Electricity Price Forecasting with Principal
Component-Guided Sparse Regression
Takuji Matsumoto

Florian Ziel

Faculty of Transdisciplinary Sciences for Innovation
Kanazawa University
Kanazawa, Japanmtakuji@staff.kanazawa-u.ac.jp

House of Energy Markets and Finance
University of Duisburg–Essen
Essen, Germany
Florian.Ziel@uni-due.de

Abstract— This study investigates forecasting day-ahead
electricity prices in markets influenced by weather-dependent
energy sources. We utilize the principal component-guided sparse
regression (pcLasso) technique, developed by Tay et al., tomanage multicollinearity among weather and grid variables
effectively. Our focus is on the Japanese Electricity Power
Exchange (JEPX), which integrates significant solar capacity,
demonstrating how various weather variables impact electricity
prices. Our results show that pcLasso surpasses state-of-the-art
models like Lasso and Ridge regression in stability andconsistency of parameter estimation. Importantly, pcLassoenhances forecast accuracy as more variables are incorporated,
providing insights into the seasonality and inter-annual
variations of weather impacts. These findings underscore
pcLasso’s ability to generate robust, interpretable models forcomplex forecasting scenarios. A key finding when applying
pcLasso to JEPX price is the significant improvement in accuracy
using day-ahead reserve margin forecasts over weekly forecasts,
highlighting the importance of timely disclosure of grid
information.
Index Terms-- electricity price forecasting, pcLasso, renewableenergy sources, weather forecastingI.

INTRODUCTION

In competitive electricity markets, day-ahead priceforecasting is essential for electricity trading practices such as
efficient generation and procurement planning and risk
management by market participants. In recent years, thepenetration of intermittent renewable energy sources such as
solar power has increased supply and demand uncertainty,
which has had a significant impact on the formation ofwholesale electricity prices [1]. Given that much of thevariation in supply and demand depends on weather
conditions, clarifying how multiple weather conditions
simultaneously affect electricity prices would be an interesting
research question to understand the electricity market in recent
years, where weather-related risks have increased. In addition,1

In relatively recently liberalized markets such as Japan, there is insufficientgrid forecast information, so weather forecasts are often used for priceThis research is funded by Grants-in-Aid from the Japan Society for the
Promotion of Science (JSPS) – 21K14374, 22KK0217, and 24K16396 (toT.M.), and the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) – 505565850 (to F.Z.).

979-8-3503-8174-0/24/$31.00 ©2024 IEEE

since weather effects should vary seasonally and over time,visualizing their occurrence would have practical implications
for electricity trading practices. Furthermore, exploring themethodological refinements could contribute to the technicalaspects of model development. In this sense, the objective of
this study is to explore a highly interpretable and accurate
electricity price forecasting model using multiple weather
forecast and grid information, and to clarify its effectivenessthrough extensive empirical analysis.
Many models have been proposed in the context ofelectricity price forecasting [2][3], often using forecast
information about the power system as exogenous variables.
For example, some use electricity demand and reserve margins[4][5], and others use forecast information on renewableenergy generation such as solar and wind [6][7]. Anotherapproach is to construct a price model using weather
information instead of grid information, based on the idea thatdemand and renewable energy production are strongly related
to weather conditions, and there are some previous studies,
albeit limited, on this approach as well1. However, estimating
a robust price model is not an easy task due to the strong
multicollinearity among weather variables, and several
previous studies [10]–[12] have only used temperature as aweather variable.
When it comes to studies that deal with multiple weather
forecasts simultaneously and try to identify their impact, theexamples are more limited and, to our knowledge, only [13]and [14]. Huurman et al [13] estimated models combined with
ARIMA and GARCH using temperature and wind speed
forecasts for electricity prices in Norway and Denmark andshowed the predictive power of this weather information interms of forecast error reduction. Sgarlato and Ziel [14]analyzed the impact of multiple weather forecasts, such as
wind speed and solar radiation, on German market prices.
Using the variable selection approach of Lasso regression [15],they present a suggestive analysis of the degree of influence of

forecasting, such as in [8] and [9], but these studies do not focus on weather
information.

