlations". See a stats reference for more detail.

I'm not sure if the following command line references will help:

>> lookfor 'partial correlation'

partialcorr     - Linear or rank partial correlation coefficients.
partialcorri    - Partial correlation coefficients with internal adjustments.

Use the help and doc commands for details.

 % From the code below, 1. What does the value 35 mean?

I have no idea. It could stand for the 35th value in the cumulative probability ditribution.

 % 2. Do i just use the values: inputdelays and feedackdelays and input them straight into the net like this?:
 %  net = narxnet( inputdelays , feedbackdelays , hiddenLayerSize, 'open', trainFcn) ...............

As I said previously, I just choose a subset using trial and error.

 % The delays were gotten with this code 
 % 

 % x = OilRate;          % 1×1500 cell 
 % t = GasProduced; % 1×1500 cell
 % X = zscore(cell2mat(x));
 % T = zscore(cell2mat(t));
 % [ I N ] = size(X)
 % [ O N ] = size(T)
 % crosscorrXT = nncorr(X,T,N-1);
 % autocorrT = nncorr(T,T,N-1);
  % crosscorrXT(1:N-1) = []; % Delete negative delays
 % autocorrT(1:N-1) = [];
 % 
 % sigthresh95 = 0.21 % Significance threshold

Incorrect value for N = 1500

 % sigcrossind = crosscorrXT( crosscorrXT >= sigthresh95 )
 % sigautoind = autocorrT( autocorrT >= sigthresh95 )
 % inputdelays = sigcrossind(sigcrossind <= 35)
 % feedbackdelays = sigautoind(sigautoind <= 35)
 % feedbackdelays(1)=[] % Delete zero delay

Incorrect. You are confusing correlation values and delay values

Hope this helps.

Thank you for formally acepting my answer

Greg

Best Answer

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MATLAB: NARXnet non-integer delays problem

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