Daniel Ambach

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).

Short-term wind speed forecasting in Germany

The importance of renewable power production is a set goal in terms of the energy turnaround. Developing short-term wind speed forecasting improvements might increase the profitability of wind power. This article compares two novel approaches to model and predict wind speed. Both approaches incorporate periodic interactions, whereas the first model uses Fourier series to model the periodicity. The second model takes generalised trigonometric functions into consideration. The aforementioned Fourier series are special types of the p-generalised trigonometrical function and therefore model 1 is nested in model 2. The two models use an autoregressive fractionally integrated moving average–asymmetric power generalised autoregressive conditional heteroscedasticity process to cover the autocorrelation and the heteroscedasticity. A data set which consist of 10 min data collected at four stations at the German–Polish border from August 2007 to December 2012 is analysed. The most important finding is an enhancement of the forecasting accuracy up to three hours that is directly related to our new short-term forecasting model.

A new high-dimensional time series approach for wind speed, wind direction and air pressure forecasting

Many wind speed forecasting approaches have been proposed in literature. In this paper a new statistical approach for jointly predicting wind speed, wind direction and air pressure is introduced. The wind direction and the air pressure are important to extend the forecasting accuracy of wind speed forecasts. A good forecast for the wind direction helps to bring the turbine into the predominant wind direction. We combine a multivariate seasonal time varying threshold autoregressive model with interactions (TVARX) with a threshold seasonal autoregressive conditional heteroscedastic (TARCHX) model. The model includes periodicity, conditional heteroscedasticity, interactions of different dependent variables and a complex autoregressive structure with non-linear impacts. In contrast to ordinary likelihood estimation approaches, we apply a high-dimensional shrinkage technique instead of a distributional assumption for the dependent variables. The iteratively re-weighted least absolute shrinkage and selection operator (LASSO) method allows to capture conditional heteroscedasticity and a comparatively fast computing time. The proposed approach yields accurate predictions of wind speed, wind direction and air pressure for a short-term period. Prediction intervals up to twenty-four hours are presented.

Obtaining Superior Wind Power Predictions from a Periodic and Heteroscedastic Wind Power Prediction Tool

The Wind Power Prediction Tool (WPPT) has successfully been used for accurate wind power forecasts in the short to medium term scenario (up to 12 hours ahead). Since its development about a decade ago, a lot of additional stochastic modeling has been applied to the interdependency of wind power and wind speed. We improve the model in three ways: First, we replace the rather simple Fourier series of the basic model by more general and flexible periodic Basis splines (B-splines). Second, we model conditional heteroscedasticity by a threshold-GARCH (TGARCH) model, one aspect that is entirely left out by the underlying model. Third, we evaluate several distributional forms of the model’s error term. While the original WPPT assumes gaussian errors only, we also investigate whether the errors may follow a Student’s t-distribution as well as a skew t-distribution. In this article we show that our periodic WPPT-CH model is able to improve forecasts’ accuracy significantly, when compared to the plain WPPT model.

An Implementation of the Mycielski Algorithm as a Predictor in R

Univariate time series analysis is usually performed by arbitrarily complex parametric modeling. At least for prediction, a simple non-parametric alternative is the Mycielski algorithm, a forecasting method based on pat- tern matching. The reproducible research presented here shows how to perform out of sample forecasts using the methodology of Mycielski. The algorithm provides well results in scenarios where usual univariate models such as ARIMA family models return limited accuracy. In this article we describe the idea of the Mycielski based prediction algorithm in general. We contribute a reference implementation in R and give a short example.