One-week-ahead electricity price forecasting
using weather forecasts, and its application toarbitrage in the forward market: an empirical
study of the Japan Electric Power Exchange
メタデータ

言語: English
出版者:
公開日: 2022-09-26
キーワード (Ja):
キーワード (En):作成者: Matsumoto, Takuji, Endo, Misao, 松本, 拓史
メールアドレス:所属:

URL

https://doi.org/10.24517/00067122
This work is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 3.0
International License.

Journal of Energy Markets 14(3), 1–26
DOI: 10.21314/JEM.2021.004
Copyright Infopro Digital Limited 2021. All rights reserved. You may shareusing our article tools. This article may be printed for the sole use of the
Authorised User (named subscriber), as outlined in our terms and conditions. https://www.infopro-insight.com/termsconditions/insight-subscriptions

Research Paper

One-week-ahead electricity price forecasting
using weather forecasts, and its application toarbitrage in the forward market: an empirical
study of the Japan Electric Power Exchange
Takuji Matsumoto and Misao Endo
Socio-economic Research Center, Central Research Institute of Electric Power Industry,
1-6-1 Otemachi, Chiyoda-ku, Tokyo 100-8126, Japan;
emails: matsumoto3832@criepi.denken.or.jp, endo@criepi.denken.or.jp(Received March 23, 2021; revised June 9, 2021; accepted June 15, 2021)

ABSTRACT
Although forecasting one-week-ahead average electricity prices is necessary fordecision-making such as evaluating forward contracts, its modeling has not been sufficiently studied. Therefore, to find a suitable forecasting approach, this study constructs and compares multiple parsimonious models using widely published weekly
weather forecasts and then applies them to arbitrage trading in the forward market.
In particular, we clarify the following empirical results using the data from Japan
Electric Power Exchange. First, instead of using forecasted temperature directly as
an explanatory variable, the two-step forecasting method using measured temperature as an intermediate variable is more likely to reduce forecast errors. Second,quantile regression has better density forecast accuracy than the generalized autoregressive conditional heteroscedasticity model. Third, the logarithmic conversion forprices tends to improve forecast accuracy. Fourth, one-week-ahead weather forecasts can significantly improve both the price forecast accuracy and the arbitrage
profit. The proposed arbitrage strategy can be used by many participants because
it can be flexibly changed according to the player’s risk tolerance. In addition, ourPrint ISSN 1756-3607 j Online ISSN 1756-3615
c 2021 Infopro Digital Risk (IP) Limited

Corresponding author: T. Matsumoto1

2

T. Matsumoto and M. Endo

forecasting/trading method, based on published weather forecasts, has wide applicability in that it can be constructed even in markets where system information is not
sufficiently disclosed.
Keywords: arbitrage trading; electricity spot price forecasting; forward market; quantile regression; weather forecast.

1 INTRODUCTION
Accurate forecasting of electricity market prices is key for electricity utilities to run
their businesses economically. As shown systematically by Weron (2014), there havebeen many previous studies on electricity price forecasting, particularly for dealing
with a short-term forecasting horizon from one hour ahead to a few days ahead.
Electricity prices with a mid- or long-term horizon, on the other hand, are often dealt
with in the context of risk management and derivative pricing, so the literature on
their forecasting methods is relatively limited, but some distinctive studies have been
conducted (Eydeland and Wolyniec 2003; Weron 2014). For long-term price forecasting, a typical method uses market equilibrium models that can take into accountstructural changes in the market (Bastian et al 1999; Ventosa et al 2005), which areoften based on stylized fundamental assumptions of economic behavior (Green andNewbery 1992; Barquı́n and Vázquez 2008). For the mid-term horizon, from a few
days to a few months ahead, a hybrid approach (Karakatsani and Bunn 2008; Marcos
et al 2020) that can take into account both fundamental price formation and econometric recalibration has been reported to be effective (Bello et al 2017). However,for a one-week-ahead horizon, modeling approaches focusing on historical prices areoften preferred (see, for example, Chen et al (2008), who used manifold learning,and Mandal et al (2006), who used an artificial neural network). Of these, however,there have been few related studies focusing especially on one-week-ahead average
prices; to the best of our knowledge, such studies only include building univariate
models from historical prices in the Singapore market (Loi and Le Ng 2018) andusing historical prices plus lagged (measured) weather values in the Nord Pool market (Torró 2007). In practice, though, weekly average price forecasting is critical forelectric utilities and is needed especially when evaluating prices of weekly electricity delivery contracts (including bilateral and forward contracts). The issue of how
to effectively use week-ahead hedging instruments (futures and forward) is particularly important for (relatively small) retailers, where short-term risk management is a
key management issue. For generators that need to submit weekly power generationplans to system operators (Suzuki 1991), week-ahead price forecasts can have a significant impact on their decisions. In particular, the operation of pumped storage isusually based on weekly scheduling (Popa et al 2010), and its operation scheduling
Journal of Energy Markets

www.risk.net/journals

One-week-ahead electricity price forecast and arbitrage

has become more important with the recent expansion in renewable energy (Aihara
and Yokoyama 2016). In reality, optimizing such operation scheduling requires granular forecasting, eg, hourly. However, to improve accuracy or reliability, it is important to practically verify forecasted week-ahead hourly prices separately by using theweekly average value.
Against this background, our paper focuses on the forecasting of one-week-ahead
average prices, which has been relatively rarely studied. To do this effectively, we
use widely published week-ahead weather forecasts, which have also received little
attention in previous studies. Although weather forecasts with a long forecast horizon
are known not to be very accurate (even the latest research says that the “practicalpredictability limit” is about 10 days (Zhang et al 2019)), it is nevertheless possible toimprove the forecast accuracy of the one-week-ahead electricity price. Therefore, inthis paper we construct several forecasting models for the one-week-ahead electricity
spot price using published weekly weather forecasts, and explore a desirable modeling approach that can leverage the information value of weather forecasts. Further,in addition to forecasting the weekly average value, we also propose a density forecasting method using the quantile regression (QR) (Koenker 2005) and generalized
autoregressive conditional heteroscedasticity (GARCH) models (Bollerslev 1986),
and apply them to strategic arbitrage trading methods for weekly forward products.1
In particular, we tackle the following four problems that are thought to be usefulfor constructing accurate forecast models in practice.
(i) Which of the forecasted weather values or the measured (realized) weather
values should be incorporated into the price regression formula?
(ii) Should we perform logarithmic conversion on the price series to be regressed?
(iii) Which of the QR or GARCH models should be used for forecasting the weekly
price density?
(iv) What is the information value of the week-ahead weather forecast in terms ofimproving forecast accuracy and arbitrage profit?
These are all open questions regarding week-ahead average price forecasts. The
more detailed motivations for addressing these issues are as follows. First, issue (i)arises from the hypothesis that constructing a price regression equation using measured weather may have higher explanatory power and greater forecast accuracy thanusing forecasted weather as explanatory variables, considering that the week-ahead
1 This study uses the word “arbitrage” because transactions that profit from price differences

