# Probabilistic Quantile Multi-step Forecasting of Energy Market Prices: A UK Case Study

Petros Tzallas, Napoleon Bezas, Ioannis Moschos, Dimosthenis Ioannidis, Dimitrios Tzovaras

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Petros Tzallas, Napoleon Bezas, Ioannis Moschos, Dimosthenis Ioannidis, Dimitrios Tzovaras. Probabilistic Quantile Multi-step Forecasting of Energy Market Prices: A UK Case Study. 18th IFIP International Conference on Artificial Intelligence Applications and Innovations (AIAI), Jun 2022, Hersonissos, Greece. pp.301-313, 10.1007/978-3-031-08341-9_25. hal-05335636

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# Probabilistic Quantile Multi-step
Forecasting of Energy Market Prices:
A UK Case Study

Petros Tzallas(✉)ID, Napoleon Bezas(✉)ID, Ioannis MoschosID,
Dimosthenis IoannidisID, and Dimitrios TzovarasID

Information Technologies Institute, Centre for Research and Technology,
57001 Thessaloniki, Greece
{ptzallas,bezas,imoschos,djoannid,Dimitrios.Tzovaras}@iti.gr

**Abstract.** The transition from traditional dispatchable generation units to intermittent supply from renewable energy sources, as well as the continuous rise in energy demand, partially due to the growing popularity of electric vehicles (EVs), has sparked an upsurge in research interest for energy related forecasting in recent decades. The heavy reliance on weather conditions adds unpredictability in energy generation, resulting in fluctuations in the electricity system and, as a result, in electricity prices. Therefore, in order to support more efficient energy management, high-quality forecasts are required not just for energy demand and generation, but also for energy market prices. While most approaches aim to achieve point forecasts for the energy market prices, a probabilistic forecast approach could further assist the decision making process. This paper proposes a lightweight forecasting model for accurate multi-step forecasts of day-ahead and intra-day prices of the UK electricity market, while providing different quantiles of the forecast in order to estimate the potential uncertainty of price forecasts. The methodology focuses heavily on the feature engineering step by utilizing features extracted from numerical weather values, load and generation forecasts of the respective region, temporal features and historical values of day-ahead and intra-day prices. Furthermore, new metrics for evaluating the forecasted quantile intervals are introduced and defined in the analysis, in addition to the commonly used evaluation metrics implemented in time series forecasting.

**Keywords:** Electricity price forecast · Time series forecasting · Probabilistic forecast · Quantiles forecasting · Feature engineering

# 1 Introduction

Electricity, transportation and heating are some of the most vital needs of humanity and their fulfillment is of vital importance. Thus, the economic process is highly dependent on the energy sources. Since the beginning of the century

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Published by Springer Nature Switzerland AG 2022

I. Maglogiannis et al. (Eds.): AIAI 2022 Workshops, IFIP AICT 652, pp. 301–313, 2022.

https://doi.org/10.1007/978-3-031-08341-9_25
a significant rise in the energy demand has been observed [1]. Additionally, the conventional energy resources, such as oil, coal, and natural gas, are starting to be depleted [2]. Finally, due to high CO2 emissions, the aforementioned resources can cause certain environmental issues [3]. These three reasons have led stakeholders of the energy sector to explore more sustainable and environmentally friendly resources, which has boosted the focus on renewable energy research [4].

The transition from conventional energy sources to renewables that was observed in the electricity system, has inevitably affected the energy market, which introduced different kinds of markets that assist in facilitating more efficient generation and demand-side management [5].

Despite the large increase in investment and consumption of renewable energy sources, there is still a strong obstacle to almost all renewable energy holdings. This obstacle is the uncertainty of source supply. Renewable energy sources show significant sporadicity, variability, and randomness. The former, not only threatens the stability and reliability of these power plants, and inevitably the stability of the electricity grid but also, introduces uncertainties in energy market prices. As a result, precise energy market forecasting, as well as generation and demand forecasting, has become necessary for a dispatcher to optimally plan the energy related transactions, making the most profitable decisions [6].

