Building Econometric Models

Detecting Chaos

• ‘Introductory Econometrics for Finance’ © Chris Brooks 2013

• A system is chaotic if it exhibits sensitive dependence on initial conditions (SDIC)
• So an infinitesimal change is made to the initial conditions (the initial state of the system), then the corresponding change iterated through the system for some arbitrary length of time will grow exponentially
• The largest Lyapunov exponent is a test for chaos
• It measures the rate at which information is lost from a system
• A positive largest Lyapunov exponent implies sensitive dependence, and therefore that evidence of chaos has been obtained
• Almost without exception, applications of chaos theory to financial markets have been unsuccessful
• This is probably because financial and economic data are usually far noisier and ‘more random’ than data from other disciplines

Neural Networks

• ‘Introductory Econometrics for Finance’ © Chris Brooks 2013

• Artificial neural networks (ANNs) are a class of models whose structure is broadly motivated by the way that the brain performs computation
• ANNs have been widely employed in finance for tackling time series and classification problems
• Applications have included forecasting financial asset returns, volatility, bankruptcy and takeover prediction
• Neural networks have virtually no theoretical motivation in finance (they are often termed a ‘black box’)
• They can fit any functional relationship in the data to an arbitrary degree of accuracy.

Feedforward Neural Networks

• ‘Introductory Econometrics for Finance’ © Chris Brooks 2013

• The most common class of ANN models in finance are known as feedforward network models
• These have a set of inputs (akin to regressors) linked to one or more outputs (akin to the regressand) via one or more ‘hidden’ or intermediate layers
• The size and number of hidden layers can be modified to give a closer or less close fit to the data sample
• A feedforward network with no hidden layers is simply a standard linear regression model
• Neural network models work best where financial theory has virtually nothing to say about the likely functional form for the relationship between a set of variables.