between short-term electricity markets are generally called this in much of the literature, but itshould be noted that the strategies proposed here carry certain risks (ie, they could also be called“speculative” trading).
www.risk.net/journals

Journal of Energy Markets

3

4

T. Matsumoto and M. Endo

weather forecast is inherently not very accurate. The viewpoint of (ii) corresponds
to the problem of whether to use an additive model or a multiplicative model. The
review by Weron (2014) positions them as the “two most important categories”
among statistical forecasting methods but merely states that the additive model is“far more popular”; there seems to be no previous research focusing on the comparison between these classifications. Problem (iii) is based on the hypothesis that evenif we use the weekly average electricity price, there may still be a distorted density
shape, and the QR that can express an arbitrary density shape may be superior to
GARCH, which assumes a (log)normal distribution in terms of forecast accuracy.
Regarding (iv), previous studies have analyzed the effect of weather forecast information on forecasting the daily average (Huurman et al 2012) and hourly (Bigerna2018) electricity prices, but there are no studies that have verified it using weekly
average prices. Thus, these four problems have not been solved in previous studies; this study aims to fill those gaps. Considering the above, this study performs
various empirical analyses using actual data from the Japanese market, for which
the past weekly weather forecasts can be obtained in full, to observe useful implications for solving these open questions. In response to issues (i)–(iv), our results using
out-of-sample-period data reveal that the adoption of a two-step model, a multiplicative model and a QR model, as well as the use of weather forecast information, hasadvantages in improving forecast accuracy.
In addition, in order to apply the constructed forecasting method to arbitrage
strategies for the forward market, we build a trading strategy that can be flexibly
changed according to the player’s risk tolerance; the results of simulations demonstrate the effectiveness of the proposed trading strategy and the existence of considerable arbitrage opportunities in the Japan Electric Power Exchange (JEPX) forward
market. The previous literature that dealt with trading strategies between multiple
electricity markets based on price comparisons includes the following topics: arbitrage between the intraday market and the balancing market (Bunn and Kermer 2021;
Just and Weber 2015), day-ahead and real-time prices (Boogert and Dupont 2005),
incorporating storage batteries (Krishnamurthy et al 2017) and proposing a sales
strategy for renewable electricity by comparing the prices of day-ahead and intraday markets (Maciejowska et al 2019). However, to the best of our knowledge, ourstudy is the first attempt to perform an empirical analysis on the trading profit on oneweek-ahead forward products. In addition, the previously proposed trading strategies
that targeted shorter term markets did not consider weather forecasts, so this study
also provides a new perspective in terms of measuring the monetary value of weather
forecasts in the electricity trading market.
This paper is organized as follows. In Section 2, we construct a series of different
types of forecast models for the weekly electricity price. Section 3 formulates thearbitrage strategies in the forward market. Section 4 validates the forecast accuracy
Journal of Energy Markets

www.risk.net/journals

One-week-ahead electricity price forecast and arbitrageof the models and demonstrates the effectiveness of the arbitrage strategies. Lastly,
Section 5 presents our conclusions.

2 CONSTRUCTION OF FORECAST MODELSIn this section, in order to consider the key issues in constructing an effective forecast model for JEPX spot prices, we first review the spot price and weekly weather
forecast data used in our forecast models, and then we build multiple models relating
to the average value forecast and the density forecast.

2.1 Overview of data
2.1.1 Weekly average price distribution
Since several previous studies have shown that hourly or daily average prices haveextremely distorted densities due to price spikes, the price density may still be distorted even if averaged per week. In order to grasp the rough density shape of theweekly average price, the histograms of the weekly average prices for three areasin the JEPX spot market (24-hour average base load and weekday 08:00 to 18:00
daytime loads) are shown in Figure 1, on which the fitted normal distribution andthe lognormal distribution are superimposed. The weekly average price has a leftskewed distribution and is closer to the lognormal distribution than the normal distribution (the Akaike information criterion (AIC) given in the legend of each graphalso indicates that the lognormal distribution is better fitted).

2.1.2 Weekly temperature forecast
Next, we review the forecast accuracy of the weekly weather forecast, which is the
key factor in the model proposed in this study. Figure 2 shows the R-squared value
when the measured value of temperature is regressed by the forecasted value of theseven different forecast horizons.2 The next day’s forecast has an explanatory powerof about 77%, but as the forecast horizon becomes longer, the explanatory power
gradually declines, reaching about 18% for seven days ahead.

2.2 Construction of weekly average price forecast model
In this section, we construct the forecast models for the weekly average price. As
previously mentioned, there are several previous studies on statistical forecastingmodels for electricity prices using weather forecasts, but usually the weather forecast value is used directly as an explanatory variable. However, in the case of weekly
2 We used historical data in Tokyo for each day in 2019, and the seasonality was removed bysubtracting the climatological normal value. See Appendix A online for the original scatter plot.
www.risk.net/journals

Journal of Energy Markets

56

T. Matsumoto and M. Endo
FIGURE 1 Weekly average price histogram and fitted density.

(a)

(b)

(c)

(d)

(e)

(f)

Journal of Energy Markets

www.risk.net/journals

One-week-ahead electricity price forecast and arbitrage
FIGURE 2 Contribution ratio of forecasted temperature to measured value.

