Variance Stabilizing Transformations for Electricity Spot Price Forecasting

Abstract

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 conduct a comprehensive forecasting study involving 12 datasets from diverse power markets and evaluate 16 variance stabilizing transformations. We find that the probability integral transform (PIT) combined with the standard Gaussian distribution yields the best approach, significantly better than many of the considered alternatives.

Efficient Forecasting of Electricity Spot Prices with Expert and LASSO Models

“…The N-PIT, misleadingly called the Nataf transformation, was used by Diaz and Planas [24] to normalize Spanish electricity prices. It was also used together with the t-PIT (a Student-t transformed PIT) in a recent extensive EPF study [16]. In Figure 3, we can clearly see that the histogram of N-PIT-transformed prices looks like the standard normal density.…”

“…However, is this approach also beneficial in case of parameter-rich and LASSO-estimated models? If yes, which of the VSTs discussed and evaluated in Uniejewski et al [16] are to be recommended?…”

“…It has been used in the context of electricity prices, e.g., by Schneider [23] and Ziel and Weron [4]. The mirror-log and polynomial transformations were introduced by Uniejewski et al [16] as generalizations of the robust Box-Cox transformation for λ = 0 and λ = 0, respectively. The former is a straightforward generalization of the log-transformation with a mirror image of the logarithm for negative values:…”

“…It is a one parameter family. Here, we used c = 1 3 , as suggested by Uniejewski et al [16]. Similarly to the standard log-transformation and asinh, the mlog exhibits a log-damping effect.…”

“…A heat map is used to indicate the range of the p-values-the closer they are to zero (→ dark green), the more significant the difference is between the forecasts of a model on the X-axis (better) and the forecasts of a model on the Y-axis (worse). To better understand the impact of applying a VST, it is necessary to refer to the article of Uniejewski et al [16], where 16 transformations were tested across 12 datasets. Importantly, only models without exogenous variables were used in the cited study-an AR counterpart of our ARX2 and its neural network equivalent-and the price series were not decomposed into the LTSC and the stochastic component.…”