While in most energy related forecasting problems, point predictions could be considered adequate for the optimal dispatch of the assets, in energy market forecasting, a probabilistic approach could further assist the decision making process. Therefore, in this paper, we propose a lightweight machine learning based model that provides quantile forecasts for energy price data. More specifically, forecasts are going to be made for the two main price values in EU electricity wholesale markets, the day-ahead price and the intra-day price.

The day-ahead market refers to the bidding process that occurs on day X, during which stakeholders commit to selling or buying particular amounts of power at each hour of day X+1. The price of energy is not established at the moment of bidding, but rather after all of the bids from energy generators have been released. The amount of energy that each participant sells or buys, as well as the price of power, are the results of the day-ahead market mechanism.

The day-ahead market bids submitted by each participant have a high level of variability, due to the unpredictable nature of renewable energy sources, as mentioned previously. To address this issue and provide more accurate price forecasts, the intra-day market was established as a complement to the day-ahead market. Participants can make adjustments in the transaction of energy that are committed from the day-ahead process closer to the actual time of energy delivery using this mechanism, and thus have more certain information about the availability of assets and needs.

## 2 Related Work

There is limited literature review regarding the probabilistic electricity price forecasting. Achieving an accurate point forecast can provide a solid foundation
for flexible investment decisions, but does not take into account the possibility
of extreme events, which can have huge implications for the business as a whole.
In recent years, the topic of probabilistic electricity price forecasting research
received a lot of attention. By quantifying the development of published papers
from the first related article written in 2003 [7] until the year 2016, [8] was able
to demonstrate this trend in detail

Some researchers have sought to address this problem in the past by evaluat-
ing and modeling the variance. Zhao used a heteroscedastic and non-linear model
to compute the prediction intervals (PIs) for electricity prices in [9]. Zhao, in par-
ticular, provides a statistical forecasting model for SVM that explicitly models
the mean and the variance of electricity models. Similar approach was proposed
by [10], where a hybrid approach is used to construct the prediction intervals
with a two-stage formulation. The first step includes the estimation of point
forecasts based on an extreme learning machine (ELM) model, while the second
step involves assessing model uncertainty and noise variance using a bootstrap
approach and the maximum likelihood method, respectively. The bootstrap and
ELM method of generating PIs has also been employed in other studies. For
example, Chen et al. [11] use the same technique to construct half-hourly point
and interval forecasts in the Australian energy market. Also, Rafiei et al. [12]
uses a hybrid approach for probabilistic electricity price forecasting based on the
concept of bootstrap. A two-layer neural network is developed using the clonal
selection algorithm and extreme machine learning (ELM). A decomposition of
the time series is performed prior to the application of the model to partition
the time series into one approximation and three details series. Each of the is
fitted with a neural network, and the bootstrap is used to estimate the model
uncertainty. The data uncertainty for the aggregated series is then assessed using
the bootstrap approach one more.

However, it has been proven that focusing on specific moments of the dis-
tribution, particularly the mean and variance, is insufficient on its own. Hence,
modeling the whole-time dependent distribution function of prices was consid-
ered as an alternative solution to this problem. One of the most common app-
roach is to construct PIs utilizing the quantile regression. The authors in [13,14]
use the notion of quantile regression and a pool of point forecasts generated
by averaging individual models to achieve better results in the context of inter-
val forecasts of electricity prices resulting to a Quantile Regression Averaging
(QRA) model. The previous approach is extended in [15] by extracting important
information from all the individual models using Principal Component Analysis
(PCA) before utilizing quantile regression, whereby the authors refer to as Fac-
tor Quantile Regression Averaging (FQRA). A different approach is suggested
by the authors of [16], that outperforms the two previous methods and is con-
sidered as a regularized variant of QRA. The model utilizes the Least Absolute
Shrinkage and Selection Operator (LASSO) to automate the process of select-
ing the most appropriate regressors, resulting in much better results in terms of
profitability during energy trading activities.
# 3 Methodology

The adopted forecasting framework is described in detail in this section. Multi-step forecasts were produced for both day-ahead and intra-day price forecasting, and more specifically, an individual forecast for each horizon of the entire day (day-ahead forecasts). The general methodology can be separated into four main steps, as shown in Fig. 1. The data was acquired from the online electricity price service offered by ELEXON [17]. Following data collection, missing values were addressed and handled accordingly, either by removing them or by utilizing interpolation techniques. The next step is the implementation of feature engineering techniques and the training of machine learning algorithms. Finally, the model’s forecasting results are then assessed using the appropriate error metrics.