FIGURE 3
forecast.

Conceptual diagram of comparison between direct forecast and two-step

Weekly temperature
forecast

Actual (measured)temperature
Two-step
forecast

Directforecast

Electricity spot
price

weather forecasts, as seen in the previous section, the forecast accuracy deteriorates
significantly when the forecast horizon is long. Therefore, if we adopt a model that
directly uses the forecasted temperature as an explanatory variable (we call it a direct
forecast model), it may be difficult to robustly model the intricate interactions thatshould inherently exist between the temperature and the electricity price (such as
nonlinear seasonality and annual change of temperature sensitivity). Therefore, in
www.risk.net/journals

Journal of Energy Markets

78

T. Matsumoto and M. Endo

this study, we construct a two-step forecasting model using both the forecasted temperature and the measured temperature. First, we estimate the price forecast regression using the measured temperature as an explanatory variable, and then we (separately) forecast the conditional probability density of the measured temperature inwhich the forecasted temperature is given. Lastly, we combine these two forecasts.
In this manner, we compare the performance of these two approaches. A conceptual
diagram of the comparison of these two models is shown in Figure 3.
Further, this study also compares two models, namely the price series model andthe log-price series model, for each of the above two modeling approaches. The
actual models are constructed in the following sections.

2.2.1 Price series model
Considering that several papers in the literature clarified that the JEPX spot price hasa remarkable seasonal trend and strong correlations with fuel price and temperature(Matsumoto and Endo 2021; Matsumoto and Yamada 2021), in this study we will
also build a model that can incorporate a seasonal trend and fuel price correlations.
First, the following two types of ordinary least squares (OLSs) are formulated forthe price series models (without logarithmic conversion), where model P1 uses theforecasted temperature and model P2 uses the measured temperature.
Model P1 W

S t D ˛S t 1 C ˇ.t/G t C f .t / C g.t /O" t C  t ;(2.1)

Model P2 W

S t D ˛S t 1 C ˇ.t/G t C f .t / C g.t /" t C  t ;(2.2)

where S t is the weekly average spot price in week t , G t is the spot price of liquid
natural gas (Platts JKM LNG), which is observed as of week t 1 (the spot pricefor LNG cargo that will be delivered in the month following the month in which
the start date of week t belongs), and " t .O" t / is the weekly average measured (forecasted) temperature residual (defined as the temperature minus its yearly cyclicaltrend, eg, " t WD Temp t '.t/, for measured temperature; see Appendix B online).
˛ is a fixed coefficient, ˇ.t/, f .t/ and g.t/ are variable coefficients (yearly cyclicaltrends) estimated based on the concept of a Fourier series expansion (see Appendix B
online) and  t is a residual term with an average of 0. Note that the forecasted temperature residual used in this study may be expressed as "O t jt 1 because it is observedin week t 1, but the notation "O t is used for simplicity.
Here, as can be seen from (B4) in Appendix B online, the point of our model isthat the intersection term – which consists of the periodic trend '4;1 .t /, the elapsed
week trend (Period t ) and the temperature residual (O" t or " t ) – is included in each
price forecast model. This interaction term is included because a characteristic of
the JEPX spot price is that the temperature sensitivity has changed over time due to
Journal of Energy Markets

www.risk.net/journals

One-week-ahead electricity price forecast and arbitrage

the increase in the photovoltaic power generation capacity in Japan (Matsumoto andEndo 2021). The estimation result for this term will be detailed in Section 4.1.
The forecasted spot price (of week t forecasted in week t 1) of the price seriesmodel SQ t jt 1 can be obtained by the following equation as the predictor part of both(2.1) and (2.2):
SQ tjt 1 D ˛S t 1 C ˇ.t/G t C f .t / C g.t /O" t :(2.3)

Note that in (2.3), the forecasted temperature residual is used even when the measured temperature is used (ie, for (2.2)). This is because, when the conditional expectation value is taken for both sides of (2.2), the measured temperature residual, which
is not observed at the time of the forecast, changes into the forecasted (expected) temperature residual. Note also that the price series model is a linear model with respect
to the temperature residual, so when obtaining the forecasted price, there is no needto consider the conditional variance of the measured temperature residual in which
the forecasted temperature residual is given.

2.2.2 Log-price series model
Next, the following OLSs (models L1 and L2), which are isomorphic to (2.1) and(2.2), are constructed for the logarithmic series of spot prices.
Model L1 W

log S.t/ D .t/ C g.t /O" t C  t ;(2.4)

Model L2 W

log S.t/ D .t/ C g.t /" t C  t ;(2.5)

where .t / WD ˛ log.S t 1 / C ˇ.t/ log.G t / C f .t/.
When these log-price OLSs are used, it is not appropriate to use the predictor partsof (2.4) and (2.5) by just converting them to the original price (exp. .t /Cg.t /O" t /) as
the desired forecast values. This is because this forecast method includes a downward
bias, as the variances of the random variables are not considered (for convenience,
we call this the forecast without bias correction). This fact can be understood byexpanding (2.5) as follows:
SO t jt 1 D EŒS t j F t 1  D EŒexp. .t/ C g.t /" t C  t / j F t 1 
D e .t/ EŒexp.g.t/" t / j F t 1 EŒe t j F t 1 2g/;D exp. .t/ C g.t/O" t C 12 f.g.t/";t /2 C ;t(2.6)

where we assume that the random variables " t and  t follow normal distributions
independent of each other and that time series correlations do not exist for simplicity.3 We assume a complete probability space .˝; F ; P / and finite time horizon
3 Even without making such an assumption of independence, this equation holds approximately;

see Appendix C online.
www.risk.net/journals

Journal of Energy Markets

910

T. Matsumoto and M. Endo

Œ0; T . fF t W t 2 Œ0; T g represents the filtration generated by the price process, andwe assume FT D F . EŒ j F t 1  denotes the conditional expected value in weekt 1 (at this time, the forecasted temperature has already been obtained), and ";tand ;t denote the standard deviation of " t "O t and  t , respectively.
In other words, when using a log-price series model such as (2.5), we need toforecast separately the standard deviation of the temperature forecast error and thestandard deviation of the residual ;t of OLS (2.5), respectively, and by substituting
them into (2.6), we can obtain the appropriate price forecast. The forecasted price2
obtained in this way is exp. 21 f.g.t/";t /2 C ;tg/ times larger than the forecast
without bias correction. The same argument applies to the L1 model (2.4) using theforecasted temperature value, by setting the variance of the forecast error ";t to 0. In
this study, the forecasted values of ";t and ;t are obtained by applying (separately)
the GARCH(1,1) model to the series of " t "O t and  t , respectively, up to week t 1.

