Quantifying Volatility Reduction in German Day-ahead Spot Market in the Period 2006 through 2016

In Europe, Germany is taking the lead in the switch from the conventional to renewable energy. This poses new challenges as wind and solar energy are fundamentally intermittent, weather-dependent and less predictable. It is therefore of considerable interest to investigate the evolution of price volatility in this post-transition era. There are a number of reasons, however, that makes the practical studies difficult. For instance, EPEX prices can be zero or negative. Consequently, the standard approach in financial time series analysis to switch to logarithmic measures is inapplicable. Furthermore, in contrast to the stock market prices which are only available for trading days, EPEX prices cover the whole year, including weekends and holidays. Accordingly, there is a lot of underlying variability in the data which has nothing to do with volatility, but simply reflects diurnal activity patterns. An important distinction of the present work is the application of matrix decomposition techniques, namely the singular value decomposition (SVD), for defining an alternative notion of volatility. This approach is systematically more robust toward outliers and also the diurnal patterns. Our observations show that the day-ahead market is becoming less volatile in recent years

Regularisation for PCA- and SVD-type matrix factorisations

Singular Value Decomposition (SVD) and its close relative, Principal Component Analysis (PCA), are well-known linear matrix decomposition techniques that are widely used in applications such as dimension reduction and clustering. However, an important limitation of SVD/PCA is its sensitivity to noise in the input data. In this paper, we take another look at the problem of regularisation and show that different formulations of the minimisation problem lead to qualitatively different solutions

A statistically principled approach to histogram segmentation

This paper outlines a statistically principled approach to clustering one dimensional data. Given a dataset, the idea is to fit a density function that is as simple as possible, but still compatible with the data. Simplicity is measured in terms of a standard smoothness functional. Data-compatibility is given a precise meaning in terms of distribution-free statistics based on the empirical distribution function. The main advantages of this approach are that (i) it involves a single decision-parameter which has a clear statistical interpretation, and (ii) there is no need to make a priori assumptions about the number or shape of the clusters

One Class Classification for Anomaly Detection: Support Vector Data Description Revisited

The Support Vector Data Description (SVDD) has been introduced to address the problem of anomaly (or outlier) detection. It essentially fits the smallest possible sphere around the given data points, allowing some points to be excluded as outliers. Whether or not a point is excluded, is governed by a slack variable. Mathematically, the values for the slack variables are obtained by minimizing a cost function that balances the size of the sphere against the penalty associated with outliers. In this paper we argue that the SVDD slack variables lack a clear geometric meaning, and we therefore re-analyze the cost function to get a better insight into the characteristics of the solution. We also introduce and analyze two new definitions of slack variables and show that one of the proposed methods behaves more robustly with respect to outliers, thus providing tighter bounds compared to SVDD

Enabling Future Smart Energy Systems

The on-going transition to more sustainable energy production methods means that we are moving away from a monolithic, centrally controlled model to one in which both production and consumption are progressively decentralised and localised. This in turn gives rise to complex interacting networks. ICT and mathematics will be instrumental in making these networks more efficient and resilient. This article highlights two research areas that we expect will play an important role in these developments

Propagating uncertainty in tree-based load forecasts

This paper discusses the use of ensembles of regression trees as a straightforward but versatile methodology to generate short term (day-ahead) load forecasts for real data from the Global Energy Forecasting Competition 2014. Since temperature is a strong predictor of load, we investigate how forecast uncertainty in temperature can affect the performance of the prediction model. To this end, a singular value decomposition (SVD) based approach is harnessed to simulate noisy but realistic temperature profiles. Our results show that as long as uncertainty is not exceedingly large, it is worthwhile to include temperature forecasts as predictors

Quantifying volatility reduction in German day-ahead spot market in the period 2006 through 2016

In Europe, Germany is taking the lead in the switch from the conventional to renewable energy. This poses new challenges as wind and solar energy are fundamentally intermittent, weather-dependent and less predictable. It is therefore of considerable interest to investigate the evolution of price volatility in this post-transition era. There are a number of reasons, however, that makes the practical studies difficult. For instance, EPEX prices can be zero or negative. Consequently, the standard approach in financial time series analysis to switch to logarithmic measures is inapplicable. Furthermore, in contrast to the stock market prices which are only available for trading days, EPEX prices cover the whole year, including weekends and holidays. Accordingly, there is a lot of underlying variability in the data which has nothing to do with volatility, but simply reflects diurnal activity patterns. An important distinction of the present work is the application of matrix decomposition techniques, namely the singular value decomposition (SVD), for defining an alternative notion of volatility. This approach is systematically more robust toward outliers and also the diurnal patterns. Our observations show that the day-ahead market is becoming less volatile in recent years