Dr M F Abbod 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 GMDH Genetic Algorithms Particle Swarm Optimisation Financial Data Prediction Results Conclusions

Dr M F Abbod 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 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 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 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 GMDH

Dr M F Abbod GMDH Each 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: The Choice of Plymomial Eq

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

Dr M F Abbod Genetic Algorithms It was developed by Goldberg in Genetic Algorithms (GAs) are randomised search and optimisation techniques guided by the principles of evolution and natural genetics

Dr M F Abbod 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 Rules of movement – the formulas: x y

Dr M F Abbod The Data USD2EURO from 29 Sept, 2004 to 5 Oct, GBP2USD from 29 Sept, 2004 to 5 Oct,

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

Dr M F Abbod Training Data Performance

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

Dr M F Abbod 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 model predictions on testing set for (a) USD2EUR and (b) GBP2USD

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

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

Dr M F Abbod Testing Data Performance

Dr M F Abbod USD2EUR

Dr M F Abbod GBP2USD

Dr M F Abbod Performance Improvements

Dr M F Abbod Computational Requirements

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