2.3 Construction of price density forecast model
In this section, we construct the density forecast model for the week-ahead spot
price using QR, with a view to applying it to an arbitrage strategy in the forward
market. For simplicity we do not consider the abovementioned two-step forecast;
we deal only with the direct forecast method using the forecasted temperature as the
explanatory variable. In order to evaluate the accuracy of the QR model, a model thatcombines OLS and GARCH (which we call the OLS C G model) is constructed forcomparison.
For both QR and OLS C G, we construct the price series model as well as the
log-price series model and verify the effect of logarithmic conversion on the forecast
accuracy. In each case, we use regression formulas with exactly the same terms as(2.1) and (2.4), each of which is applied for QR or OLS C G. In the OLS C G model,
after estimating the OLS, GARCH(1,1) is applied to the residual series to obtain
the probability density forecast of one week ahead. Note that this study uses the R(version 3.6.3) package fGarch (prediction method by the garchFit./ function) for
GARCH, and the package quantreg (lasso penalized QR by the rq./ function)for QR.

3 ARBITRAGE STRATEGY IN THE FORWARD MARKETThe forward product in JEPX is a contract that assumes that electricity will be delivered within a certain period at the forward price, contracted in advance, but the actual
settlement is financially performed by the difference between the spot price realized
in the future and the forward price (JEPX 2019). JEPX forward contracts are classified as a 24-hour type (for 24-hour delivery each day) or a daytime type (for delivery
Journal of Energy Markets

www.risk.net/journals

One-week-ahead electricity price forecast and arbitrage

times from 08:00 to 18:00 on weekdays excluding weekends and holidays). Each
type of contract has three different products with delivery periods of one week, onemonth and one year, respectively. Because the forward market is conducted in a continuous session, contracts are executed as soon as the conditions of the seller and thebuyer are met while the market is open. As for the weekly forward products handled
in this study, the contractable period is set from the 20th of the month before themonth of the delivery start date to three days before the delivery start date. Note that
because the delivery start date is every Saturday, every Wednesday is the last tradable
day (JEPX 2020).4
The arbitrage-trading strategies dealt with in this study assume two forecastingcases, one using OLS-based average forecasting and the other using QR-based denQR.q/
sity forecasting. The decision variables for each case Y tOLS
(ie, variables
1 and Y t 1
of decision-making made in week t 1 regarding electricity delivered in week t) aredefined as follows:8ˆ
if SO tjt 1 > F t jt 1 ;
ˆ
<1
(3.1)
Y tOLS
1 if SO tjt 1 < F t jt 1 ;
1 D
ˆ
ˆ
:0
otherwise;

Y tQR.q/
D
1

8
ˆ
1
ˆ
<
ˆ
ˆ
:
0

.q/
if SO tjt
> F t jt 1 ;1.1 q/
1 if SO tjt< F tjt 1 ;
1

(3.2)

otherwise;

where Y D 1 means a long position in forward trading (buying the forward productthat will be settled at the realized spot price after the spot market contract is executed), Y D 1 means a short position (the reverse of the above) and Y D 0 means.q/no deal. SO tjt 1 (SO tjt) are the forecasted weekly average spot prices (the quantile1
forecasted prices at percentile q 2 f0:05; 0:10; 0:25g), which are forecasted in weekt 1. F t jt 1 denotes the forward price for the electricity that will be delivered inweek t observed in week t 1. At this time, the arbitrage profit  t is calculated by

4 The JEPX forward market also lists monthly products, but for these the final trading day is the

19th of the penultimate month before the delivery month, so the forecast horizon is extremely long(difficult to predict precisely) for arbitrage trading; hence, it is not dealt with in this study. Notealso that, since JEPX is a market for the purpose of physical electricity trading, it is not permitted
to carry out purely financial arbitrage virtually, as proposed here (JEPX 2020). However, even if
we make a simple assumption that financial trading can be conducted in JEPX, the results obtained
can have significant implications for traders’ strategic forward market trading.
www.risk.net/journals

Journal of Energy Markets

11

12

T. Matsumoto and M. Endo

the following formula:8ˆˆ<S t F t jt 1
 t D F t jt 1 S t
ˆˆ
:0

if Y t 1 D 1;
if Y t 1 D

(3.3)

1;

if Y t 1 D 0:

Note that this paper ignores the impact of interest rates due to different trading points
on futures and spots.

4 EMPIRICAL ANALYSISThis section validates the forecast accuracy of each model and the effectiveness of
the arbitrage strategy using the following empirical data:(1) the spot price S t and forward price F t (U/kWh) is the JEPX system price,
Tokyo area price and Kansai area price;5(2) the LNG spot price G t (U/MMBtu) is the Platts JKM spot price;6(3) the measured temperature Temp t (ı C) is the maximum temperature measured
by the Japan Meteorological Agency;7 and1(4) the forecasted temperature Temp t (ı C) is the maximum temperature forecasted
by the Japan Meteorological Agency.8
All forecasted values are calculated as out-of-sample values, and the weekly average spot price and the series of explanatory variables observed in the past three years
are used to forecast the weekly average price one week ahead, in a weekly rollingmanner; we thereby obtain the price forecast for the four-year out-of-sample period
from April 1, 2016 to March 31, 2020. The validation of the forecast accuracy performed in Section 4.2 uses all the data from the out-of-sample period, and the evaluation of the forward arbitrage profit in Section 4.3 will only use the sample when theforward price is observed in the out-of-sample period. That is, we assume the players
can make the arbitrage trading decision, which requires a comparison between theforecasted spot price and the observed forward price, only when a forward contractby another player is realized. Note that, due to the extremely low liquidity of the
JEPX forward market, there are many more weeks in which trading contracts are notexecuted than there are weeks in which they are executed.
5 URLs: http://jepx.org/market/index.html and http://jepx.org/market/forward.html.
6 Platts, Benchmark Statement for LNG Japan/Korea Spot Crg DES.
7 URL: http://data.jma.go.jp/gmd/risk/obsdl/index.php.
8 URLs: http://weather-transition.gger.jp/ and http://pe-sawaki.com/WeatherForecast/.

