Understanding changes in the frequency, severity, and seasonality of daily temperature extremes is important for public policy decisions regarding heat waves and cold snaps. A heat wave is sometimes defined in terms of both the daily minimum and maximum temperature, which necessitates the generation of forecasts of their joint distribution. In this paper, we develop time series models with the aim of providing insight and producing forecasts of the joint distribution that can challenge the accuracy of forecasts based on ensemble predictions from a numerical weather prediction model. We use ensemble model output statistics to recalibrate the raw ensemble predictions for the marginal distributions, with ensemble copula coupling used to capture the dependency between the marginal distributions. In terms of time series modelling, we consider a bivariate VARMA-MGARCH model. We use daily Spanish data recorded over a 65-year period, and find that, for the 5-year out-of-sample period, the recalibrated ensemble predictions outperform the time series models in terms of forecast accuracy.

了解每日极端温度的频率、严重程度和季节性变化对于有关热浪和寒流的公共政策决策非常重要。有时根据每日最低和最高温度来定义热浪，这需要生成它们的联合分布预测。在本文中，我们开发了时间序列模型，旨在提供联合分布的洞察力和预测，这些模型可以挑战基于数值天气预报模型集合预测的预测准确性。我们使用集成模型输出统计来重新校准边缘分布的原始集成预测，使用集成 copula 耦合来捕获边缘分布之间的依赖关系。在时间序列建模方面，我们考虑一个二元 VARMA-MGARCH 模型。我们使用 65 年期间记录的每日西班牙数据，发现在 5 年样本外期间，重新校准的集合预测在预测准确性方面优于时间序列模型。