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Extrapolating the long-term seasonal component of electricity prices for forecasting in the day-ahead market
\let\thefootnote\relax\footnotetext{
Paper published in Journal of Commodity Markets 37, 100449 (2025)
DOI: 10.1016/j.jcomm.2024.100449}
Seasonal decomposition is a fundamental technique in time series analysis and forecasting whose origins can be traced back to the middle of the 19th century hyn:ath:21,pet:etal:22. In its basic form, it decomposes the signal $P_{d,h}$ into three components: a deterministic slowly varying trend-cyclical component $T_{d,h}$ also called the long-term seasonal component (LTSC), a deterministic regularly repeating pattern $s_{d,h}$ called the (short-term) seasonal component, and the remaining part, i.e., the “residual”, also called the stochastic component $\eta_{d,h}$, in an additive fashion, i.e., $P_{d,h} = T_{d,h} + s_{d,h} + \eta_{d,h}$. Note that we use here the notation prevailing in the electricity price forecasting (EPF) literature, especially in day-ahead forecasting, where $d$ refers to the day and $h$ to the hour of delivery wer:14.
Although commonly used in multi-step ahead forecasting, seasonal decomposition has not been extensively utilized in day-ahead EPF until now:wer:16 provided empirical evidence that it can be advantageous to decompose the electricity price $P_{d,h}$ into the deterministic LTSC and a stochastic component that includes the short-term seasonality, i.e., $Y_{d,h} = s_{d,h} + \eta_{d,h}$, predict both components separately, and then combine their forecasts: $\hat{P}_{d,h} = \hat{T}_{d,h} + \hat{Y}_{d,h}$. The rationale behind this approach is that the residuals obtained after seasonal decomposition better satisfy the assumptions underlying typical model architectures, including the regression-type models considered in this study. Interestingly, the approach has proven effective for both parsimonious autoregressive afa:fed:19,gro:nan:19,Shah2021,Zafar2022 and non-linear autoregressive neural network-type models mar:uni:wer:19:narx, as well as parameter-rich models estimated using the least absolute shrinkage and selection operator jed:mar:wer:21. However, to our best knowledge, all existing studies in the context of day-ahead EPF have relied on a naive prediction of the LTSC, where the last 24 hourly values of the estimated trend-seasonal pattern were simply copied for the target day.
To address this gap, we introduce a novel approach to extrapolating the LTSC for the next day. We show that extending the time series of electricity spot prices by the 24 hourly forecasts for the next day -- obtained with a base model that does not involve seasonal decomposition -- and then extracting the LTSC component for the 24 hours of the target day from the extended time series can lead to statistically significant accuracy gains compared to the naive approach used in the literature so far. We employ two techniques to extract the LTSC: a simple moving average wer:14 and wavelet smoothing per:wal:00. Moreover, we use averaging to capture the benefits of combining forecasts from different models pet:etal:24.
To allow for a thorough evaluation of the studied models, like wag:ram:sch:mic:22, and in line with the best practices outlined in lag:mar:des:wer:21, we use very long test sets from more than one market. Namely, we consider 9 years of data (2015-2023) from two major European power markets -- EPEX in Germany and OMIE in Spain. The out-of-sample test period spans 5 years (2019-2023), covering the Covid-19 pandemic and the 2021-2022 energy crisis with skyrocketing prices of electricity. The day-ahead electricity price forecasts are obtained either using a parsimonious autoregressive expert model with exogenous variables bil:gia:del:rav:23,gai:gou:ned:16,mac:nit:wer:21,zie:wer:18 or a parameter-rich, LASSO-estimated regression model lag:mar:des:wer:21,wag:ram:sch:mic:22. We assess the significance of differences in predictive performance using the multivariate variant of the Diebold-Mariano (DM) test, as introduced by zie:wer:18. In line with a recent trend in the EPF literature mac:uni:wer:23, we also consider a realistic trading strategy involving day-ahead bidding and battery storage in order to quantify the benefits in monetary terms.
