Estimating Trends in Weather Series: Consequences for Pricing Derivatives

Predictions of future weather conditions play an important role in pricing weather derivatives. In many instances, the dates for which we require predictions are well beyond the point where physical forecasts have any skill. Under these circumstances, predictions are generated from statistical models of historic data. This paper derives conditions for which the predictive performance in regression is improved by ignoring or shrinking the contribution from some of the explanatory variables. We suggest methods for estimating the degree of shrinkage required in practice. We illustrate our methods using surface temperature data from fifteen stations in the United States.