P1259184613WeifS

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Autoregressive Models and Artificial Neural
Networksin Time Series Prediction
Institute of Chemical Technology PragueFaculty
of Chemical EngineeringDepartment Computing and
Control Engineering
Konference MATLAB 2002
Ing. Aleš Pavelka andProf. Ing. Aleš Procházka,
CSc.
7th November 2002
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Introduction
Application of Autoregressive Models and
Artificial Neural Networks in Time Series
Prediction
Aleš Pavelka and Aleš Procházka

• Predictions Models

• Methods and Results

• Next Possible Improvements

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Predictions Models
Application of Autoregressive Models and
Artificial Neural Networks in Time Series
Prediction
Aleš Pavelka and Aleš Procházka

• Autoregressive Models

• Linear Neural Networks

• Feed-Forward Neural Networks

• Recurrent Neural Networks

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Application of Autoregressive Models and
Artificial Neural Networks in Time Series
Prediction
Aleš Pavelka and Aleš Procházka
Autoregressive Models (AR)
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Application of Autoregressive Models and
Artificial Neural Networks in Time Series
Prediction
Aleš Pavelka and Aleš Procházka
Autoregressive Models (AR)calculation scheme
determination of full AR model
parameter recalculation
reducing of parameters
SVD
QRcp
final subsetmodel
final subsetmodel
diagonal matrix S
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Linear Neural Network
Application of Autoregressive Models and
Artificial Neural Networks in Time Series
Prediction
Aleš Pavelka and Aleš Procházka
Processing layerof output neurones
Weights
Input layer
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Feed-Forward Neural Network
Application of Autoregressive Models and
Artificial Neural Networks in Time Series
Prediction
Aleš Pavelka and Aleš Procházka
Processing layer ofoutput neurones
Processing layerof hidden neurones
Input layer
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Recurrent Neural Network
Application of Autoregressive Models and
Artificial Neural Networks in Time Series
Prediction
Aleš Pavelka and Aleš Procházka
Processing layer of hidden and output neurones
Forward and feedback connections
Concatenated input - output layer
Source 1, S. Haykin (1994).
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Methods and Results
Application of Autoregressive Models and
Artificial Neural Networks in Time Series
Prediction
Aleš Pavelka and Aleš Procházka
WWW presentation
http//phobos.vscht.cz/pavelkaa
WWW presentation
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Comparing of Modelsdata from 1.10.2000 -
27.2.2002 (150 days)
Model Architecture mean std MSE in 5
AR Model AS 1571-1 0.496 3.94 16.61 55.1
AR Model AF 1500-1 0.048 2.22 4.85 53.1
AR Model TS 1571-1 -2.630 6.58 49.88 28.9
AR Model TF 1500-1 -2.609 6.52 48.96 33.3
Linear NN A 1500-1 2.28e-14 1.71 2.87 63.6
Linear NN L 1571-1 1.16e-15 2.10 4.36 63.7
Linear NN T 1571-1 -2.678 6.50 49.08 34.8
Feed Forward NN A 1571-5-1 0.454 1.72 3.13 40.8
Feed Forward NN T 1570-5-1 -2.683 6.57 49.98 26.7
Recurrent NN A 1570-5-1 0.652 6.04 36.52 28.6
Recurrent NN T 1500-5-1 -2.539 5.96 41.76 25.2
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Next Possible Improvements
Application of Autoregressive Models and
Artificial Neural Networks in Time Series
Prediction
Aleš Pavelka and Aleš Procházka

• add another data into the models - data of gas
  consumption differences or daily temperature
  differences, wind speed, gas prices,
• use possibilities of more prediction methods
  and combine its results
• achieving of multi step prediction by
  improving (or modification) of one step
  prediction model

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End of Presentation.
http//phobos.vscht.cz/pavelkaa