Multivariate constrained robust M‐regression for shaping forward curves in electricity markets

Abstract

In this paper, a multivariate constrained robust M‐regression method is developed to estimate shaping coefficients for electricity forward prices. An important benefit of the new method is that model arbitrage can be ruled out at an elementary level, as all shaping coefficients are treated simultaneously. Moreover, the new method is robust to outliers, such that the provided results are stable and not sensitive to isolated sparks or dips in the market. An efficient algorithm is presented to estimate all shaping coefficients at a low computational cost. To illustrate its good performance, the method is applied to German electricity prices.

Cellwise robust M regression

“…The option to construct the estimator as a cellwise robust M regression as opposed to alternative paths, such as MCD regression (Rousseeuw, 1984), comes from the observation that robust M regression estimators have proven to yield a very good trade-off between efficiency and robustness in simulations and applications in fields as di-verse as quantitative structure-property relationships (QSPR) (Serneels et al, 2006), gravimetry (Hu et al, 2017), marketing (Guerard, 2016), chemometrics (Hoffmann et al, 2015), analytical chemistry with applications to e.g. analysis of archaeological glass (Serneels et al, 2005) and meteorite samples (Hoffmann et al, 2016), as well as estimation of shaping coefficients for futures trading in the electricity markets (Leoni et al, 2018). Note though, that S-regression has also proven a valid path in this context ( Öllerer et al, 2016).…”