The world around us is a a very detailed and intricate system. In particular, real-world systems tend to comprise of many interacting parts, yielding a macroscopic dynamical behavior which features a complicated mix of unpredictability and predictability at various scales, e.g., ranging from the actions of each atom to each chemical to each animal to the human mind which is in many ways still a mystery leading to politics and society. These are all very particular examples of how it is a complex system, but one can imagine many more examples such as petals on a flower or even global warming.
In fact everything around us is a complex system Wouldn’t it be neat to predict how this complex system evolves? Well predicting this particular system is beyond the scope of this thesis and may even be philosophically or scientifically argued to be impossible. However, in order to attack such an absurd question, we might find ourselves immediately thinking along the lines of two main questions. The first question is that of modeling. How does one model a complex system? After all it is complex, right And we notice complexity at different scales.
Well, the modeling step is extremely difficult for capturing the intricacies and will always be left with something to desire. The other main question is if given such a model, purely as an observer how could we go about predicting the time evolution of the model for the complex system. This will largely depend on how predictable the model is. If we are dealing with a purely deterministic model, the evolution is trivial. However, even in this case, if we assume some error in both our model and observation of the complex system, intelligently perturbing our prediction to match the observation is no longer trivial.
Contents
1 Introduction
1.1 Financial Markets
1.2 Protein Ecologies
2 Financial Markets
2.1 The Artificial Market Model
- 2.1.1 A Binary Agent Resource Game
2.1.2 The Minority Game
2.1.3 Extension to an Artificial Market Model
2.2 Choosing Parameters
2.3 Recursive Optimization Scheme
- 2.3.1 Kalman Filter
2.3.2 Nonlinear Equality Constraints
2.3.3 Nonlinear Inequality Constraints
2.4 Covariance Matching Techniques
- 2.4.1 Determining the Process Noise and Measurement Noise
2.4.2 Upper and Lower Bounds for Covariance Matrices
2.4.3 Choosing Bounds for a Probability Measure
2.5 Application to a Simulated Minority Game
- 2.5.1 Generating Simulation Data
2.5.2 Forming the Estimation Problem
2.5.3 Effective Forecasting
2.5.4 Results of simulation
2.6 Application to a Real Foreign Exchange Series
- 2.6.1 Scaling the difference series
2.6.2 Forming the Estimation Problem
2.6.3 Results on the Real Data
2.7 Additional Algorithm Tests
- 2.7.1 State Estimate Errors
2.7.2 Measurement Residuals Process
2.8 Removing the Probability Sum Constraint
2.9 Estimation with Many Possible Types of Agents
- 2.9.1 Averaging over Multiple Runs
2.9.2 Bias Estimation
2.10 Another Look at the Same Foreign Exchange Series
2.11 Extension to Other Games
3 Non-Genomic Evolution
3.1 Background and Previous Work
3.2 The Protocell Model
- 3.2.1 Global Utility
3.2.2 Protocell Dynamics
3.3 Agent Framework for Protein Model
- 3.3.1 Type Agents
3.3.2 Breaker-Specialization Agents
3.3.3 Cluster Assignment of New Proteins
3.3.4 Agent Utilities
3.4 Results
3.5 Discussion
4 Conclusions
5 Future Work
5.1 Magnitude v. Direction
5.2 Forecasting using an Artificial Multi-Market Model
5.3 Approximating a Continuously Adjusting Minority Game
5.4 The Effects of News
5.5 Evolving the Model for Protein Ecologies
Bibliography
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Predicting Behavior in Agent-Based Models for Complex Systems