The remainder of the paper is structured as follows. In Section (ref) we describe the datasets, then in Section (ref) we present the methodology, i.e., describe the ARX and LEAR models, discuss the methods used to estimate and extrapolate the LTSC, and briefly explain the transformation used to stabilize the variance of the stochastic component. In Section (ref) we discuss the main results. Finally, in Section (ref) we wrap up the findings and conclude.
We consider data from two major European power markets -- EPEX in Germany (see Figure (ref)) and OMIE in Spain (see Figure (ref)). The German market is one of the more studied ones, likely due to the central position in Europe, large wind and solar penetration amounting to over 45% of net electricity generation in 2023 entsoe, challenging price dynamics with abundant negative prices, and high trading liquidity in most segments cal:fus:ron:17,hag:etal:16,jan:24,kat:zie:18,mar:nar:wer:zie:23,nar:zie:20JCM,uni:24:ORD. Although less studied in the literature dia:pla:16,g-m:car:san:15,gia:rav:ros:20,lip:uni:wer:24, the Spanish market is very interesting because of the rapid increase in the share of solar generation -- from 5.1% of net electricity generation in 2015 to 16.5% in 2023 entsoe.
Both datasets are of hourly resolution and include day-ahead electricity prices as well as forecasts of electricity consumption and generation from renewable energy sources (RES; here solar and wind) downloaded from the ENTSO-E transparency platform entsoe. With the growing share of RES in the generation stack and the impact of its volume on electricity prices, day-ahead forecasts of solar and wind generation have become fundamental inputs to EPF models bil:gia:del:rav:23,jan:woj:22,wes:fle:etal:21. Both datasets have been preprocessed to handle missing/duplicate values that occur when switching to/from daylight saving time -- missing observations have been replaced by the arithmetic mean of two neighboring values, while duplicate ones have been replaced by their arithmetic mean wer:14. To make the marginal distributions of prices and fundamental variables less leptokurtic and thus more suitable for modeling, we use the area hyperbolic sine (asinh) transformation uni:wer:zie:18. Note that unlike the logarithmic transformation that is popular in finance, the asinh can also handle negative values.
Furthermore, in line with the EPF literature, we use a rolling window scheme gro:nan:19,lag:mar:des:wer:21,mar:ser:wer:18 to obtain day-ahead forecasts of electricity prices. Inspired by recent research which involved parameter-rich models mar:nar:wer:zie:23, we use a calibration window of 208 weeks or 1456 days. To obtain electricity price forecasts for the first day of the test period, i.e., 1.01.2019, the models are calibrated to data spanning from 6.01.2015 to 31.12.2018. Next, the calibration window is moved forward one day and the forecasts are made for 2.01.2019. This process continues until electricity price forecasts are obtained for the last day in the test set, i.e., 31.12.2023.
In this study, we compute point forecasts of the 24 hourly prices for day $d$ using the information known at ca.\ 8 am on day $d-1$. Although the forecast horizon formally spans 16-40 hours, we actually make one step (day) ahead predictions in a multivariate modeling framework that uses a set of 24 interrelated models, one for each hour of day $d$ zie:wer:18.
More specifically, we use a multi-stage procedure. First, the electricity price is decomposed into the LTSC and a stochastic component that includes the short-term seasonality: $P_{d,h} = T_{d,h} + Y_{d,h}$. Then we apply a so-called variance stabilizing transformation uni:wer:zie:18 to $Y_{d,h}$ and obtain standardized series $y_{d,h}$. The latter is predicted using one of the models described in Section (ref) to yield $\hat y_{d,h}$. In the last two stages, we apply the inverse VST and add the LTSC forecast to obtain the final price forecast $\hat P_{d,h}$:
Note that the data are transformed after removing the LTSC and not vice versa, as this has been found to yield more accurate predictions in EPF jed:mar:wer:21. Note also that for the benchmark models that do not use seasonal decomposition, we apply the VST directly to the raw price series, thus omitting the first and last stages of the above procedure.
