(This is post 5 of 5 on the ‘Limits to prediction’ ACtioN (applied complexity network) meeting organised by the Santa Fe Institute (SFI) and hosted by Willis Towers Watson on 9 September 2016.)
Prof Farmer made an early and interesting distinction between forecasting and prediction. He defined forecasting as the prediction of trajectories, and therefore necessarily involving the concept of time. Prediction, on the other hand, is not related to time and is instead concerned with how two things relate. He proceeded to outline his personal credentials with respect to prediction. His first practical experience was as a graduate student when he, and collaborators, decided to take on the casinos at roulette – the game traditionally considered to be the epitome of randomness. They, however, as physicists decided that the ball must obey the laws of motion and therefore its resting point must be at least partially predictable. Through trial and error, and building the first computer that would fit into a shoe, they were able to achieve a 70% success rate on the roulette table.
Later in life, Farmer decided to apply his physics knowledge (and algorithms) to stock market data and formed The Prediction Company (subsequently sold to UBS). Again, through hypothesis testing and honing, they were able to generate a success rate of 60% or more through quantitative analysis (shocking, back then).
These experiences usefully illustrate the two methods for prediction: (1) using a fundamental model, such as Newton’s laws for roulette balls, and (2) using a statistical model, or drawing analogues – this relationship between data items could also show up here. As for the limits to prediction, Farmer also proposed two explanations: chaos and ignorance.
Chaos occurs in deterministic systems (which should be 100% predictable, because they are deterministic) that exhibit ‘sensitive dependence on initial conditions’. The problem here is our inability to measure the initial conditions accurately enough, and so the error in our prediction gets bigger the further out in time we go.
Farmer used ignorance and noise interchangeably, to describe what we don’t know. This could be our inability to measure initial conditions as above, could be estimation error, but also includes our lack of fundamental understanding.
Bringing these thoughts together, Farmer turned to market efficiency – which means that markets are difficult to predict (more likely to be ignorance than chaos, as markets are unlikely to be deterministic systems). Farmer suggested that markets were an example of ‘self-organised criticality’, meaning that an apparent equilibrium state can change suddenly past a critical point. He highlighted the role of arbitrageurs in promoting market efficiency, which introduced a paradox as arbitrageurs require inefficiency. He therefore concluded that if markets are efficient at first order they are necessarily inefficient at second order (an argument shared by Grossman and Stiglitz in their famous 1980 paper on the impossibility of efficient markets). This led him to suggest an evolutionary theory of the market, where inefficiencies are the food source for trading strategies.
Doyne Farmer is a professor at the University of Oxford (Institute for New Economic Thinking) and an external professor of the Santa Fe Institute