each weather information. Although their interest was in
identifying the role of weather forecasts in the horizon beyond
the day-ahead, and thus focused on a specific period, theirweather variable selection approach would be helpful for the
purpose of this study, i.e., to capture (medium- and long-term)seasonal and interannual changes in weather impacts.
Therefore, in this study, based on the analytical approachof [14], we consider applying a more robust methodology toallow for stable model estimation across all seasons. The Lasso
regression used in their research, along with Ridge regression[16] and others, is classified as sparse regression. Sparse
regression is a model suitable for building highly interpretablemodels as it can eliminate (or shrink) redundant variables andextract essential variables. Regarding Ridge regression, ameta-analysis [17] showed that the stronger themulticollinearity in the explanatory variables, the higher thepredictive accuracy of Ridge regression than general OLS, etc.
As for other sparse regressions, several extended models withvarious innovations have been proposed in recent years [18]–[21]. Among them, principal component-guided sparse
regression (pcLasso), developed by Tay et al. [18], is reported
to be excellent for extracting variables from feature-rich data
and more accurate than similar conventional methods in theliterature. As pcLasso is a relatively recently proposed method,
there are few examples of its application to empirical studies.
To the best of our knowledge, it has only been applied to data
analysis in bioinformatics [22][23] and cryptocurrency priceanalysis [24][25]. Thus, we believe that applying pcLasso toenergy market analysis and forecasting models will be a newresearch contribution in terms of expanding the applications of
the method.
For the empirical analysis, we choose the Japanese market,
where solar power generation is increasingly installed. In
markets with high solar generation, weather factors that affectelectricity supply (e.g., temperature and rainfall) also have asignificant impact on the demand side (albeit differently in
different seasons), so the way weather affects price would be
more complex than in markets with high wind generation.
Since a robust estimation of the price model is assumed to bedifficult, an empirical analysis using data from the Japanesemarket is considered an ideal case study to validate theeffectiveness of the model. With this in mind, this study
applies pcLasso to JEPX spot price forecasts to visualize thedegree of influence of various weather and other information,and to perform a multi-faceted verification of the model'svalidity and predictive accuracy. This study is organized asfollows. The next section provides an overview of the pcLassomodel, followed by an empirical analysis in Section III.
Finally, Section IV presents the conclusions.
II.

METHOD

A. pcLasso ModelIn the pcLasso model, when the explanatory variablematrix is singular value decomposed as =(whereis a diagonal matrix whose elements are singular values≥ …≥> 0, = rank( )), consider the problem ofminimizing ( ) in the following formula [18].

1
"
(1)
‖ −
‖ + !‖ ‖ +#$% &#'%
22
where is the vector of objective variables, is the parameter(coefficient) vector to be estimated, #$%&#% is an
×
( )=

'

diagonal matrix with− ) (* = 1, … , ) as elements, and !
and " are parameters that adjust the strength of the penalty(regularization) in the second and third terms ． Up to thesecond term of (1), it is equivalent to Lasso regression, and thesecond term is the usual L1 penalty. On the other hand, thecharacteristic third term is derived from the+form(where + is a diagonal matrix whose diagonal elements arefunctions of the squared singular values), a generalization of
the L2 (quadratic) penalty, and is a more elaborate variant of
it. The idea is to penalize each component (i.e., the original
coefficients that synthesize each component) according to thedeviation of its eigenvalue from the principal components. In
other words, by weighting the penalties so that the coefficientsof variables with smaller contributions to the principal
component are more likely to be shrunk, the extraction of
essential variables is made more efficient.
B. Parameter Estimation ModelIn this study, we set the objective variable as the daily
average electricity day-ahead price ,- (on day .) and estimate
the following model:,- = /0 + / ,12 ,- + / 345 ,- + /6 ,12 ,- + /7 345 ,+/8 . + /9 :4;1 <=- + /> ,<.?@ <=+/A B42 <=- + /C D @- + / 0 D @(2)+/ D@<2EF- + / G<12- + / 6 B<@E12+ ∑JK7 / 7IJ ,-&J + LRM-