<figure><img src="image_3.png" /><figcaption>Fig. 1. Forecasting methodology flowchart</figcaption></figure>

## 3.1 Forecasting Strategy and Feature Creation

Our approach is heavily centered in the feature engineering aspect of time series forecasting. For the multi-step point forecasting separate models were developed for each time-step of the forecast horizon, based on the approach described in [18], as seen in Fig. 2. In addition to the traditional model’s mean point forecasts, three different quantiles are predicted, namely the 0.05 quantile, which is the lower limit of the interval, the 0.95 quantile which is the upper limit of interval, and the 0.5 quantile that corresponds to median of the interval. Hence, for each time-step four models are created, and for the whole day ahead horizon 96 models are created, when the data set is in hourly resolution, 24 for each of the four predictions.

There are three main categories that can separate the features used for energy forecasting, namely the historical energy price values, additional external features, and cyclical temporal features to capture time-series periodicity.

More specifically, we utilize the historical energy market prices values within a previously determined time range, referred to as history. As a result, in order to anticipate the t + 1 price, the models use historical load values from t through t-(history-1) time-steps. The history of the forecasting models of our approach is set to 24 h. More details for the energy market prices datasets are provided in Sect. 4.
The additional features consist of day-ahead generation and load forecasts and aggregated numerical weather values for the region of UK. The day ahead generation and load forecasts were retrieved from the online service of ENTSO-E [19]. They describe the total energy demand and energy generation predictions for the entire UK region.

<figure><img src="image_4.png" /><figcaption>Fig. 2. Energy market price forecasting strategy</figcaption></figure>

The aggregated numerical weather measurements are retrieved through the online weather data service Meteostat [20]. Meteostat is a public API that provide different weather measurements from the majority of the meteorological stations around the globe. In our approach, several weather measurements were received from the weather stations in the UK and their average was computed and used as a feature. The weather measurements that we used in this paper are temperature, dew point, relative humidity, total precipitation, wind direction, average wind speed, and finally sea-level air pressure.

## 3.2 Prediction Models

In our approach we decide to utilize common machine learning models, and more specifically tree based models, namely Random Forest Regressor (RF), Gradient Boosting Regressor (GBR), Light Gradient Boosting Machine (lightGBM), and Extra Trees Regressor. The selected models offer highly accurate results, without
the need for a large dataset or data scaling [21]. In addition, as compared to deep
learning models, their training and testing time is negligible. Lastly, these models
offer easy to implement quantile predictions, either in their implementation in
sklearn [22] library or in sklern Quantile [23] library.

Grid search was conducted in order to tune the hyper-parameters of
the models to achieve the most accurate results. More specifically, for Ran-
dom Forest and Extra Trees Regressor and the hyper-parameters were set
to n_estimators=100 and max_depth=9, for Gradient Boosting Regressor
n_estimators=100, max_features=auto and max_depth=8 and finally, for Light
GBM the hyper-parameters that we tuned were n_estimators=100, num_leaves
= 64, max_depth=-1, n_jobs=-1.

3.3 Evaluation Metrics

For the evaluation of the mean and median point results the most common
evaluation metrics used in time series forecasting were utilized. More specif-
ically, there are four distinct metrics utilized for the evaluation of the exist-
ing approaches, namely Mean Absolute Error (MAE) or Mean Absolute Devia-
tion (MAD), Root Mean Square Error (RMSE), symmetric Mean Square Error
(sMAPE) and MAD/Mean Ratio. Although, MAE and RMSE are the most
commonly used and accepted metrics for regression problems, to consider them
qualitatively significant, they must be compared to the data set mean and stan-
dard deviation. For easier interpretation of the results, percentage metrics, such
as sMAPE and MAD/Mean Ratio are utilized that describe the absolute dif-
ference of the predicted and actual values divided by the absolute sum of their
values and MAD metric divided by the arithmetical average of the observations
respectively [24].

