Genetic Programming for the Induction of Seasonal Forecasts: A Study on Weather Derivatives

The last 10 years has seen the introduction and rapid growth of a market in weather derivatives, financial instruments whose payoffs are determined by the outcome of an underlying weather metric. These instruments allow organisations to protect themselves against the commercial risks posed by weather fluctuations and also provide investment opportunities for financial traders. The size of the market for weather derivatives is substantial, with a survey suggesting that the market size exceeded $45.2 Billion in 2005/2006 with most contracts being written on temperature-based metrics. A key problem faced by buyers and sellers of weather derivatives is the determination of an appropriate pricing model (and resulting price) for the financial instrument. A critical input into the pricing model is an accurate forecast of the underlying weather metric. In this study we induce seasonal forecasting temperature models by means of a machine learning algorithm. Genetic Programming (GP) is applied to learn an accurate, localised, long-term forecast of a temperature profile as part of the broader process of determining appropriate pricing model for weather derivatives. Two different approaches for GP-based time series modelling are adopted. The first is based on a simple system identification approach whereby the temporal index of the time-series is used as the sole regressor of the evolved model. The second is based on iterated single-step prediction that resembles autoregressive and moving average models in statistical time-series modelling. The major issue of effective model generalisation is tackled though the use of an ensemble learning technique that allows a family of forecasting models to be evolved using different training sets, so that predictions are formed by averaging the diverse model outputs. Empirical results suggest that GP is able to successfully induce seasonal forecasting models and that search-based autoregressive models compose a more stable unit of evolution in terms of generalisation performance for the three datasets considered. In addition, the use of ensemble learning of 5-model predictors enhanced the generalisation ability of the system as opposed to single-model prediction systems. On a more general note, there is an increasing recognition of the utility of evolutionary methodologies for the modelling of meteorological, climatic and ecological phenomena, and this work also contributes to this literature.