Chaos Theory and Economics – Neural Networks and Forecasting

Course Outline:

Introduction to Chaotic dynamics – The Logistic equation –Lorenz System – Phase space – Method of delays – Mutual information –Autocorrelation function –Information Dimension – Correlation integral –Fractal &Correlation dimension – Embedding dimension – False neighbors methods – Lyapunov component – Kolmogorov Entropy – Routes to Chaos – Noise reduction – Stationary test – Time series prediction with phase state space reconstruction  (Local Models Global models) – Modeling economic systems – Detection of economic variables – Dynamic Control of Economy – Applications of nonlinear time series analysis with TISEAN package and TSTOOL (Matlab implementation).

Introduction to neural networks – Supervised learning – Self-learning – Back propagation Neural Networks – Time Lagged Neural networks – Radial Basis Neural Networks – Neural network architectures based on nonlinear analysis – Classification – Time series prediction (one step & multistep) – Cross prediction – Modeling economic systems – Detection of economic variables – Applications with Alyuda Neuro Intelligence – Matlab neural networks and Zaitun time series.

Aim:

This course aims to be an introduction to chaos theory and neural networks. It includes two stages:

• the first stage includes an introduction to nonlinear dynamics and provide students with the knowledge needed to understand nonlinear dynamics applications, with emphasis on economics. Financial time series prediction is also between the specific targets of this stage.
• the second stage includes an introduction to neural networks and their applications, with a focus on economic systems, providing students with the essential background to understand neural network applications in combined with nonlinear analysis. Emphasis is put on time series prediction, classification and data mining.

Learning Objectives:

This course is designed for students who aspire to be analystsandexecutives in financial companies and banks or want to be financialadvisors tobusinesses andgovernments. Applying Chaos Theory and Neural Networks in economical time series, the students of this course will be able to forecast in eitherthe short or the long horizon, the evolution of financial magnitudes, such as the Stock Exchange index, the Euro/Dollar index, the gold price index etc. It is apparent that predictions are a crucial elementforfinance and banking. A major example it the prediction of the returns provided by the Stock Market on Daily, weekly and monthly basis. Initially, the feasibility of the prediction task is examined, by providing evidence that markets are not randomly fluctuating. Detection of the interconnection and the bias between economic and finance variables is another objective. Additionally, the knowledge of routes to chaos would enable students to predict periods of order and periods of instability and measure their efficiency.

On completion of this module, students are expected to be able to:

• Find the importance of Economic variables affecting a system
• Predict and cross predict economic time series
• Have an understanding of how they, as future leaders of innovative organizations, can predict and make the correct decisions
• Analyze economic time series
• Decide if an economic system behaves as deterministic chaotic or stochastic
• Find the hidden variables that affect a system

Suggested for further reading:

1. G.L. Baker and J.P. Gollup, “Chaotic dynamics: An introduction”, 2nd edition, Cambridge University Press, 1996.

2. H. Kantz and T. Schreiber, “Nonlinear Time Series Analysis”, 2nd edition, Cambridge University Press, 2003.

3. E.E. Peters ,“Chaos and Order in the Capital Markets”, John Wiley and sons, USA, 1991.

4. F. Morrison, “The Art of Modeling Dynamic Systems: Forecasting for Chaos, Randomness and Determinism”, Dover, 2008.

5. R. Kautz, “Chaos: The Science of Predictable Random Motion”, Oxford University Press, USA, 2010.

6. S. Haykin, “Neural networks a comprehensive foundation”, Prentice Hall, 2005.

7. Juan R. Rabuñal and Julián Dorado, “Artificial Neural Networks in Real Life Applications”, IDEA GROUP PUBLISHING, 2006.

8. Paul D. McNelis, “Neural Networks in Finance: Gaining Predictive Edge in the Market”, ELSEVIER, 2005.

9. A.K. Dhamija, “Forecasting Exchange rate: Use of Neural Networks in Quantitative Finance”, VDM Verlag,2009.

10. P.P. Wang, “Computational Intelligence in Economics and Finance”, Springer,2010.