In order to evaluate the accuracy of the prediction interval, there are two
factors that need to be examined. Initially, the target must be inside the limits
of the forecasted intervals, thus the evaluation metric In Bounds was defined
to showcase the percentage of the real values that fall within the intervals. By
making the limits wide, the In Bounds metric can easily be very high, although
the results is not the optimal. Thus, there is a need for metrics that highlight
the error of the interval. In this approach the MAE of the upper and lower
limit is utilized, together with the MAE of the interval, that corresponds to the
average of the limit errors. Additionally, violin plots are provided to showcase
the absolute error for each value.

4 Experimental Dataset

The two datasets used for our approach for quantile energy market was retrieved
from Elexon API [17]. The datasets correspond to day-ahead and intra-day
energy prices for the UK between 2021-01-04 and 2021-06-14. The measurement
unit of the datasets is €/MWh and the time resolution was set on a hourly basis.
Table 1 provides useful information about the two datasets and Fig. 3 provide
indicative plots for the datasets. The two datasets were relatively clean, with some missing values that were filled using linear interpolation.

<table><caption>**Table 1.** Day-ahead and intra-day price data information.</caption><thead><tr><th></th><th>Day-ahead price</th><th>Intra-day price</th></tr></thead><tbody><tr><td>Count</td><td>3888</td><td>3888</td></tr><tr><td>Mean</td><td>72.76</td><td>63.76</td></tr><tr><td>Std. deviation</td><td>38.49</td><td>27.63</td></tr><tr><td>Min</td><td>2.24</td><td>-40.30</td></tr><tr><td>Max</td><td>1192.33</td><td>369.51</td></tr><tr><td>Start date</td><td>2021-01-04</td><td>2021-01-04</td></tr><tr><td>End date</td><td>2021-06-14</td><td>2021-06-14</td></tr></tbody></table>

The additional data used as features in our approach, namely day ahead load and generation forecasts, and average weather values, correspond to the same time period and also have the same resolution.

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Day-ahead price (upper) and intra-day price (lower) datasets example plots.</figcaption></figure>
# 5 Results

As noted in Sect. 3.3, the review method for both day-ahead and intra-day price forecasts was divided into two stages. To begin, the aforementioned metrics were used to assess the mean and median results, as well as the training and testing execution time for each model. Violin plots were used to visualize the inaccuracies when evaluating the quantiles and intervals. The tables and figures required to demonstrate the accuracy of our findings are provided in the following sections.

## 5.1 Day-Ahead Price Results

In Table 2 we can observe the metrics for the predictions of the simple model that computes the mean value and the model that predicts the 0.5 quantile or median. Generally, the results of the selected tree-based models can be characterized adequate, with the best performing model being the Extra Tree Regressor, with Light Gradient Boosting Regressor and Random Forest Regressor also performing well. Furthermore, the required training time of the models is quite short, with the slowest model having a training and testing time of less than ten minutes. LightGBM was the fastest model, delivering results in under two minutes.

<table><caption>Table 2. Day-ahead price median and mean results.</caption><thead><tr><th>Models</th><th></th><th>MAE (€/MWh)</th><th>RMSE (€/MWh)</th><th>MMR (%)</th><th>sMAPE (%)</th><th>Time (s)</th></tr></thead><tbody><tr><td rowspan="2">RF</td><td>Median metrics</td><td><strong>8.59</strong></td><td>11.46</td><td>18.4</td><td>9.55</td><td>386.93</td></tr><tr><td>Mean metrics</td><td>8.69</td><td>11.86</td><td>10.37</td><td>5.34</td><td></td></tr><tr><td rowspan="2">GBR</td><td>Median metrics</td><td>8.84</td><td>11.73</td><td>19.09</td><td>9.86</td><td>570.8</td></tr><tr><td>Mean metrics</td><td>8.64</td><td>11.99</td><td>10.3</td><td>5.31</td><td></td></tr><tr><td rowspan="2">LightGBM</td><td>Median metrics</td><td>8.57</td><td><strong>11.35</strong></td><td>19.19</td><td>9.86</td><td><strong>93.17</strong></td></tr><tr><td>Mean metrics</td><td>8.59</td><td><strong>11.32</strong></td><td>10.24</td><td>5.44</td><td></td></tr><tr><td rowspan="2">Extra Trees</td><td>Median metrics</td><td>9.15</td><td>12.21</td><td><strong>17.93</strong></td><td><strong>9.35</strong></td><td>142.69</td></tr><tr><td>Mean metrics</td><td><strong>8.3</strong></td><td>11.34</td><td><strong>9.9</strong></td><td><strong>5.18</strong></td><td></td></tr></tbody></table>

