Information Value of Weekly Weather Forecasts: An EmpiricalAnalysis of Electricity Price Forecasting and Forward Arbitrage
Takuji Matsumoto (a) and Misao Endo (b)(a) Faculty of Transdisciplinary Sciences, Kanazawa University, Japan(b) Socio-economic Research Center, Central Research Institute of Electric Power Industry, Japan

September 27-28, 2022 in Essen
11th INREC 2022 - Uncertainties in Energy Markets* This presentation is based on the following paper:
Matsumoto, T., & Endo, M. (2021). 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. Journal of Energy Markets, 14(3).
** The first author is funded by Grant-in-Aid for Young Scientists 21K14374 from the Japan Society for the Promotion of Science (JSPS)

Research Overview
Background and purpose◆ Despite the need for price forecasts one week ahead, there are few previous studies
We develop:

Researchquestions

1

forecasting methods for the weekly average JEPX spot price2

arbitrage trading strategies in the JEPX forward market

For 1 , which modeling approach is more accurate?
(i) For weather value: measured value vs. forecasted value(ii) For price time series: logarithmic series vs. original series(iii) For probability distribution model: Quantile Regression vs GARCH
For 1

2 , (iv) How much is the information value of the weekly weather forecast?

In particular…
◆ Examine modeling methods to enhance the information value of weekly weather forecasts◆ Identify the monetary value of weekly weather forecasts in arbitrage trading2

Weekly average price density◆ The weekly average price density (of JEPX) is generally skewed to the right and has a shapecloser to the lognormal distribution than the normal distribution
AICAICAICAICAICAIC3

Explanatory power for weekly temperature forecast◆ The accuracy of the forecasted temperature is about 76% for the day-ahead forecast
but drops to about 18% for the 7-day-ahead forecast

measured temperature

Explanatory power for weekly temperature forecasts (by forecast horizon; Tokyo, 2019)

forecasted temperature

Source: The Japan Meteorological Agency
Note: For both axes, seasonality isexcluded by using the value of deviationfrom the normal value4

Explanatory power for weekly temperature forecast◆ Plotted the R2 extracted from the scatter plot on the previous page◆ As the forecast horizon becomes longer, the forecast accuracy decreases linearly➢ The weather forecast (temperature forecast) that exceeds 7 days hardly hits
Explanatory power for weekly temperature forecasts (Tokyo, 2019)5

Model comparison (i): Direct forecast vs. two-step forecast◆ Weather “forecasts” are often used directly in electricity price forecasting: ① Direct forecast➢ However, the correlation between the weather “forecast” and the spot price is small◆ Therefore, we combined the following two models:②-a➢ a model that forecasts the temperature density from the forecasted temperature➢ a model that forecasts the electricity price from the measured temperature ②-b
Conceptual diagram of two-step forecast

Forecasted
temperature① Direct forecast
Correlation is weak, andseasonality is challenging
to extract= Difficult to build
robust models②-a② Two-step forecast

Measuredtemperature②-bElectricity spot
price

② Two-step forecast
Expected to have arelatively strong correlation= Robust models canbe built
6Model comparison (ii): Original series vs. Logarithmic series◆ “Logarithmic series" model is constructed in addition to the "original series" (∵𝑆𝑡 > 0)
◆ For the average spot price 𝑆𝑡 of 𝑡th week, the following two types of OLS are constructed
Original series model:

𝑆𝑡Logarithmic series model:= 𝛼𝑆𝑡−1+ 𝛽 𝑡 𝐺𝑡

+ 𝑓 𝑡 + 𝑔 𝑡 𝜖𝑡 + 𝜂 𝑡log 𝑆𝑡 = 𝛼log 𝑆𝑡−1 + 𝛽 𝑡 log 𝐺𝑡 + 𝑓 𝑡 + 𝑔 𝑡 𝜖𝑡 + 𝜂 𝑡

Outline of symbols in formulas and data to be used
Symbols

Description

Data source

𝑆𝑡Electricity spot priceJapan Electric Power Exchange (JEPX)𝐺𝑡

LNG spot price

Platts JKM spot price𝛽, 𝑓, 𝑔Seasonal trend (Fourier seriesexpansion) and annual change trend-𝜖𝑡Temperature deviation from the normalvalue (𝜖𝑡 ≔ 𝑇𝑒𝑚𝑝𝑡 − 𝑇𝑒𝑚𝑝_𝑛𝑜𝑟𝑚𝑡 )The Japan Meteorological Agency

𝜂𝑡Residual term with average of 07

Model comparison (iii): Quantile Regression vs. GARCH◆ For density forecast, we compare two models, Quantile Regression (QR) and GARCH◆ We use the same form of model formulas as defined on the previous page:
Original series model:
Logarithmic series model:

