A comparison of temperature density forecasts from GARCH and atmospheric models

Abstract

Density forecasts for weather variables are useful for the many industries exposed to weather risk. Weather ensemble predictions are generated from atmospheric models and consist of multiple future scenarios for a weather variable. The distribution of the scenarios can be used as a density forecast, which is needed for pricing weather derivatives. We consider one to 10 dayahead density forecasts provided by temperature ensemble predictions. More specifically, we evaluate forecasts of the mean and quantiles of the density. The mean of the ensemble scenarios is the most accurate forecast for the mean of the density. We use quantile regression to debias the quantiles of the distribution of the ensemble scenarios. The resultant quantile forecasts compare favourably with those from a GARCH model. These results indicate the strong potential for the use of ensemble prediction in temperature density forecasting.

Density forecasting for weather derivative pricing

“…As one would expect, there is strong within-year seasonality in the mean of the series, and a reasonable degree of variation about that seasonal pattern. ***** Figure 1 ***** We used the same AR-GARCH models considered in our previous study (see Taylor and Buizza, 2004). These models were proposed by Franses et al (2001) and Campbell and Diebold (2005), and are presented in expression (2).…”

“…Table 1 presents our estimated model for each of our five temperature series. For more details regarding these models, see Taylor and Buizza (2004). ***** Table 1 ***** The AR-GARCH models enable predictions to be made for the mean and variance at a given forecast horizon.…”

“…Therefore, our conclusion is that there is strong potential for the use of ensemble predictions in forecasting the payoff density. Please note that this table has previously appeared in Taylor and Buizza (2004). Table 3.…”

“…Mean rankings of the post-sample dynamic quantile chi-square statistic across the five locations. Please note that this figure has previously appeared in Taylor and Buizza (2004). …”

“…We compare the ensemble-based density forecasts of the derivative payoff with those based on a univariate time series model for temperature with variance modelled as a generalized autoregressive conditional heteroskedastic (GARCH) process. This paper is a follow up to a study that considered density forecasting for temperature variables (Taylor and Buizza, 2004). Although useful in establishing that there is strong potential for the use of ensemble predictions in temperature density forecasting, that study did not address the pricing of weather derivatives, which is the focus of the current paper.…”