In Fig. 4 there is an example plot of the day ahead price predictions provided by the Extra Trees Regressor. The grey area correspond to the prediction interval, with 0.05 and 0.95 quantile being its limits. From this figure, it is easy to first visualize the results of our experimentation.

Table 3 displays the performance of the forecasted quantiles in terms of the evaluation metrics. It can be observed that the highest In Bounds metric can be achieved by Extra Trees Regressor; however, GBR and LightGBM achieved lower quantiles and interval errors, indicating that they were able to make accurate prediction intervals without increasing the interval limits.

The violin plots in Fig. 5 demonstrate the absolute errors over the whole test set. We can see that the models have mostly low absolute errors, with the exception of the absolute error of the 0.95 quantile, which is the upper limit of the interval. The violin plots are a convenient way to visualize the errors in the test set and focus on the models that need further improvement.
<figure><img src="image_6.png" /><figcaption>Fig. 4. Extra Trees Regressor day-ahead price quantile predictions example plot.</figcaption></figure>

<table><caption>Table 3. Day-ahead price quantile metrics.</caption><thead><tr><th rowspan="2">Models</th><th rowspan="2">In Bounds (%)</th><th colspan="5">MAE (€/MWh)</th></tr><tr><th>0.05 quant</th><th>0.95 quant</th><th>Interval</th><th>Median</th><th>Mean</th></tr></thead><tbody><tr><td>RF</td><td>92.5</td><td>22.2</td><td>28.48</td><td>25.34</td><td>8.59</td><td>8.69</td></tr><tr><td>GBR</td><td>80.5</td><td>26.6</td><td><strong>13.81</strong></td><td>20.21</td><td>8.84</td><td>8.64</td></tr><tr><td>LightGBM</td><td>80.75</td><td><strong>21.52</strong></td><td>18.8</td><td><strong>20.16</strong></td><td><strong>8.57</strong></td><td>8.59</td></tr><tr><td>Extra Trees</td><td><strong>95.0</strong></td><td>25.59</td><td>27.16</td><td>26.38</td><td>9.15</td><td><strong>8.3</strong></td></tr></tbody></table>

<figure><img src="image_7.png" /><figcaption>Fig. 5. Extra Trees Regressor day-ahead price quantile error violin plots.</figcaption></figure>

## 5.2 Intra-day Price Results

LightGBM produced the best and fastest results for intra-day price forecasts, with Extra Trees Regressor also performing well. In Table 4 the final results of all the models are displayed for intra-day price forecasting, and in Fig. 6 an example plot is shown of the intra-day price predictions using LightGBM.
<table><caption>**Table 4.** Intra-day price median and mean results.</caption><thead><tr><th>Models</th><th></th><th>MAE (€/MWh)</th><th>RMSE (€/MWh)</th><th>MMR (%)</th><th>sMAPE (%)</th><th>Time (s)</th></tr></thead><tbody><tr><td rowspan="2">RF</td><td>Median metrics</td><td>12.18</td><td>16.69</td><td>21.7</td><td>11.73</td><td rowspan="2">363.9</td></tr><tr><td>Mean metrics</td><td>12.15</td><td>16.79</td><td>16.72</td><td>9.36</td></tr><tr><td rowspan="2">GBR</td><td>Median metrics</td><td>11.83</td><td>16.24</td><td><strong>21.17</strong></td><td><strong>11.41</strong></td><td rowspan="2">559.29</td></tr><tr><td>Mean metrics</td><td>12.52</td><td>17.75</td><td>17.23</td><td>9.49</td></tr><tr><td rowspan="2">LightGBM</td><td>Median metrics</td><td><strong>11.33</strong></td><td><strong>15.76</strong></td><td>21.63</td><td>11.47</td><td rowspan="2"><strong>85.21</strong></td></tr><tr><td>Mean metrics</td><td><strong>11.41</strong></td><td><strong>15.79</strong></td><td><strong>15.71</strong></td><td><strong>8.8</strong></td></tr><tr><td rowspan="2">Extra Trees</td><td>Median metrics</td><td>12.33</td><td>16.41</td><td>22.05</td><td>12.03</td><td rowspan="2">146.0</td></tr><tr><td>Mean metrics</td><td>11.89</td><td>15.9</td><td>16.36</td><td>9.24</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Light Gradient boosting Machine intra-day price quantile predictions example plot.</figcaption></figure>