The day-ahead electricity price forecasts are obtained using two model classes. The first is a parsimonious autoregressive expert model with exogenous variables (ARX), originally proposed by mis:tru:wer:06, later modified and compared in a number of EPF studies under different names and acronyms bil:gia:del:rav:23,gai:gou:ned:16,mac:nit:wer:21,mac:now:16,tay:21:expectile,zie:16:TPWRS,zie:wer:18. In the ARX model the electricity price for day $d$ and hour $h$ is given by the following formula:
where the first three regressors account for the autoregressive effects of the prices for the same hour on days $d-1$, $d-2$ and $d-7$, $y_{d-1,24}$ provides information on the last known price level, i.e., midnight of day $d-1$, $y^{max}_{d-1}$ and $y^{min}_{d-1}$ stand for the maximum and minimum price of the previous day, $X^1_{d,h}$ and $X^2_{d,h}$ are the exogenous variables -- respectively the day-ahead forecasts of the system-wide load and RES generation, $D_1,\dots,D_7$ are daily dummies, and $\varepsilon_{d,h}$ is the noise term. The coefficients $\beta_j$ are estimated using ordinary least squares (OLS).
The second model class is a parameter-rich LASSO-estimated regression (LEAR) introduced to the EPF literature by uni:now:wer:16 and zie:16:TPWRS, and later used by lag:rid:sch:18, mac:uni:wer:23, wag:ram:sch:mic:22 and zie:wer:18, among others. Here, we consider a variant proposed by lag:mar:des:wer:21, who coined the acronym LEAR:
where the first 96 regressors are autoregressive terms that include prices from all hours of days $d-1$, $d-2$, $d-3$ and $d-7$, and the following $2\times 72$ regressors are all hourly values of the exogenous variables $X^1$ and $X^2$ for days $d$, $d-1$ and $d-7$. Such a model structure allows all cross-hour dependencies to be incorporated into the price forecasts. The LEAR model is estimated using the least absolute shrinkage and selection operator (LASSO) of tib:96, which automatically selects the most relevant regressors for predicting $y_{d,h}$. Although many different regularization methods have been proposed in the literature, uni:24:ORD identified LASSO as a parsimonious yet robust and well-performing variant in a comprehensive EPF evaluation study.
Along with seasonal decomposition, data transformation is the primary preprocessing technique in time series analysis hyn:ath:21. Its purpose is to remove known sources of variation, make the data more consistent across the sample, and -- particularly in EPF -- allow the handling of close to zero or negative values dia:pla:16,jan:24,kat:zie:18. For comprehensive comparisons of different variance stabilizing transformations (VSTs) see cia:mun:zar:22, shi:wan:che:ma:21 and uni:wer:zie:18, and for a discussion of the order of applying seasonal decomposition and VSTs before model calibration see jed:mar:wer:21.
Following lag:mar:des:wer:21 and zie:wer:18, we use here the area hyperbolic sine (asinh) transformation with the (median, MAD) normalization:
where
$\text{Med}_\tau$ is the median and $\text{MAD}_\tau$ is the median absolute deviation of $Y_{d,h}$ in the calibration window $\tau$, and 1.4826 is the inverse of the 75th percentile of the standard normal distribution; this factor ensures asymptotic normal consistency with the standard deviation uni:wer:zie:18.
Once $\hat{y}_{d,h}$ is computed, we apply the inverse transformation:
where $\textrm{sinh}$ is the hyperbolic sine. As nar:zie:20JCM note, the latter is not the correct inverse transformation since, given random variable $X$, $\mathbb{E}\textrm{sinh}(X)$ does not have to equal $\textrm{sinh}(\mathbb{E}X)$. Nevertheless, the difference between Eq.\ (ref) and the correct inverse VST is not substantial and is generally ignored in the literature.
