Simulation of temperature time-series on long time scales with application to pricing weather derivatives

• Main Author: Andrianova, Anna
• Published: London School of Economics and Political Science (University of London) 2009
• Subjects: 551.63
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.645896

Long term weather forecasts are in great demand across many industries, such as the agricultural, tourism, and energy sectors. In this thesis a new long-term temperature forecasting benchmark is proposed. In particular, the Ensemble Random Analog Prediction (ERAP) dynamic resampler is developed. ERAP allows one to generate temperature scenarios over long time scales without making assumptions about the underlying model of temperature. ERAP works by identifying similar patterns in the historical data across multiple time scales. We also propose a new non-linear weather resembling test system - a weather-like process that mimics the real temperature with additional long term non-linear patterns. Finally we study the mixing of physical weather forecasts with the historical data. In particular, combination forecasts are developed that mix information from both physical forecasting models and historical data. The methodology is developed by exploring kernel dressing of forecast scenarios and ignorance skill-score based optimization of parameters. The new weather generator ERAP is then extensively tested in the perfect model scenario, by studying its performance in terms of the generated statistics, using both a noisy Lorenz system and the new weather like test process. ERAP is also tested on real weather data by assessing its performance on the Berlin daily maximum temperature in terms of the generated statistics. Finally ERAP is also used for pricing a weather derivative, and the prices compared to other existing techniques including pricing based on the historical statistics, Monte-Carlo using a fitted distribution, plus other statistical techniques from the weather derivative literature. For combination forecasts we study the sensitivity of parameters to ensemble size and the level of noise in the initial conditions, within the perfect model scenario. We show that ERAP performed well in the perfect model scenario, on the actual data and when used for pricing. The historical statistics were closely replicated, the statistics of a chosen verification set were also well replicated and in some cases, ERAP generated data provided a better match to the statistics of the verification set than the climatology (the statistics of the learning set itself). Some non-conventional statistics were better replicated using ERAP in both the perfect and imperfect model scenarios. Additionally, information is provided by ERAP on the uncertainty of the computed statistics. We also show that ERAP provides more reliable pricing, because it provides more reliable long-term simulations. The fake weather generator developed in this thesis has shown to provide a good test data set that is non-linear with patterns on multiple time scales and closely resembles the characteristics of real temperature time series. This process could be a viable alternative, if parameters are fully calibrated to the chosen weather data, to existing statistical temperature modeling approaches. This work could be further improved by the creating better parameter estimation techniques for ERAP. ERAP could also be extended to several dimensions allowing the generation of more enhanced synthetic weather data. For the purpose of pricing weather derivatives more work needs to be done to address the transformation of ERAP scenarios to probabilistic weather forecasts. Further work may also include studies of the performance of combined forecasts, which mix synthetic data and physical weather forecasts, in practice.