For interval evaluation Table 5 shows that the best In Bounds metric is achieved by Extra Trees Regressor. Although LightGBM has the lowest In Bounds metric, the MAE of the quantiles is significantly lower, meaning that it produced narrower intervals, closer to the actual values of intra-day prices. The overall absolute errors of the LightGBM can be observed in Fig. 7.

<table><caption>**Table 5.** Intra-day price quantile metrics</caption><thead><tr><th rowspan="2">Models</th><th rowspan="2">In bounds (%)</th><th colspan="5">MAE (€/MWh)</th></tr><tr><th>0.05 quant</th><th>0.95 quant</th><th>Interval</th><th>Median</th><th>Mean</th></tr></thead><tbody><tr><td>RF</td><td>87.875</td><td>31.94</td><td>26.70</td><td>28.77</td><td>12.18</td><td>12.15</td></tr><tr><td>GBR</td><td>78.25</td><td>26.91</td><td>17.04</td><td>21.98</td><td>11.82</td><td>12.51</td></tr><tr><td>LightGBM</td><td>75.88</td><td><strong>22.55</strong></td><td><strong>17.01</strong></td><td><strong>19.78</strong></td><td><strong>11.33</strong></td><td><strong>11.41</strong></td></tr><tr><td>Extra Trees</td><td><strong>91.25</strong></td><td>30.25</td><td>23.77</td><td>27.01</td><td>12.33</td><td>11.89</td></tr></tbody></table>
<figure><img src="image_9.png" /><figcaption>Fig. 7. LightGBM intra-day price quantile error violin plots.</figcaption></figure>

# 6 Conclusion and Future Work

In our approach we presented simple and lightweight models for probabilistic quantile forecasting of energy market prices, which are heavily depended to the feature extraction techniques. Moreover, we provided a simple explanatory way to evaluate the intervals of our prediction, using the In Bounds metric together with MAE metrics for the interval and its limits, and violin plots to showcase the absolute error in all the data on our test sets.

The tree-based models performed adequately, without the need of a large dataset, in predicting all the requested values, namely the mean, median and 0.05 and 0.95 quantiles, in the 24-time-step ahead forecasting. In addition, a significant benefit of tree-based models is their short training period, which was highlighted in our study.

For future work, the experimentation in other machine learning and deep learning models for quantile forecasting could be beneficial. Our approach utilizes a plethora of features for energy market forecasting, but there are also more features to explore that could have a major impact on our results, namely the prices of gas or petrol in the UK, the day-ahead electricity generation from only renewable energy sources, numerical weather predictions, and more. Furthermore, the probability forecasting could provide an even richer information than the quantile forecasting, giving decision making tools the opportunity to make even more profitable decisions. Finally, different models could be utilized for the predictions of the interval's limits and the mean and median values, depending on the results of the experimentation.