When now:wer:16 introduced the seasonal component approach, they used two techniques for extracting the long-term seasonal component (LTSC): the Hodrick-Prescott filter cal:fus:ron:17,lis:nan:14,mar:uni:wer:19:narx,Zafar2022 and wavelet smoothing. Here, we replace the HP filter with a much simpler but equally effective simple moving average.
In the moving average (MA) approach the LTSC is approximated by averaging observations within a window centered at $t=24d+h$:
where $m=2k+1$ is the width of the window. The latter affects the shape of the trend-seasonal component, i.e., low $m$ yields a more volatile series, while high $m$ smooths out the fluctuations. In our study, we consider five smoothing levels: 1, 7, 28, 56, and 91 days, corresponding to window sizes ranging from $m=24+1$ (about 1 day) to $m=91\cdot 24+1$ (about 3 months). This allows us to obtain models that react differently to sudden changes in market conditions. Such an approach is similar to averaging across calibration windows of different lengths in macroeconometrics pes:tim:07 or in EPF hub:mar:wer:19.
On the other hand, wavelet smoothing per:wal:00 applies the discrete wavelet transform to decompose the original series into a sum of the so-called approximation series $S_J$ capturing the general trend and a set of detail series $D_1,D_2,...,D_{J}$. At each step $j=1,...,J$ of this iterative procedure, details $D_j$ of a given frequency are removed to yield a smoother, but twice shorter signal $S_j$. In this study, we consider five smoothing levels $S_J$ with $J \in (5,7,9,10,11)$, corresponding to time scales ranging from $2^5=32$ hours (or “1 day”) to $2^{11} = 2048$ hours (or “3 months”). Similar to the MA approach, the use of different smoothing levels allows us to capture changes in market conditions. Following now:wer:16, we use the Daubechies wavelet family of order 24. For sample applications of wavelet smoothing in EPF see afa:fed:19, gro:nan:19, jed:mar:wer:21 lis:nan:14 and mar:uni:wer:19:narx, among others.
The contemporary forecasting literature agrees that combining predictions from different models generally improves forecasting accuracy ati:20,pet:etal:22. The same has been reported for energy forecasting hon:etal:20:OAJPE, and EPF in particular ber:zie:24,hub:mar:wer:19,lag:mar:des:wer:21,nit:wer:23. In this study, we use simple arithmetic averaging to combine forecasts obtained with (i) different levels of decomposition and (ii) different methods of decomposing the data. As a result, we consider three different classes of forecasting models and denote them by suffixes. The average the forecasts obtained for the five moving average windows is denoted by --MA. Similarly, the average of the forecasts obtained for the five different levels of wavelet smoothing is denoted by --S. Finally, the average of all 10 forecasts is denoted by --MAS. Although more sophisticated ensembling methods have been considered in the literature, the simple arithmetic average has been repeatedly shown to be robust and competitive rav:bou:dij:15, mar:ser:wer:18, uni:mac:23.
To our best knowledge, all studies that use the seasonal component approach introduced by now:wer:16 rely on a naive prediction of the LTSC, where the last 24 hourly values of the estimated trend-seasonal pattern are simply copied for the target day. Depending on the pool of individual forecasts, we denote this approach by SCARX-$*$ or SCLEAR-$*$, where $*$ takes the value MA, S or MAS, see Section (ref), when referring to the model defined by Eq.\ (ref) or Eq.\ (ref), respectively.
In this paper, we introduce a new approach to predicting the LTSC for the next day by extrapolating the input price vector before calculating the LTSC. The proposed algorithm consists of the following steps:
By following this procedure, we obtain the LTSC forecast for the target day along with the seasonal component of the prices in the calibration window. Therefore, this approach preserves the continuity of the LTSC vector, which transitions smoothly from the calibration period to the target day, see Figure (ref). In our study, the seasonal component models that use the extrapolated LTSC approach are denoted by a prefix e: eSCARX-$*$ for ARX-based models and eSCLEAR-$*$ for LEAR-based models.