Journal of Energy Markets

www.risk.net/journals

One-week-ahead electricity price forecast and arbitrage
FIGURE 4 Time series transition of estimated temperature sensitivity.

Blue line, base load. Orange line, daytime load.

Because the JEPX forward price has not been announced for each contract timing (ie, F t jt 1 cannot be obtained), we use the average value of all the contracted
forward prices in week t, F t WD MeanŒF tj , which has been published. Regarding
the temperatures needed for forecasting the Tokyo area price (east), the Kansai area
price (west) and the system price, the maximum temperatures of Tokyo, Osaka andthe average values of both cities are used. In addition, when forecasting the following
week’s average price, the weather forecast on Wednesday is used, which is the last
day of the weekly forward trading.

4.1 Estimation result
This section summarizes the estimation results of the forecast model before verifying
the forecast accuracy and analyzing the arbitrage profit. This is because, as we stated2
g/ times the bias correction is necessary for the L2
that using exp. 21 f.g.t/";t /2 C;twww.risk.net/journals

Journal of Energy Markets

13

14

T. Matsumoto and M. Endo
FIGURE 5 Time series transition of estimated .g.t/";t /2 (green line) and .;t /2 (blueline).

model, which is in the explanation of (2.6), we need to understand what time series
data such as .g.t /";t /2 and .;t /2 look like.
First, Figure 4 shows the time series transition of the estimated temperature sensitivity.9 This is g.t/ (coefficient of temperature residual " t ) estimated from (2.5),
9 Color figures are available in the online version of this paper.

Journal of Energy Markets

www.risk.net/journals

One-week-ahead electricity price forecast and arbitrage

which was estimated as a one-period-ahead (one-week-ahead) value and plotted over
all out-of-sample periods in a weekly rolling manner. It can be confirmed that thetemperature sensitivity of the spot price is negative in winter and positive in summer, and that the absolute value of sensitivity is generally larger on the daytime load
than on the base load. It is interesting to note that its amplitudes have increased significantly year by year. This is thought to be mainly due to the recent expansion ofrenewable energies (especially photovoltaic power generation in the case of Japan).
Second, Figure 5 shows the time series transition of the estimated .g.t /";t /2 and.;t /2 . As ";t is the standard deviation of the temperature forecast error and ;t isthe standard deviation of the residual of OLS (2.5), .g.t /";t /2 and .;t /2 denote thevariances resulting from the temperature prediction error and those from the others(residuals of the price model) regarding the forecasted densities of the logarithmic
spot prices. As shown by the plots in Figure 5, both variances tend to expand overtime for each of the six cases, which is probably due to increasing competitivenessever since the full liberalization of the electricity retail business in 2016 as well as
to the expansion in renewable energies. Regarding the daytime loads for times when
price spikes are likely to occur, .g.t/";t /2 is larger than .;t /2 overall. This reflects
the fact that the price fluctuation risk resulting from spikes that occur probabilistically (not necessarily linked to the weather) is greater (ie, the predictability of spikes
is lower) than that of the temperature prediction error.

4.2 Validation of forecast model
In this section, we compare the forecast performance of the different average value
forecast and density forecast models defined in Section 2, and we verify the effectof the weather forecast on reducing the price forecast error. That is, we verify theforecast accuracy for each of the following comparisons.
Average forecast models: direct forecast versus two-step forecast, price series versus log-price series,
 model with weather forecast versus model without weather forecast.
Density forecast models: price series versus log-price series,
 QR versus OLS C G, model with weather forecast versus model without weather forecast.
www.risk.net/journals

Journal of Energy Markets

15

16

T. Matsumoto and M. Endo
FIGURE 6 Comparison of MAE for the different modeling approaches.

4.2.1 Validation of weekly average forecast model
In this section, in order to verify the accuracy of the weekly average forecast model
constructed in Section 2.2, the forecast error is measured by the mean absolute
error (MAE). Figure 6 shows the MAE for the different modeling approach (thetwo-step/direct forecast and the price/log-price series). The case without weather
information (Temp t or Temp t ) is also considered. In addition, in order to makethe comparison between models easier to understand, the difference in the valueof MAEM =MAEL2 1, ie, the ratio of the MAE of each model M (MAEM ) to the
MAE of the log-price two-step forecast model (MAEL2 ), is calculated for each of thesix cases .3 areas  2 loads/ and displayed as a bar graph; the line graph shows thesimple average values of the six cases.
First, the log-price series models have smaller MAEs overall than the price seriesmodels (this result corresponds to issue (ii) in Section 1). In addition, the MAEs of
the two-step forecast are smaller than those of the direct forecast as a whole (thisresult corresponds to issue (i) in Section 1) and the MAE of the two-step forecast
is 4.2% smaller on average even when comparing highly accurate log-price seriesmodels. We probably get this result because the regression formula using the weekly
weather forecast with low forecast accuracy as the explanatory variable does not suf-

1

Journal of Energy Markets

www.risk.net/journals

One-week-ahead electricity price forecast and arbitrage

ficiently express the nonlinearity and the interaction between the variables, and thus
the explanatory power is low. On the other hand, in the two-step forecast approach,the relationship between the measured weather value and the spot price is expressedmore robustly, so the model could be constructed more flexibly.
In terms of the effect of using the weather forecast information, the log-priceseries model confirmed a remarkable MAE improvement of 14.4%, which suggeststhat the weekly weather forecast is an important factor for improving the price forecast accuracy. In addition, the modeling approach of the popular additive model (theprice series model) with the direct forecast approach (ie, the P1 model) has a larger
MAE (14.4%) than the L2 model. In other words, the effect of devising the modelingapproach is comparable with using the information of weekly weather forecasts, interms of improving the forecast accuracy.
In addition, for the log-price series model of average value forecast, the bias correction as described in Section 2.2.2 was performed; as a result, it eliminated all
the significant downward bias confirmed in some of the six cases (see Appendix D
online).