**Acknowledgements.** This work is supported by the project IANOS - a novel for IntegrAted SolutionNs for the DecarbOnization and Smartification of Islands funded by the EU H2020 Programme, grant agreement no. 957810.
References

1. Statistical review of world energy-energy economics-home. https://www.bp.com/en/global/corporate/energy-economics/statistical-review-of-world-energy.html. Accessed 03 Mar 2022

2. Home—ecotricity. https://www.ecotricity.co.uk/. Accessed 03 Mar 2022

3. Bereiter, B., et al.: Revision of the epica dome c co2 record from 800 to 600 kyr before present. Geophys. Res. Lett. **42**(2), 542–549 (2015)

4. Ajadi, T., et al.: Global trends in renewable energy investment 2019. Bloomberg New Energy Finance, p. 76 (2019)

5. Status - enexgroup. https://www.enexgroup.gr/eu-market-in-tegration. Accessed 03 Mar 2022

6. Yuan, S., Kocaman, A.S., Modi, V.: Benefits of forecasting and energy storage in isolated grids with large wind penetration-the case of Sao Vicente. Renew. Energy **105**, 167–174 (2017)

7. Zhang, L., Luh, P.B., Kasiviswanathan, K.: Energy clearing price prediction and confidence interval estimation with cascaded neural networks. IEEE Trans. Power Syst. **18**, 99–105 (2003)

8. Nowotarski, J., Weron, R.: Recent advances in electricity price forecasting: a review of probabilistic forecasting. Renew. Sustain. Energy Rev. **81**, 1548–1568 (2018)

9. Zhao, J.H., Dong, Z.Y., Xu, Z., Wong, K.P.: A statistical approach for interval forecasting of the electricity price. IEEE Trans. Power Syst. **23**(2), 267–276 (2008)

10. Wan, C., Xu, Z., Wang, Y., Dong, Z.Y., Wong, K.P.: A hybrid approach for probabilistic forecasting of electricity price. IEEE Trans. Smart Grid **5**(1), 463–470 (2014)

11. Chen, X., Dong, Z.Y., Meng, K., Xu, Y., Wong, K.P., Ngan, H.W.: Electricity price forecasting with extreme learning machine and bootstrapping. IEEE Trans. Power Syst. **27**(4), 2055–2062 (2012)

12. Rafiei, M., Niknam, T., Khooban, M.H.: Probabilistic electricity price forecasting by improved clonal selection algorithm and wavelet preprocessing. Neural Comput. Appl. **28**(12), 3889–3901 (2016). https://doi.org/10.1007/s00521-016-2279-7

13. Nowotarski, J., Weron, R.: Merging quantile regression with forecast averaging to obtain more accurate interval forecasts of Nord pool spot prices. In: 11th International Conference on the European Energy Market (EEM14), pp. 1–5 (2014)

14. Nowotarski, J., Weron, R.: Computing electricity spot price prediction intervals using quantile regression and forecast averaging. Comput. Stat. **30**(3), 791–803 (2014). https://doi.org/10.1007/s00180-014-0523-0

15. Maciejowska, K., Nowotarski, J., Weron, R.: Probabilistic forecasting of electricity spot prices using factor quantile regression averaging. Int. J. Forecast. **32**, 957–965 (2016)

16. Uniejewski, B., Weron, R.: Regularized quantile regression averaging for probabilistic electricity price forecasting. Energy Econ. **95**, 105121 (2021)

17. Electricity data summary—bmrs. https://www.bmreports.com/bmrs/?q=eds/main. Accessed 03 Feb 2022

18. Xue, P., Jiang, Y., Zhou, Z., Chen, X., Fang, X., Liu, J.: Multi-step ahead forecasting of heat load in district heating systems using machine learning algorithms. Energy **188**, 116085 (2019)

19. Home. https://www.entsoe.eu/. Accessed 03 Feb 2022

20. The weather's record keeper—meteostat. https://meteostat.net/en/. Accessed 03 Feb 2022
21. Advantages of tree-based modeling. https://www.summitllc.us/blog/advantages-of-tree-based-modeling#:~:text=Are. Accessed 03 Oct 2022

22. scikit-learn: machine learning in python - scikit-learn 1.0.2 documentation. https://scikit-learn.org/stable/. Accessed 03 Mar 2022

23. jasperroebroek/sklearn-quantile. https://github.com/jasperroebroek/sklearn-quantile. Accessed 03 Mar 2022

24. Kolassa, S., Schütz, W.: Advantages of the mad/mean ratio over the mape. Forecast: Int. J. Appl. Forecast. 6, 40–43 (2007)