Note that we also considered a simpler method to extrapolate the LTSC, where the price series is extended for the next 24 hours using a naive forecast, i.e., $\hat{P}_{d,h} = P_{d-1,h}$, not an ARX or LEAR forecast as in steps 1-2 of the above algorithm. However, this approach resulted in inferior performance and its results are not reported here.
We evaluate the results using two metrics of prediction accuracy and a statistical test to assess the statistical significance of the results obtained lag:mar:des:wer:21,pet:etal:22. For ensuring the reliability of our forecasts, we use 5-year long test periods, i.e., from 1.01.2019 to 31.12.2023, for both datasets.
We use the two most popular error metrics in the EPF literature cia:mun:zar:22,lag:mar:des:wer:21,mac:uni:wer:23,wer:14,zie:16:TPWRS to measure the prediction accuracy of point forecasts, namely the Mean Absolute Error:
and the Root Mean Square Error (RMSE)
where $N_d=1826$ stands for the number of days in the out-of-sample test period, i.e., 1.01.2019--31.12.2023, see Figures (ref) and (ref), and $P_{d,h}$ and $\hat{P}_{d,h}$ respectively denote the actual and predicted price for day $d$ and hour $h$.
In Tables (ref) and (ref) we report the MAE and RMSE errors for the considered models over the 5-year test period. Note, that cells are colored (red $\rightarrow$ high, green $\rightarrow$ low) independently for each market (EPEX, OMIE) and model class (ARX, LEAR). For instance, in Table (ref) the MAE of 11.309 is red because it is the highest (i.e., worst) value among LEAR-class models for the OMIE dataset. In both tables columns labeled “%chng.” show the percentage difference between the error (MAE or RMSE) for an extrapolated LTSC-type model (eSCARX, eSCLEAR) and a naive LTSC-type model (SCARX, SCLEAR). Recall from Section (ref) that suffixes -MA, -S and -MAS denote combined predictions for three pools of individual forecasts.
Several important conclusions can be drawn:
In more detail, for models based on the parsimonious ARX structure, the reductions range from 2.89% to 7.70% in MAE and from 3.29% to 8.49% in RMSE. For the parameter-rich LEAR-type models, the improvements are even more striking -- from 5.71% to 13.87% in MAE and from 5.45% to 15.01% in RMSE. This shows the high effectiveness of the method introduced in this paper compared to the naive approach used so far. This is especially true for the German EPEX market, where much higher improvements in accuracy are observed, see the 7th column in Tables (ref) and (ref). Interestingly, the improvements with respect to the classical ARX and LEAR models that do not use seasonal decomposition are higher for the Spanish OMIE market and reach up to 10.65% for SCLEAR-S and -MAS models in terms of the MAE and 7.98% for the SCLEAR-MAS model in terms of the RMSE; not reported in the Tables. Apparently, the SCARX and SCLEAR models, which naively extrapolate the LTSC for the next day, cannot cope with the extreme electricity price dynamics in Germany over the studied period, see Figure (ref).
In the case of the EPEX dataset, the best performing averaging approach is -MAS, which combines all MA- and wavelet-based forecasts. It is worth noting that only the extrapolated LTSC approach is able to outperform the corresponding benchmarks in Germany, as the SC-type models provide less accurate price forecasts. For the OMIE market, all three averaging schemes -MA, -S, and -MAS show good performance. This time, both the naive and the extrapolated LTSC approaches outperform the corresponding benchmarks, although the latter are more accurate.