4.2.2 Validation of density forecast model
4.2.2.1 Pinball loss comparison between models. The goodness of fit of the den-sity forecast model was evaluated using the pinball loss (PL) score (see, for example, Nowotarski and Weron 2018); we calculated the average PL of 19 percentiles.q D 0:05; 0:01; : : : ; 0:95/. Figure 7 shows the difference in the ratio of the PL ofeach model M to the PL of the model based on the log-price series QR model (the“LQ model”): PLM =PLLQ 1.
First, regarding the comparison between QR and OLS C G, the PL was smaller
overall for QR, which can simulate an arbitrary density shape, regardless of whether
logarithmic conversion was performed (this result corresponds to issue (iii) in
Section 1).
Second, the log-price models generally have higher forecast accuracies than theprice series models for both QR and OLS C G (this result corresponds to issue (ii)in Section 1). This result may be natural for the OLS C G model in light of the factthat the weekly price distributions are close to the lognormal distributions, as seen in
Figure 1. On the other hand, even for the QR model that can forecast arbitrary density
shapes, the result where logarithmic transformation improved the forecast accuracy
suggests the superiority of the multiplicative model over the additive model.
4.2.2.2 Reduction of PL by weather forecast. Here, in order to help solve issue (iv)in Section 1, we consider the extent to which incorporating the weekly weather forecast can contribute to reducing the forecast error (PL, in this case) for each season
www.risk.net/journals

Journal of Energy Markets

17

18

T. Matsumoto and M. Endo
FIGURE 7 Comparison of PL in modeling approaches.

(month). Our problem awareness is similar to that in Huurman et al (2012), whoverified this effect using the daily average price. As shown in Figure 8, when theweather forecast is incorporated (pink line), the forecast error is reduced, especiallyin summer (and slightly in winter), compared with when it is not incorporated (blueline). The reason why the forecast accuracy was hardly improved by the weather
information in spring and autumn may be because the price (demand) has almost no
relation to the temperature.

4.3 Profit by arbitrage
This section verifies the difference in arbitrage profit and loss risk between thevarious trading strategies by using the average-forecast-based OLS and quantileforecast-based QR methods, each constructed in Section 3. Table 1 summarizes the
profit and loss risk of arbitrage trading for each of the six cases (where OLS uses
the L2 model and QR uses the LQ model, both incorporating the weather forecast).
In Table 1, N is the number of arbitrage opportunities (ie, the number of observed
weekly forward prices during the out-of-sample period), Narb is the number of times
the arbitrage was executed (ie, when Y is nonzero), Nloss is the number of times a loss
Journal of Energy Markets

www.risk.net/journals

One-week-ahead electricity price forecast and arbitrage

FIGURE 8 PL reduction effect from weather forecast (monthly average).

www.risk.net/journals

Journal of Energy Markets

19

Journal of Energy Markets

N

35

17

7

Area

System

East

West

OLS

—

5
10
25

—

OLS

QR

5
10
25

—

OLS

QR

5
10
25

Percentile
(%)

QR

Model

7

2
3
6

17

3
4
10

35

19
23
28

Narb

0

0
0
0

5

0
0
2

6

2
2
2

Nloss

0

0
0
0

29

0
0
12

17

6
6
6

Loss
(%)

(a) Base load

N/A

N/A
N/A
N/A

1.70

0.00
0.00
1.70

2.35

0.18
0.18
0.18

VaR
95%

N/A

N/A
N/A
N/A

1.70

0.00
0.00
1.70

2.45

0.28
0.28
0.28

CVaR
95%

TABLE 1 Profit and loss risk brought about by arbitrage. [Table continues on the next page.]

1.07

0.32
0.57
0.89

1.04

0.23
0.24
0.73

0.81

0.59
0.82
0.96

Mean
profit(12.5)(3.7)(6.7)(10.4)(10.6)

(2.3)
(2.4)
(7.4)

(9.0)

(6.6)
(9.1)
(10.7)

Mean
profit (%)

0.0043

0.29490.14180.0192

0.0437

0.12270.10050.0525

0.0012

0.0013
0.0002
0.0000p-value

20
T. Matsumoto and M. Endowww.risk.net/journals

www.risk.net/journals

78

19

22

System

East

West

5
10
25
—

OLS

—

OLS

QR

5
10
25

—

OLS

QR

5
10
25

Percentile
(%)

QR

Model

22

6
6
13

19

2
3
10

78

19
25
42

Narb

7

0
0
3

6

0
0
2

25

2
5
13

Nloss

32

0
0
14

32

0
0
11

32

3
6
17

Loss
(%)

6.43

0.00
0.00
1.42

12.81

0.00
0.00
0.88

1.75

0.00
0.42
1.89

VaR
95%

(b) Daytime load

6.43

0.00
0.00
1.42

12.81

0.00
0.00
0.88

2.09

0.84
1.42
2.18

CVaR
95%

0.67

0.82
0.82
1.00

0.9

0.04
0.08
1.05

1.34

0.68
0.73
0.84

Mean
profit

(6.5)

(7.9)
(7.9)
(9.6)

(7.6)

(0.3)
(0.7)
(8.8)

(12.6)

(6.4)
(6.9)
(7.9)

Mean
profit (%)

0.22380.0215
0.0215
0.0125

0.39260.19010.12610.0776

0.0000

0.0022
0.0020
0.0021

p-value

The units of VaR95% and CVaR95% are U/kWh. The unit of mean profit is U/kWh. The percentage values in parentheses are the ones obtained by dividing the mean profitsby the average spot prices during the out-of-sample period. The p-value is for the mean profit.  and  denote statistical significance at the 5% and 10% confidence levels,
respectively.

N

Area

TABLE 1 Continued.

