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英文文献：Rough electricity: a new fractal multi-factor model of electricity spot prices-粗糙电:一种新的分形多因素电价模型
英文文献作者：Mikkel Bennedsen
英文文献摘要：
We introduce a new mathematical model of electricity spot prices which accounts for the most important stylized facts of these time series: seasonality, spikes, stochastic volatility and mean reversion. Empirical studies have found a possible fifth stylized fact, fractality, and our approach explicitly incorporates this into the model of the prices. Our setup generalizes the popular Ornstein Uhlenbeck-based multi-factor framework of Benth et al. (2007) and allows us to perform statistical tests to distinguish between an Ornstein Uhlenbeck-based model and a fractal model. Further, through the multi-factor approach we account for seasonality and spikes before estimating - and making inference on - the degree of fractality. This is novel in the literature and we present simulation evidence showing that these precautions are crucial to accurate estimation. Lastly, we estimate our model on recent data from six European energy exchanges and we find statistical evidence of fractality in five out of six markets. As an application of our model, we show how, in these five markets, a fractal component improves short term forecasting of the prices.
我们介绍了一个新的电力现货价格的数学模型，它解释了这些时间序列中最重要的程式化事实:季节性、尖峰、随机波动和均值回归。经验研究发现了第五种可能的程式化事实，即分形，而我们的方法明确地将其纳入了价格模型中。我们的设置概括了Benth等人(2007)流行的基于Ornstein uhlenbeck的多因素框架，并允许我们执行统计测试来区分基于Ornstein uhlenbeck的模型和分形模型。此外，通过多因素方法，我们在估计和推断分形程度之前考虑了季节性和峰值。这在文献中是新颖的，我们提出的模拟证据表明，这些预防措施是至关重要的准确估计。最后，我们根据欧洲6个能源交易所的最新数据对我们的模型进行了估计，我们发现6个市场中有5个市场存在分形现象。作为我们模型的应用，我们展示了在这五个市场中，分形成分是如何改进价格的短期预测的。
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