Following zie:wer:18, we use the multivariate variant of the die:mar:95 test (DM) to assess the statistical significance of differences in predictive performance. This version of the DM test is an asymptotic z-test of the hypothesis that the mean of the `daily' or `multivariate' loss differential series mac:uni:wer:23,nar:zie:20JCM:
is zero, where $||\varepsilon_{d}^Z||_r = (\sum_{h=1}^{24} |\varepsilon_{d,h}^Z|^r)^{1/r}$ is the $r$-th norm of the 24-dimensional vector $\varepsilon_d^Z$ of out-of-sample errors for model $Z$. In our study, we use the $||.||_1$ norm, i.e., set $r=1$. Naturally, we assume that the loss differential series is covariance stationary.
In Figure (ref) we present the results using four chessboards, separately for the two datasets (EPEX, OMIE) and the two model classes (ARX, LEAR). Like in lag:mar:des:wer:21 and zie:wer:18, each chessboard uses a heat map to indicate the range of the $p$-values: green and yellow for $p<0.05$, red for $0.05\le p <0.10$, and black for $0.10 \le p$.
For both markets, the eSCARX-based models significantly outperform the ARX, and similarly, the eSCLEAR-based models outperform the LEAR benchmark. On the other hand, only in the case of the OMIE market do the SCARX- and SCLEAR-based models provide more accurate forecasts than the respective benchmark models, but at a lower level of significance.
Furthermore, all models with extrapolated LTSC significantly outperform the corresponding naive LTSC-based models and for all averaging schemes, i.e., -MA, -S, and -MAS. In the majority of cases, the -MAS approach outperforms both the -MA and -S averaging schemes, which is not surprising since -MAS models use a larger and more diverse pool of individual forecasts. Overall, the eSCLEAR-MAS model is significantly better than any of the other models, with the exception of eSCLEAR-S for the OMIE market, but even in that case it is not significantly worse.
In Figures (ref) and (ref) we plot the rolling 365-day relative mean absolute errors (rMAE) for the best performing models, i.e., based on the richest pool of individual forecasts labeled --MAS, with respect to the error of the ARX model:
where $P_{d,h}$, $\hat{P}_{model,d,h}$ and $\hat{P}_{\text{ARX},d,h}$ respectively denote the actual price, its $model$-derived forecast and its ARX-derived forecast for day $d$ and hour $h$, and $\delta=1.01.2020, 2.01.2020, ..., 31.12.2023$. Note that if $model = \text{ARX}$ then $\text{rMAE} \equiv 1$, see the dashed horizontal lines. Values of rMAE below 1 indicate better performance than that of the benchmark ARX model, while values above 1 indicate worse performance.
Several important conclusions can be drawn from Figures (ref) and (ref):
To assess the practical value of reducing price forecasting errors for decision-makers, we now consider a realistic trading strategy in the day-ahead market. More specifically, we assume that we own a 1.25 MWh battery, which for technical reasons cannot be discharged below 0.25 MWh (or 20% of the nominal capacity) and its efficiency of charging as well as discharging is ca.\ 90% sik:etal:19. Originally proposed by uni:wer:21, the strategy involves placing a bid to buy electricity when prices are low and charge the battery, and simultaneously placing a bid to sell electricity when prices are high after discharging the battery; see also mar:nar:wer:zie:23 and nit:wer:23 who used variants of this strategy.
The maximum profit for day $d$, called the profit of the crystal ball strategy, is given by:
where $h1$ and $h2$ respectively are the hours with the lowest and the highest price of day $d$, and $P_{d,h}$ is the actual price for day $d$ and hour $h$. Clearly, $model$-derived forecasts will yield a profit of
where $\widehat{h1}$ and $\widehat{h2}$ respectively are the hours with the lowest and the highest $model$-predicted prices for day $d$, regardless of the actual price forecasts $\hat{P}_{d,h}$ for this day. In other words, the $model$-derived forecasts will yield a profit equal to that of the crystal ball strategy only if the $model$ correctly predicts the hours with the lowest and highest prices of the day, i.e., if $\widehat{h1}=h1$ and $\widehat{h2}=h2$.