One-week-ahead electricity price forecast and arbitrage

Journal of Energy Markets

21

22

T. Matsumoto and M. Endo
FIGURE 9 Difference in average arbitrage profit with and without weather forecast.

was incurred, and Loss is the ratio of Nloss to N . VaR95% means the 95th percentile
value of the distribution of arbitrage profit (loss if minus) and CVaR95% means theaverage of the loss that was below the 95th percentile.
As a whole, when the quantile forecast using QR is performed, the risk of loss due
to arbitrage (Nloss , VaR95% and CVaR95%) can be significantly suppressed compared with the OLS case. On the other hand, in terms of the average profit, OLS
generally has a larger profit; thus, there is a trade-off between risk and return. In
arbitrage using OLS, the average arbitrage profit should be maximized because thedecision is made to always take the position where the expected return is positive
regardless of the loss risk; hence, the calculation results obtained here are consistent. In addition, the fact that there are significant arbitrage opportunities of around
1 U/kWh on average (which corresponds to around 10% when viewed as a proporJournal of Energy Markets

www.risk.net/journals

One-week-ahead electricity price forecast and arbitragetion of the average spot prices of each load and area during the out-of-sample period)
may reflect the situation such that the JEPX forward market is quite illiquid and thatfew market participants will find extreme prices (far from the fair prices) and carryout arbitrage trading.
Finally, in order to evaluate the effect of using the weekly weather forecast fromthe viewpoint of improving the arbitrage profit, we also separately calculated thearbitrage profit obtained from the forecast model without the weather forecast, andwe summarize the average profits of all the cases in Figure 9. The pink bar graphmatches the value in parentheses for mean profit in Table 1 and the dotted line is a
simple average profit with or without the weather forecast. In all the four cases ofusing OLS and QR, the arbitrage profit was significantly improved when the weekly
weather forecast was used. We suggest that improving the accuracy of electricity
price forecasts by incorporating the temperature forecast information could greatly
contribute to more economic market trading.
As described above, it was empirically shown that the proposed arbitrage method
works effectively in the JEPX market and can adjust the balance between risk andearned profit according to the player’s risk tolerance. In particular, the empiricalanalysis revealing that weekly weather forecasts greatly contribute to higher transaction profit clearly indicates the information value of weather forecasts. The incrementin earned profit due to weather forecasts (1.5–3.3 times for each strategy) is a significant amount compared with the reduction in forecasting error, which may meanthat even a marginal improvement in forecast accuracy can significantly increase
profitability in market trading.

5 CONCLUSION
In this study, we constructed a model using weekly weather forecasts for forecasting week-ahead average electricity prices, which has hardly been studied in the past,
and we applied it to an arbitrage strategy in the forward market, demonstrating its
effectiveness by using six different cases of market data from JEPX. The empirical analyses of this research clarified the following new perspectives on unresolved
questions, yielding useful suggestions and ideas for the development and practicaluse of the model.
(1) When forecasting the weekly average price, instead of using the weather forecast directly as an explanatory variable, the two-step forecast approach, where
the measured temperature values mediate, is more advantageous in reducing
the forecast error.
www.risk.net/journals

Journal of Energy Markets

23

24

T. Matsumoto and M. Endo

(2) When forecasting the price density, QR, which can directly forecast the percentile values of any density shape, has better forecast accuracy than GARCH,
which assumes a lognormal distribution.
(3) Common to both average forecast and density forecast, the multiplicativemodel using the logarithmic series tends to have greater forecast accuracy
overall than the additive model using the original price series.
(4) The weekly weather forecast improves the forecast accuracy of the weekly
average electricity price for the following week and plays an important role inearning profits in forward market trading.
Of these, regarding the case of using a log series in the two-step forecast (point 1
above), we pointed out that an estimation bias may occur if the probability densityof the log price due to meteorological prediction errors and price residuals is notconsidered, and we provided a method to correct it, demonstrating its effectiveness.
Weekly weather forecasts are generally thought not to be particularly accurate dueto the long forecast horizon, as also demonstrated in this paper, and so they may
be overlooked by practitioners who forecast electricity prices, as evidenced by thelack of previous studies. However, the value of such information can be enhanced
by devising modeling methods such as the logarithmic conversion and the two-step
forecast approach proposed in this study. In particular, we showed that using weather
forecasts can increase the arbitrage profit by 1.5–3.3 times.
The proposed arbitrage trading method that can consider the loss risk is likely
to be used by many businesses as the strategy can be flexibly changed to suit thelevel of acceptable risk. In addition, our forecasting method using publicly available
weather forecasts has wide applicability in many markets. It can be constructed evenfor the (relatively recently liberalized) markets where forecast information such as
demand and renewable energy generation is not available. In future work, we willfurther explore whether our price forecasting and trading methods based on weather
forecasts can also be applied to different time granularity or horizons.

DECLARATION OF INTEREST
The authors report no conflicts of interest. The authors alone are responsible for thecontent and writing of the paper.

REFERENCES
Aihara, R., and Yokoyama, A. (2016). Optimal weekly operation scheduling of pumped
storage hydropower plant considering optimal hot reserve capacity in a power system with a large penetration of photovoltaic generation. Electrical Engineering in Japan
195(2), 35–48 (https://doi.org/10.1002/eej.22820).
Journal of Energy Markets

