Closed Form Expressions for the Uncertainty from Linear Detrending, and the Pricing of Weather Derivatives

Abstract

Weather derivative pricing is often based on a statistical analysis of past weather data. Such data may be non-stationary, and detrending methods can be used to attempt to remove the non-stationarity in the mean. The performance of different methods can be compared by considering aspects of the distribution of errors in the predictions they make. In this paper we derive closed-form expressions for the mean error, error variance and mean square error for flat line and linear trend models in the case where the real trend is linear.

Keywords: weather derivatives, trends, detrending, recentering

JEL Classification: G12, G13