RM-

where ,12M,- : = sin Q698. 8T , 345M,- : = cos(698. 8) ; :4;1 <=(which includes national holidays and Sundays),,<.?@ <=- , and B42 <=- are day-type dummy variables;
D @- and D@<2EF- are mid-range and range of maximumminimum temperature forecasts, i.e., D @- ≔ (D <X- +D 12- )/2 , D@<2EF- ≔ D <X- − D 12- ; G<12- , B<@E12are the rainfall probability and reserve margin forecast,respectively; / is coefficient, and L- is the residual. Note thatfor the mid-range temperature, the quadratic term D @- isincluded based on the results in [26].
In this study, (2) is estimated using OLS, Lasso, Ridge, andpcLasso, and the coefficients and prediction errors arecompared. We standardize all data sets used in each estimation(returning to the original series when checking the prediction
error). This not only gives equal weight to the penalties of thefeatures, but also makes it possible to compare the influence of(different units of) explanatory variables when validating theestimated parameters. Note that Lasso and Ridge estimate theregularization parameter ! with 5-fold cross-validation. The
pcLasso also estimates ! with 5-fold cross-validation, but weadditionally assume six different "@<.14" parameters (relatedto "; see [18]): @<.14 ∈ [0.25, 0.5, 0.75, 0.9, 0.95, 0.99_, andchoose the combination of ! and @<.14 that yields the smallest
mean squared error.

III.

RESULTThe data used in this study for the empirical analysis are as
follows and each explanatory variable after processing areplotted them in Fig. 1.
•

Electricity day-ahead (spot) price [JPY/kWh]: JEPX
spot price (Tokyo area) 2•

Maximum and minimum temperature [°C], rainfall
probability: Day ahead weather forecast by JMA3•

Reserve margin [%]: Weekly reserve margin publishedby OCCTO 4

radiation or solar power generation, but is relatively small inthe summer season. This may be due to the additional cooling
effect (lower demand) of rainfall. The coefficient of thetemperature squared variable tends to be positive especiallywhen the absolute value of the temperature coefficient is large,
which is consistent with the fact that the nonlinearity increases
when the sensitivity to temperature is high. The coefficientsfor the reserve margin are generally negative, consistent withthe tendency that the smaller the reserve margin, the more
likely a price spike will occur. The temperature difference
coefficient (Trange) tends to be negative, but tends to approachzero when the reserve margin coefficient is large. This isprobably because the temperature difference is related to theamount of solar power generated (solar radiation around noon)
and therefore has a smaller effect during periods of higher
margin sensitivity (when supply and demand are tight, causing
price spikes in the evening).

Fig. 1: Data description

For the out-of-sample period, we use a two-year period
from January 1, 2022 to December 31, 2023 to include periodsof extreme electricity price spikes and calm periods in thevalidation process, and for the forecast for each day t, we use
observed data for the past 42 days (i.e., daily rolling forecasts
are made using data for the in-sample period `. − 42, . − 1b).
Note that in the Japanese market, in addition to the weekly
reserve margin, the day-ahead reserve margin is also
published. However, the day-ahead reserve margin ispublished in the evening of the previous day and cannot be
used for bidding in the spot market, which is conducted in themorning, so the weekly reserve margin is used in this study. In
addition, as a hypothetical case, we also measure the forecast
error if the day-ahead reserve margin could be used forforecasting, and the results are presented at the end of Section
III-B.

Fig. 2: Changes in estimated parameters

Next, to confirm the validity of pcLasso's estimation
results, a comparison of each method is shown in Fig. 3.
pcLasso shows the smoothest results with the least fluctuation,
followed by Ridge and Lasso, which become increasingly
unstable. Although not shown in the graph, the OLS estimation
results were incomparably more unstable. This can beinterpreted as the unstable parameter estimation in OLS due tomulticollinearity among variables is stabilized by theregularization of sparse regressions. And it may also mean thatthe more the quadratic penalty is refined, the smoother theestimation becomes.

A. Model Estimation Results
First, to confirm the rationality of the estimation results ofthe pcLasso model, we plot the coefficients of temperaturerelated variables, rainfall probability and weekly reserve
margin in Fig. 2. As can be seen, the sign of the temperature
coefficient is positive in summer and negative in winter, whichis consistent with the increasing/decreasing demand forcooling/heating. The rainfall probability coefficient isgenerally positive, presumably due to the decrease in solar

We then extract variables with signs of the estimatedparameters that are considered consistent across seasons andsummarize in TABLE I the percentage of estimated results thatare consistent with these signs (where the percentage iscalculated as the area of coefficients with consistent signs
relative to the total area of estimated coefficients in Figure 3).
From this table, we can also see that the estimation result ofpcLasso is highly consistent.

2

4

3

Downloaded from http://www.jepx.org/market/index.html.

Downloaded from https://pe-sawaki.com/WeatherForecast/. Note that JMA
is Japan Mereological Agency, Japan.