www.risk.net/journals

One-week-ahead electricity price forecast and arbitrage
Barquı́n, J., and Vázquez, M. (2008). Cournot equilibrium calculation in power networks:
an optimization approach with price response computation. IEEE Transactions on
Power Systems 23(2), 317–326 (https://doi.org/10.1109/TPWRS.2008.919198).
Bastian, J., Zhu, J., Banunarayanan, V., and Mukerji, R. (1999). Forecasting energy prices
in a competitive market. IEEE Computer Applications in Power 12(3), 40–45 (https://doi.org/10.1109/67.773811).
Bello, A., Bunn, D. W., Reneses, J., and Muñoz, A. (2017). Medium-term probabilistic forecasting of electricity prices: a hybrid approach. IEEE Transactions on Power Systems
32(1), 334–343 (https://doi.org/10.1109/TPWRS.2016.2552983).
Bigerna, S. (2018). Estimating temperature effects on the Italian electricity market. Energy
Policy 118, 257–269 (https://doi.org/10.1016/j.enpol.2018.03.068).
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journalof Econometrics 31(3), 307–327 (https://doi.org/10.1016/0304-4076(86)90063-1).
Boogert, A., and Dupont, D. (2005). On the effectiveness of the anti-gaming policy
between the day-ahead and real-time electricity markets in the Netherlands. Energy
Economics 27(5), 752–770 (https://doi.org/10.1016/j.eneco.2005.03.006).
Bunn, D. W., and Kermer, S. O. (2021). Statistical arbitrage and information flow in an electricity balancing market. Working Paper, January 22, Social Science Research Network(https://doi.org/10.2139/ssrn.3101716).
Chen, J., Deng, S. J., and Huo, X. (2008). Electricity price curve modeling and forecastingby manifold learning. IEEE Transactions on Power Systems 23(3), 877–888 (https://doi.org/10.1109/TPWRS.2008.926091).
Eydeland, A., and Wolyniec, K. (2003). Energy and Power Risk Management: New
Developments in Modeling, Pricing, and Hedging. Wiley.
Green, R. J., and Newbery, D. M. (1992). Competition in the British electricity spot market.
Journal of Political Economy 100(5), 929–953 (https://doi.org/10.1086/261846).
Huurman, C., Ravazzolo, F., and Zhou, C. (2012). The power of weather. Computational
Statistics and Data Analysis 56(11), 3793–3807 (https://doi.org/10.1016/j.csda.2010.06.021).
JEPX (2019). Japan electric power exchange guide. (In Japanese.) URL: https://www.jepx.org/outline/pdf/Guide 2.00.pdf.
JEPX (2020). Japan electric power exchange trading regulations. (In Japanese.) URL:
https://www.jepx.org/outline/pdf/tr rules.pdf.
Just, S., and Weber, C. (2015). Strategic behavior in the German balancing energy mechanism: incentives, evidence, costs and solutions. Journal of Regulatory Economics
48(2), 218–243 (https://doi.org/10.1007/s11149-015-9270-6).
Karakatsani, N. V., and Bunn, D. W. (2008). Forecasting electricity prices: the impact offundamentals and time-varying coefficients. International Journal of Forecasting 24(4),764–785 (https://doi.org/10.1016/j.ijforecast.2008.09.008).
Koenker, R. (2005). Quantile Regression. Cambridge University Press (https://doi.org/
10.1017/CBO9780511754098).
Krishnamurthy, D., Uckun, C., Zhou, Z., Thimmapuram, P. R., and Botterud, A. (2017).
Energy storage arbitrage under day-ahead and real-time price uncertainty. IEEE Transactions on Power Systems 33(1), 84–93 (https://doi.org/10.1109/TPWRS.2017.268
5347).
www.risk.net/journals

Journal of Energy Markets

25

26

T. Matsumoto and M. Endo
Loi, T. S. A., and Le Ng, J. (2018). Anticipating electricity prices for future needs: implications for liberalised retail markets. Applied Energy 212, 244–264 (https://doi.org/
10.1016/j.apenergy.2017.11.092).
Maciejowska, K., Nitka, W., and Weron, T. (2019). Day-ahead vs. intraday: forecasting
the price spread to maximize economic benefits. Energies 12(4), 631 (https://doi.org/
10.3390/en12040631).
Mandal, P., Senjyu, T., Urasaki, N., Funabashi, T., and Srivastava, A. K. (2006). Shortterm price forecasting for competitive electricity market. In 2006 38th North American
Power Symposium, pp. 137–141. IEEE Press, Piscataway, NJ (https://doi.org/10.1109/
NAPS.2006.360135).
Marcos, R. A. D., Bunn, D. W., and Bello, A., Reneses, J. (2020). Short-term electricity
price forecasting with recurrent regimes and structural breaks. Energies 13(20), 5452
(https://doi.org/10.3390/en13205452).
Matsumoto, T., and Endo, M. (2021). Empirical analysis of risk premium in the Japaneseelectricity futures market. Report Y20004, Central Research Institute of Electric Power
Industry. (In Japanese.)
Matsumoto, T., and Yamada, Y. (2021). Simultaneous hedging strategy for price andvolume risks in electricity businesses using energy and weather derivatives. Energy
Economics 95, Paper 105101 (https://doi.org/10.1016/j.eneco.2021.105101).
Nowotarski, J., and Weron, R. (2018). Recent advances in electricity price forecasting:a review of probabilistic forecasting. Renewable and Sustainable Energy Reviews 81,
1548–1568.
Popa, R., Popa, F., Popa, B., and Zachia-Zlatea, D. (2010). Optimization of the weekly
operation of a multipurpose hydroelectric development, including a pumped storage
plant. IOP Conference Series: Earth and Environmental Science 12(1), Paper 012118(https://doi.org/10.1088/1755-1315/12/1/012118).
Suzuki, M. (1991). Power supply and demand operation plan. Measurement and Control
30(7), 557–564.
Torró, H. (2007). Forecasting weekly electricity prices at Nord Pool. Working Paper 88,
June 7, Social Science Research Network (https://doi.org/10.2139/ssrn.991532).
Ventosa, M., Ballo, A., Ramos, A., and Rivier, M. (2005). Electricity market modelingtrends. Energy Policy 33(7), 897–913 (https://doi.org/10.1016/j.enpol.2003.10.013).
Weron, R. (2014). Electricity price forecasting: a review of the state-of-the-art with a look
into the future. International Journal of Forecasting 30(4), 1030–1081 (https://doi.org/
10.1016/j.ijforecast.2014.08.008).
Zhang, F., Sun, Y. Q., Magnusson, L., Buizza, R., Lin, S. J., Chen, J. H., and Emanuel,K. (2019). What is the predictability limit of midlatitude weather? Journal of the
Atmospheric Sciences 76(4), 1077–1091 (https://doi.org/10.1175/JAS-D-18-0269.1).

Journal of Energy Markets

www.risk.net/journals