In this article, we investigate conditional mean and conditional variance forecasts using a dynamic model following a k-factor GIGARCH process. Particularly, we provide the analytical expression of the conditional variance of the prediction error. We apply this method to the German electricity price market for the period August 15, 2000–December 31, 2002 and we test spot prices forecasts until one-month ahead forecast. The forecasting performance of the model is compared with a SARIMA–GARCH benchmark model using the year 2003 as the out-of-sample. The proposed model outperforms clearly the benchmark model. We conclude that the k-factor GIGARCH process is a suitable tool to forecast spot prices, using the classical RMSE criteria.
In finance, commodity price forecasting is a crucial issue, in particular for electricity. Indeed, price forecasts can help evaluating bilateral contracts. For such a commodity, price forecasts can be based on a spot price analysis. Since electricity spot prices have a behavior which presents specific features, the price forecasts problem can be complex. In another hand, electricity price volatility has a marked variability in time. We observe both high and low periods of price reaction. Recently spot price volatility has been studied and modelled using a volatility model depending on time. Using such a model, Benini et al. [1] investigate several markets. In addition, electricity spot prices exhibit long memory behavior combined with a periodic behavior. Recent works have taken into account these last features using related ARFIMA models, see Koopman et al. [13] or Diongue et al. [6] or Diongue and Guégan [7].
After modelling these electricity prices, the forecasting problem arises. In the literature, two approaches have been considered: parametric models using AR, ARX, AR–GARCH, ARX–GARCH and Regime switching models, Misiorek et al. [14]; and non-parametric methods like the neuronal nets for instance, Ramsay and Wang [15] and [3].
In this paper, in order to provide robust forecasts for spot electricity prices, we propose a new approach based on the k-factor GIGARCH process [10], which allows taking into account a lot of stylized facts observed on the electricity spot prices, in particular stochastic volatility, long memory and periodic behaviors. The investigation of this model is done in [11]. Diongue and Guégan [5] introduced the parameter estimation of the k-factor GIGARCH process. Here, we provide new developments which concern the expression of the forecasts using the k-factor GIGARCH process and we give their properties. We apply these results on the German electricity prices market providing forecasting prices up until a one-month ahead. These results are totally new in the sense that, in most published papers, the previsions concern mostly the one-day ahead horizon and here we are interested by long term prediction. For comparison purpose, we compare our approach with a benchmark model in terms of forecasting, using the RMSE criteria.
This paper is organized as follows. The next section presents the data and contains the main empirical findings. In Section 3, we specify some notations, define the k-factor GIGARCH process along with new theoretical results on forecasting in mean and in variance. In Section 4, we provide forecasts for the German spot prices data set. The last section is dedicated to conclusions.
In this paper we have investigated forecasting’s method using a stochastic model such as a k-factor GIGARCH process. We derive a least square predictor and its properties and we characterize the conditional variance error of this predictor. The results provided in Section 3.2 are new and permit to obtain close form expressions for predictions using a k-factor GIGARCH process.
This forecasting method is applied to the German hourly electricity spot market prices. We adjust three different models on this data set: a SARIMA–GARCH model as a benchmark, a 1-factor GIGARCH model and a 3-factor GIGARCH model. The forecasting results for the year 2003 with the estimated models are highly convening in the sense of RMSE criteria. The model M2 (3-factor GIGARCH process) provides better forecasts in the sense of RMSE criteria than model M1 (SARIMA–GARCH process) and model M3 (1-factor GIGARCH process), when modelling EEX prices on the period under study. In addition, the comparing predictive accuracy test from Diebold and Mariano [4] suggest that the expected square error for the models (M1 and M2) forecasts are not equal, confirming the fact that this new modelling improves the forecasts for this kind of data set.
Thanks to this study, we have detected presence of seasonal long memory and heteroskedascity in electricity spot prices. Note that these features appear frequently inside the European electricity market.
