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Using Intelligent Optimisation Methods to Improve the Group Method of Data Handling in Time Series Prediction Maysam Abbod and Karishma Dashpande School of Engineering and Design Brunel University, West London Outline GMDH Genetic Algorithms Particle Swarm Optimisation Financial Data

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slide1

Using Intelligent Optimisation Methods to Improve the Group Method of Data Handling in Time Series Prediction

Maysam Abbod and Karishma Dashpande

School of Engineering and Design

Brunel University, West London

Dr M F Abbod

outline
Outline
  • GMDH
  • Genetic Algorithms
  • Particle Swarm Optimisation
  • Financial Data
  • Prediction Results
  • Conclusions

Dr M F Abbod

introduction
Introduction
  • The GMDH is an algorithm to learn inductively, combinatorial multi-layers for modelling complex systems.
  • The method was introduced by A. G. Ivakhnenko in 1966 and several scholars has since developed the theory GMDH for various applications.

Dr M F Abbod

slide4
GMDH

An important feature of the algorithm GMDH is providing robust polynomial regression models of linear and non-linear systems.

Dr M F Abbod

principle of selection
Principle of Selection

Ivakhnenko uses the principles of selectivity - "to get plants, for example, with certain properties, there is the first cross and then the first harvest. Later picks up the best plants and it is the second crossing and the second harvest and thus to find a plant that is desired. "

Dr M F Abbod

slide6
GMDH

GMDH-layers All combinations of inputs are generated and issued the first layer of the network. The outputs of these are classified and then selected for entry into the next layer with all combinations of selected outlets. Only those elements whose performance was acceptable survive to form the next layer. This process is continued as long as each layer (n +1) subsequent produce a better result than the layer (n). When the layer (n +1) is not better as the layer (n), the process is stopped.

Dr M F Abbod

slide7
GMDH

Dr M F Abbod

the choice of plymomial eq
The Choice of Plymomial Eq
  • GMDHEach layer consists of Polynomial Equation generated from combinations of pairs of inputs. Each node is the way Ivakhnenko polynomial which is a polynomial of the second order: The error we are computed by RMSE and MAPE:

Dr M F Abbod

the coefficients
The Coefficients

Determining the values that can produce the best adjustment of the equation

Dr M F Abbod

genetic algorithms
Genetic Algorithms

It was developed by Goldberg in 1989.

Genetic Algorithms (GAs) are randomised search and optimisation techniques guided by the principles of evolution and natural genetics

Dr M F Abbod

genetic algorithms11
Genetic Algorithms
  • Chromosomes are an encoded representations of the solutions, each gene represents a feature
  • A fitness value that reflects how good it is
  • A crossover mechanism that exchanges portions between strings
  • Mutation plays the role of regenerating lost genetic material

Dr M F Abbod

particle swarm optimisation
Particle Swarm Optimisation

Rules of movement – the formulas:

y

x

Dr M F Abbod

the data
The Data
  • USD2EURO from 29 Sept, 2004 to 5 Oct, 2007.
  • GBP2USD from 29 Sept, 2004 to 5 Oct, 2007.
  • www.oanda.com

Dr M F Abbod

the data14
The Data
  • 2 data sets (GBP2USD & USD2EUR)
  • 120 Data points
  • 100 for training
  • 20 for testing

Dr M F Abbod

slide16
GMDH

GMDH predictions on testing set for

(a) USD2EUR, and (b) GBP2USD

Dr M F Abbod

pso gmdh gbest
PSO-GMDH (gbest)

PSO-GMDH gbest model predictions on testing set for

(a) USD2EUR and (b) GBP2USD

Dr M F Abbod

pso gmdh lbest
PSO-GMDH (lbest)

PSO-GMDH lbest model predictions on testing set for

(a) USD2EUR and (b) GBP2USD

Dr M F Abbod

ga gmdh
GA-GMDH

GA-GMDH predictions on testing set for

(a) USD2EUR, and (b) GBP2USD

Dr M F Abbod

ga pso gmdh
GA-PSO-GMDH

GA-PSO-GMDH predictions on testing set for

(a) USD2EUR and (b) GBP2USD

Dr M F Abbod

usd2eur
USD2EUR

Dr M F Abbod

gbp2usd
GBP2USD

Dr M F Abbod

conclusions
Conclusions
  • Improvements can be achieved
  • Model Complexity and Computational burden
  • Parallel Processing (Matlab: Parallel Computing Toolbox)
  • Other data sets

Dr M F Abbod