Downloaded from https://occtonet3.occto.or.jp/public/dfw/RP11/OCCTO/S
D/LOGIN_login#. We use a 7-day forecast starting the following Saturday, published every Thursday. Note that OCCTO is Organization for Cross-region
al Coordination of Transmission Operators, Japan.

Fig. 4: Comparison of model performance using RMSE and MAE
TABLE II.

CORRESPONDENCE WITH EXPLANATORY VARIABLES FOR
EACH MODEL (M1-M5)
Variables

−

(

Tmr
TrangeRain
Margin((((TABLE III.

Month

Fig. 3: Changes in estimated parameters by methods
TABLE I.

COMPARISON OF PARAMETER SIGN CONSISTENCY BETWEENMETHODS

Variables

Plausible sign

OLS

Lasso

Ridge

pcLasso

Holiday

Negative

99.6%

100.0%

100.0%

100.0%

Saturday

Negative

96.7%

99.9%

100.0%

100.0%

MondayPositive

36.4%

83.3%

81.4%

88.7%

Lag1

Positive

30.0%

99.3%

99.8%

99.9%

Lag7

Positive

7.8%

68.2%

75.2%

84.2%

Rain

Positive

96.7%

99.5%

98.8%

99.8%

MarginNegative

45.0%

91.0%

87.9%

92.8%

B. Validation of Forecast Error
Next, we examine the predictive accuracy: Fig. 4 compares
the changes in the out-of-sample root mean squared error(RMSE) and mean absolute error (MAE) (divided by theaverage actual price) as the number of explanatory variables isgradually increased, comparing five models from M1 to M5
across the three sparse regression models (see TABLE II for
the correspondence between models and explanatory
variables). The results show that pcLasso tends to reduce theprediction error with each increase in the number of
explanatory variables. Also, the prediction accuracy of
pcLasso tends to be higher per month, as shown in TABLE III,
followed by Ridge, Lasso, and OLS.

202201202202202203202204202205202206202207202208202209202210202211202212202301202302202303202304202305202306202307202308202309202310202311202312
All period,12M,- , 345M,- , ., :4;1 <=- ,,<.?@ <=- ,B42 <=- , ,-&J
D @- + D @D@<2EFG<12B<@E12-

)

M1

M2

M3

M4

M5

✓

✓

✓

✓

✓

✓

✓
✓

✓
✓
✓

✓
✓
✓
✓

)
)
)
)

MONTHLY COMPARISON OF MODEL PERFORMANCE USINGRMSE AND MAE (M5)RMSE
OLS
Lasso Ridge pcLasso
0.267
1.769
0.290
0.276
0.246
0.462
0.249
0.256
0.416
0.597
0.505
0.426
0.380
0.734
0.434
0.381
0.178
0.473
0.191
0.185
0.215
0.265
0.223
0.226
0.291
0.980
0.336
0.319
0.288
0.809
0.311
0.331
0.199
0.395
0.200
0.231
0.201
0.493
0.208
0.213
0.110
0.186
0.113
0.113
0.094
0.162
0.108
0.102
0.106
0.657
0.112
0.107
0.103
0.222
0.117
0.108
0.144
0.311
0.159
0.148
0.215
0.330
0.223
0.227
0.171
0.278
0.187
0.174
0.135
0.226
0.159
0.146
0.091
0.183
0.100
0.100
0.064
0.126
0.070
0.067
0.100
0.226
0.105
0.105
0.118
0.359
0.143
0.123
0.054
0.184
0.056
0.059
0.091
0.185
0.092
0.091
0.267
0.718
0.278
0.270

MAE
OLS
Lasso Ridge pcLasso
0.216
0.532
0.235
0.223
0.161
0.340
0.168
0.170
0.276
0.461
0.338
0.279
0.282
0.520
0.336
0.285
0.135
0.402
0.144
0.136
0.124
0.155
0.126
0.126
0.167
0.670
0.195
0.180
0.164
0.599
0.168
0.185
0.150
0.279
0.160
0.181
0.151
0.372
0.157
0.160
0.088
0.146
0.089
0.092
0.077
0.133
0.085
0.084
0.088
0.253
0.096
0.088
0.075
0.165
0.086
0.078
0.116
0.248
0.125
0.118
0.176
0.293
0.185
0.189
0.132
0.217
0.150
0.133
0.100
0.162
0.116
0.108
0.069
0.152
0.076
0.077
0.050
0.106
0.051
0.053
0.077
0.167
0.081
0.081
0.095
0.251
0.113
0.100
0.044
0.148
0.046
0.047
0.076
0.162
0.077
0.077
0.145
0.324
0.150
0.147

