Florian Ziel

Efficient modeling and forecasting of electricity spot prices

The increasing importance of renewable energy, especially solar and wind power, has led to new forces in the formation of electricity prices. Hence, this paper introduces an econometric model for the hourly time series of electricity prices of the European Power Exchange (EPEX) which incorporates specific features like renewable energy. The model consists of several sophisticated and established approaches and can be regarded as a periodic VAR-TARCH with wind power, solar power, and load as influences on the time series. It is able to map the distinct and well-known features of electricity prices in Germany. An efficient iteratively reweighted lasso approach is used for the estimation. Moreover, it is shown that several existing models are outperformed by the procedure developed in this paper.

Forecasting Electricity Spot Prices Using Lasso: On Capturing the Autoregressive Intraday Structure

In this paper we present a regression based model for day-ahead electricity spot prices. We estimate the considered linear regression model by the lasso estimation method. The lasso approach allows for many possible parameters in the model, but also shrinks and sparsifies the parameters automatically to avoid overfitting. Thus, it is able to capture the autoregressive intraday dependency structure of the electricity price well. We discuss in detail the estimation results which provide insights to the intraday behavior of electricity prices. We perform an out-of-sample forecasting study for several European electricity markets. The results illustrate well that the efficient lasso based estimation technique can exhibit advantages from two popular model approaches.

Forecasting day ahead electricity spot prices: The impact of the EXAA to other European electricity markets

In our paper we analyze the relationship between the day-ahead electricity price of the Energy Exchange Austria (EXAA) and other day-ahead electricity prices in Europe. We focus on markets, which settle their prices after the EXAA, which enables traders to include the EXAA price into their calculations. For each market we employ econometric models to incorporate the EXAA price and compare them with their counterparts without the price of the Austrian exchange. By employing a forecasting study, we find that electricity price models can be improved when EXAA prices are considered.

Lasso estimation for GEFCom2014 probabilistic electric load forecasting

We present a methodology for probabilistic load forecasting that is based on lasso (least absolute shrinkage and selection operator) estimation. The model considered can be regarded as a bivariate time-varying threshold autoregressive(AR) process for the hourly electric load and temperature. The joint modeling approach incorporates the temperature effects directly, and reflects daily, weekly, and annual seasonal patterns and public holiday effects. We provide two empirical studies, one based on the probabilistic load forecasting track of the Global Energy Forecasting Competition 2014 (GEFCom2014-L), and the other based on another recent probabilistic load forecasting competition that follows a setup similar to that of GEFCom2014-L. In both empirical case studies, the proposed methodology outperforms two multiple linear regression based benchmarks from among the top eight entries to GEFCom2014-L.

Electricity Price Forecasting using Sale and Purchase Curves: The X-Model

Our paper aims to model and forecast the electricity price by taking a completely new perspective on the data. It will be the first approach which is able to combine the insights of market structure models with extensive and modern econometric analysis. Instead of directly modeling the electricity price as it is usually done in time series or data mining approaches, we model and utilize its true source: the sale and purchase curves of the electricity exchange. We will refer to this new model as X-Model, as almost every deregulated electricity price is simply the result of the intersection of the electricity supply and demand curve at a certain auction. Therefore we show an approach to deal with a tremendous amount of auction data, using a subtle data processing technique as well as dimension reduction and lasso based estimation methods. We incorporate not only several known features, such as seasonal behavior or the impact of other processes like renewable energy, but also completely new elaborated stylized facts of the bidding structure. Our model is able to capture the non-linear behavior of the electricity price, which is especially useful for predicting huge price spikes. Using simulation methods we show how to derive prediction intervals for probabilistic forecasting. We describe and show the proposed methods for the day-ahead EPEX spot price of Germany and Austria.

Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR-ARCH type processes

Shrinkage algorithms are of great importance in almost every area of statistics due to the increasing impact of big data. Especially time series analysis benefits from efficient and rapid estimation techniques such as the lasso. However, currently lasso type estimators for autoregressive time series models still focus on models with homoscedastic residuals. Therefore, an iteratively reweighted adaptive lasso algorithm for the estimation of time series models under conditional heteroscedasticity is presented in a high-dimensional setting. The asymptotic behaviour of the resulting estimator is analysed. It is found that the proposed estimation procedure performs substantially better than its homoscedastic counterpart. A special case of the algorithm is suitable to compute the estimated multivariate AR-ARCH type models efficiently. Extensions to the model like periodic AR-ARCH, threshold AR-ARCH or ARMA-GARCH are discussed. Finally, different simulation results and applications to electricity market data and returns of metal prices are shown.

Day-ahead electricity price forecasting with high-dimensional structures: Univariate vs. multivariate modeling frameworks

We conduct an extensive empirical study on short-term electricity price forecasting (EPF) to address the long-standing question if the optimal model structure for EPF is univariate or multivariate. We provide evidence that despite a minor edge in predictive performance overall, the multivariate modeling framework does not uniformly outperform the univariate one across all 12 considered datasets, seasons of the year or hours of the day, and at times is outperformed by the latter. This is an indication that combining advanced structures or the corresponding forecasts from both modeling approaches can bring a further improvement in forecasting accuracy. We show that this indeed can be the case, even for a simple averaging scheme involving only two models. Finally, we also analyze variable selection for the best performing high-dimensional lasso-type models, thus provide guidelines to structuring better performing forecasting model designs.

Forecasting wind power – Modeling periodic and non-linear effects under conditional heteroscedasticity

In this article we present an approach that enables joint wind speed and wind power forecasts for a wind park. We combine a multivariate seasonal time varying threshold autoregressive moving average (TVARMA) model with a power threshold generalized autoregressive conditional heteroscedastic (power-TGARCH) model. The modeling framework incorporates diurnal and annual periodicity modeling by periodic B-splines, conditional heteroscedasticity and a complex autoregressive structure with non-linear impacts. In contrast to usually time-consuming estimation approaches as likelihood estimation, we apply a high-dimensional shrinkage technique. We utilize an iteratively re-weighted least absolute shrinkage and selection operator (lasso) technique. It allows for conditional heteroscedasticity, provides fast computing times and guarantees a parsimonious and regularized specification, even though the parameter space may be vast. We are able to show that our approach provides accurate forecasts of wind power at a turbine-specific level for forecasting horizons of up to 48h (short- to medium-term forecasts).

Variance Stabilizing Transformations for Electricity Spot Price Forecasting

Most electricity spot price series exhibit price spikes. These extreme observations may significantly impact the obtained model estimates and hence reduce efficiency of the employed predictive algorithms. For markets with only positive prices, the logarithmic transform is the single most commonly used technique to reduce spike severity and consequently stabilize the variance. However, for datasets with very close to zero (like the Spanish) or negative (like the German) prices the log-transform is not feasible. What reasonable choices do we have then? To address this issue, we evaluate 16 variance stabilizing transformations within a comprehensive forecasting study involving two model classes (regression models, neural networks) and 12 datasets from diverse power markets. We show that the probability integral transform combined with the standard Gaussian distribution yields the best approach, significantly better than many of the considered alternatives.

Modelling and forecasting electricity load using lasso methods

We present a multivariate time series model to hourly German electricity load. We incorporate the influence of neighbouring countries, temperature, public holidays and the clock change in our non-linear conditionally heteroscedastic model. The considered model can be regarded as a time-varying threshold ARMA-GARCH process. A fast iterative lasso based algorithm is used for the parameter estimation.