In Table (ref) we report the profits obtained for selected models, expressed as fractions of the profit of the crystal ball strategy for the whole out-of-sample test period, i.e, $\Pi_{\text{CB}} = \sum_{d} \Pi_{\text{CB},d}$, where the summation is over $d=1.01.2019, 2.01.2019, ..., 31.12.2023$. In our case, $\Pi_{\text{CB}} = 110~897.27$ EUR for EPEX and $\Pi_{\text{CB}} = 55~236.55$ EUR for OMIE. Like in Section (ref), we only consider models based on the richest pool of individual forecasts (labeled --MAS). The following conclusions can be drawn:
The latter observation suggests that while the considered models predict price levels much better than the benchmarks, the benchmarks are able to identify the hours with the lowest and highest prices of the day almost as well as the eSC-type models.
We have introduced a novel approach to predicting the long-term seasonal component (LTSC) for the next day, which is a fundamental input to the seasonal component (SC) approach introduced by now:wer:16. Considering parsimonious autoregressive (ARX) and LASSO-estimated autoregressive (LEAR) models, we have provided evidence that improvements in predictive accuracy from using the proposed extrapolated SC-type (i.e., eSC-type) models compared to using a naive prediction of the LTSC can be as high as 15% for the German EPEX market (in terms of the RMSE; 14% in terms of the MAE) over a 5-year test period covering the Covid-19 pandemic, the 2021/2022 energy crisis, and the war in Ukraine.
Interestingly, the improvements with respect to the classical ARX and LEAR models that do not use seasonal decomposition are higher for the Spanish OMIE market and reach up to 10% (in terms of the MAE; and 8% in terms of the RMSE); all the differences are statistically significant, as measured by the multivariate variant of the Diebold-Mariano test zie:wer:18. Apparently, the models that naively extrapolate the LTSC for the next day do not cope well with the extreme electricity price dynamics in Germany over the period studied and are outperformed by the classical ARX and LEAR benchmarks.
Furthermore, in line with a recent trend in the electricity price forecasting (EPF) literature mac:uni:wer:23, we have considered a realistic trading strategy involving day-ahead bidding and battery storage in order to quantify the benefits in monetary terms. Although for both the German and Spanish markets the eSC-type models yield the highest profits within each group (ARX, LEAR), the differences in profits are much less pronounced than the differences in predictive performance. This may be an indication that while the considered models predict price levels much better than the benchmarks, the benchmarks are able to identify the hours with the lowest and highest prices of the day almost as well as the eSC-type models.
The latter suggests that computing probabilistic forecasts and considering quantile-based trading strategies mar:nar:wer:zie:23,nit:wer:23,uni:wer:21 may lead to more significant performance improvements. Similarly, studying other energy markets where the seasonal component plays an important role, such as natural gas, may provide evidence that the proposed approach extends beyond electricity markets. Investigating the impact of seasonal decomposition on other machine learning models, including deep neural networks, may open new avenues of research. Finally, although the use of simple averaging was effective in this study, more sophisticated ensembling techniques can be considered. All this, however, is left for future research.
Overall, our results highlight the importance of seasonal decomposition and accurate day-ahead forecasting of the trend-seasonal pattern of electricity prices. The proposed approach is robust and ensures good performance even under extremely volatile market conditions. Due to the use of forecast averaging, it does not require ex-ante selection of the LTSC parameters (width of the moving average, wavelet decomposition level). Its simplicity and low computational requirements make it a perfect tool for daily market operations, both for point forecasting tasks and as a reliable source of inputs for probabilistic forecasting models and risk management applications gne:ler:sch:23,lip:uni:wer:24.
This work was partially supported by the National Science Center (NCN, Poland) through grants No.\ 2018/30/A/HS4/00444 (to K.C.), No.\ 2023/49/N/HS4/02741 (to B.U.) and No.\ 2021/43/I/HS4/02578 (to R.W.).