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

1. 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

2. Outline • GMDH • Genetic Algorithms • Particle Swarm Optimisation • Financial Data • Prediction Results • Conclusions Dr M F Abbod

3. 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

4. GMDH An important feature of the algorithm GMDH is providing robust polynomial regression models of linear and non-linear systems. Dr M F Abbod

5. 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

6. 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

7. GMDH Dr M F Abbod

8. 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

9. The Coefficients Determining the values that can produce the best adjustment of the equation Dr M F Abbod

10. 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

11. 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

12. Particle Swarm Optimisation Rules of movement – the formulas: y x Dr M F Abbod

13. 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

14. The Data • 2 data sets (GBP2USD & USD2EUR) • 120 Data points • 100 for training • 20 for testing Dr M F Abbod

15. Training Data Performance Dr M F Abbod

16. GMDH GMDH predictions on testing set for (a) USD2EUR, and (b) GBP2USD Dr M F Abbod

17. PSO-GMDH (gbest) PSO-GMDH gbest model predictions on testing set for (a) USD2EUR and (b) GBP2USD Dr M F Abbod

18. PSO-GMDH (lbest) PSO-GMDH lbest model predictions on testing set for (a) USD2EUR and (b) GBP2USD Dr M F Abbod

19. GA-GMDH GA-GMDH predictions on testing set for (a) USD2EUR, and (b) GBP2USD Dr M F Abbod

20. GA-PSO-GMDH GA-PSO-GMDH predictions on testing set for (a) USD2EUR and (b) GBP2USD Dr M F Abbod

21. Testing Data Performance Dr M F Abbod

22. USD2EUR Dr M F Abbod

23. GBP2USD Dr M F Abbod

24. Performance Improvements Dr M F Abbod

25. Computational Requirements Dr M F Abbod

26. Conclusions • Improvements can be achieved • Model Complexity and Computational burden • Parallel Processing (Matlab: Parallel Computing Toolbox) • Other data sets Dr M F Abbod