Looking at the rates of reduction in RMSE and MAE for
the M5 model relative to the M1 model, Fig. 5 shows that the
combination of weather and other variables that contribute to
the improvement in forecast error varies from month to month.
In 2022, when the reserve margin was relatively small (due tohigh fossil fuel prices and supply shortages) and pricefluctuations were relatively large, the reduction in forecast
error due to temperature was large, but in 2023, when supply
and demand were slack and prices were stable, temperature
differences (related to solar power generation) contributed
more significantly to the reduction in error.

Fig. 6 plots the forecast error reduction rate of M5 relativeto M4 (i.e., the error reduction rate due to the weekly reserve
margin) as a gray bar (corresponding to the gray part of the barin Fig. 5) and the error reduction rate due to the reserve margin
in the model where the weekly margin is replaced by the dayahead margin as a yellow bar (as mentioned in Section III, thisis a hypothetical case because the day-ahead margin ispublished after the spot market bids and therefore cannot be
used for actual forecasting). Of the 24-month periods, theweekly margin contributed to reducing the RMSE (MAE) in
14 (12) months, while the day-ahead margin reduced theforecast error in more cases (18 (15) months) and in somemonths the RMSE and MAE improved by almost 20%.
Since reserve margin information reflects specificgenerator operating plans, etc., more immediately prior to
bidding, updating such information can improve the accuracyof the price forecast. In the Japanese market, as mentioned
above, the only reserve margin information that can bereferenced for day-ahead bidding is the weekly forecast, butpublication of the latest reserve margin forecast immediately
prior to bidding should be considered. Increased transparencyof grid information will lead to more accurate price signals formarket participants, which in turn will encourage moresophisticated planning of electricity consumption andprocurement (and thus contribute to more efficient use ofresources). Empirical results such as those presented here, inwhich reserve margin information updates contribute toimproved price forecasting accuracy, may have such policy
implications.

IV.

This study applies pcLasso, recently developed by Tay etal. [18], to electricity price forecasting using weather forecasts,
etc., and demonstrates the effectiveness of the model in termsof both rationality and forecast accuracy. In particular, thecontributions of this paper are as follows.
•

It is shown that pcLasso provides more stableparameter estimation results and better consistency
with general interpretations than OLS, Lasso, Ridge,
etc., and that it improves out-of-sample forecast errors
with each variable included.

•

Practical implications for electricity trading areprovided, such as visualizing the seasonality andinterannual changes in maximum and minimum
temperature-related variables, rainfall probability, andreserve margin coefficients, and verifying theirappropriateness with different interpretations.

•

In addition to finding that weekly reserve margin
information improves price forecasting error, the study
also found that forecast accuracy could have beenfurther improved if the day-ahead reserve margin had
been disclosed, adding to the policy discussion on theneed to improve information transparency.

pcLasso has the potential to estimate relatively robust andstable models (reasonable parameters for each variable) evenwhen there is collinearity among explanatory variables (e.g.,
lag variables, temperatures, rainfall probability, etc.) or when
explanatory variables that are not strongly related are included(e.g., squared temperature terms or weekly reserve margin). In
addition, sparse regression including pcLasso is easier tointerpret and more computationally efficient than many
machine learning methods, making it an easy model to handle
in practice (e.g. decision making in electricity trading). The
ability of pcLasso to effectively incorporate multiple
explanatory variables and still produce robust estimates is amajor advance in modeling technology, and sophisticatedmodels based on it can be expected to contribute to improved
decision making in electricity markets.

Note: Values by explanatory variable are calculated from the reduction rate of RMSE or
MAE for M2 to M5 relative to M1 in the pcLasso model.

Fig. 5: RMSE and MAE reduction rate for each exogenous variable

CONCLUSIONACKNOWLEDGMENT
This research is funded by Grants-in-Aid from the Japan
Society for the Promotion of Science (JSPS) – 21K14374,
22KK0217, and 24K16396 (to T.M.), and the Deutsche
Forschungs-gemeinschaft(DFG,
GermanResearch
Foundation) – 505565850 (to F.Z.).
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Fig. 6: RMSE and MAE reduction rate by reserve margin forecast (week ahead
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