Modeling the UK electricity price distributions using quantile regression

Abstract

In this paper we develop fundamental quantile regression models for the UK electricity price in each trading period. Intraday properties of price risk, as represented by the predictive distribution rather than expected values, have previously not been fully analysed. The sample covers half hourly data from 2005 to 2012. From our analysis we are able to show how the sensitivity towards different fundamental factors changes across quantiles and time of day. In the UK the supply of electricity is to a large extent generated from coal and gas plants, thus the price of gas and coal, as well as the carbon emission price, are included as fundamental factors in our model. We also include the electricity price lagged by one day, as well as demand and margin forecasts. We find that the sensitivities vary across the price distribution. Our findings also suggest that the sensitivity to fundamental factors exhibit intraday variation. We find that the sensitivity to gas relative to coal is higher in high quantiles and lower in low quantiles. We have demonstrated a scenario analysis based on the quantile regression models, showing how changes in the values of the fundamentals influence the electricity price distribution.

A Trading-Based Evaluation of Density Forecasts in a Real-Time Electricity Market

“…Therefore, given the observed statistical properties of imbalances series with almost zero asymmetry and moderate kurtosis (especially compared to electricity prices), the latter measure should be preferred. According to results reported in Table 2, the general superiority of the JSU and the skew student-t distributions (specifically ST2) is observed (note that computational difficulties can emerge, as with infinite values for the SHASHo distribution), consistent with Hagfors et al [8] for hourly electricity prices. Furthermore, given that the skew-t had previously also been used for hourly Australian prices in reference [6], while reference [7] used the Johnson's S U distribution for Californian and Italian electricity price densities, both distributions have been retained to test their forecasting performances.…”

“…Substantial overviews on the related literature are given in references [1,2]. For example, Jónsson et al [3] applied exponential smoothing approaches for prediction in real-time electricity markets, Bello et al [4] analyzed Parametric Density Recalibration of a Fundamental Market Model to Forecast Electricity Prices, Chan and Grant [5] compared energy price dynamics with GARCH and stochastic volatility models, Jiang et al [6] forecasted day-ahead electricity prices based on a hybrid model applying particle swarm optimization and core mapping with fuzzy logic and model selection, Uniejewski et al [7] show how variance stabilizing transformations can improve electricity spot price forecasting and Hagfors et al [8] used quantile regressions to forecast UK electricity prices. Most recently, techniques from the field of artificial intelligence have been evaluated with success.…”

“…However, as Weron [2] observes, most of this work has taken the form of point or interval forecasting, e.g., with quantile regressions, as in reference [8,12] or [15], rather than through fully parametric density representations, and almost all of it has been in the context of short-term, day-ahead modeling. Of the parametric representations for hourly prices, Panagiotelis and Smith [16] applied a skew-t distribution, Serinaldi [17] used the JSU, while Gianfreda and Bunn [18] found that the skew-t was preferable to the JSU.…”

Using quantile regression to analyze the effect of renewables on EEX price formation

“…Yet it is well known that price formation (and hence risk) varies systematically throughout the day with different models generally being specified for peak, off-peak and mid-peak hours to reflect the dynamics of load following and the various technologies setting the marginal prices. With this in mind, reference [6] investigates all 48 half hourly prices from the UK market, across the range of quantiles from 1% to 99%, estimated over the period 2005-2012. This paper also demonstrates the usage of scenario analysis where one can investigate how a change in one of the independent variables (e.g.…”

Demand and residual demand modelling using quantile regression

“…The quantile regression approach, introduced by [6], evaluates the tail dependencies and the risk on electricity consumption. The quantile regression application has been widely applied in financial risk management and been recently used in energy market studies: on electricity price [7], CO 2 emission allowance price [8], household energy consumption [9] and oil prices [10]. This paper aims to contribute to the quantile regression literature by applying this method on both the aggregated electricity demand and residual demand.…”