𝑆𝑡= 𝛼𝑆𝑡−1+ 𝛽 𝑡 𝐺𝑡+ 𝑓 𝑡 + 𝑔 𝑡 𝜖𝑡 + 𝜂 𝑡log 𝑆𝑡 = 𝛼log 𝑆𝑡−1 + 𝛽 𝑡 log 𝐺𝑡 + 𝑓 𝑡 + 𝑔 𝑡 𝜖𝑡 + 𝜂 𝑡◆ In Quantile Regression, the quantile of the price density is calculated directly➢ In this study, 5th percentile interval (the quantiles at {5,10,15,…, 95}) are calculated◆ In GARCH, volatility (standard deviation) is estimated from past time series data

➢ In this study, we obtain the standard deviation of the residuals one period ahead byapplying GARCH (1, 1) to the residual term 𝜂 𝑡 obtained from the OLS

8Bias correction in forecasts using logarithmic series◆ In log-price OLSs, it is not appropriate to use the predictor parts of the model by just𝜖𝑡 ), as the desired forecast values
converting them to the original price (𝑒 𝛾 𝑡 +𝑔 𝑡 ෞ◆ Such forecast method includes a downward bias due to not considering the variancesof the random variables; therefore, we consider “bias correction” as follows:
𝑙𝑜𝑔 𝑆𝑡 = 𝛾 𝑡 + 𝑔 𝑡 𝜖𝑡 + 𝜂𝑡
𝛾 𝑡 ≔ 𝛼𝑙𝑜𝑔 𝑆𝑡−1 + 𝛽 𝑡 𝑙𝑜𝑔 𝐺𝑡 + 𝑓 𝑡𝜖𝑡
𝑆መ𝑡ȁ𝑡−1 ≠ 𝑒 𝛾 𝑡 +𝑔 𝑡 ෞ𝑆መ𝑡ȁ𝑡−1 = E 𝑆𝑡 หℱ𝑡−1= E 𝑒 𝛾 𝑡 +𝑔 𝑡 𝜖𝑡+𝜂𝑡 หℱ𝑡−1

assuming that the random variables
𝜖𝑡 and 𝜂 𝑡 follow normal distributions
independent of each other◆ The appropriate forecast price is 𝒆
without bias correction= 𝑒 𝛾 𝑡 E 𝑒 𝑔 𝑡 𝜖𝑡 หℱ𝑡−1 E 𝑒 𝜂𝑡 หℱ𝑡−1=𝑒𝒈 𝒕 𝝈𝝐,𝒕𝟐

𝛾 𝑡 +𝑔 𝑡 ෞ𝜖𝑡 + 𝑔 𝑡 𝜎𝜖,𝑡+ 𝝈𝜼,𝒕𝟐

ൗ𝟐2+ 𝜎𝜂,𝑡2

ൗ2times larger than the forecast◆ The forecasted values of 𝜎𝜖,𝑡 and 𝜎𝜂,𝑡 are obtained by applying the GARCH (1,1) model9

Empirical analysis – Used data
Used data and sources⚫ Spot price 𝑺𝒕 and forward price 𝑭𝒕 [JPY/kWh]: JEPX system, Tokyo/Kansai area price⚫ LNG spot price 𝑮𝒕 [JPY/MMBtu]: Platts JKM spot price⚫ Measured temperature 𝑻𝒆𝒎𝒑𝒕 [℃]: Maximum temperature measured by the JMA*
෣ 𝒕 [℃]: Maximum temperature forecasted by the JMA*
⚫ Forecasted temperature 𝑻𝒆𝒎𝒑
*the Japan Meteorological Agency

In sample period⚫ the past three years

in a “weekly rolling” manner

Out-of-sample period⚫ April 1st, 2016 - March 31st, 2020 (4 years)
10Estimated temperature sensitivity◆ Temperature sensitivity of the spot price is negative in winter and positive in summer◆ The absolute value of sensitivity is larger on the daytime load than on the base load
◆ The sensitivities’ amplitudes have increased significantly year by year

➢ Probably due to the recent expansion of renewable energies (especially PV in Japan)
Time-series transition of estimated temperature sensitivity

11

Estimated 𝑔 𝑡 𝜎𝜖,𝑡2and 𝜎𝜂,𝑡2for bias correction◆ Both variances have expanded over time due to the increasing competitiveness since thefull liberalization of the market in 2016, in addition to the expansion of renewable energies

12Verification of bias correction effect◆ In the “forecast w/o bias correction,” when the predictor of the logarithmic series OLS
was used as it was, the forecast errors were negative in all six cases (downward biases)◆ In the “forecast w/ bias correction,” the forecast values were revised upward, and theforecast errors approached 0 as a whole
Average forecast error with and without bias correction13Forecast error verification: mean value forecast◆ For verifying the forecast error of the mean value forecast, (i) direct forecast vs. two-stepforecast and (ii) logarithmic series vs. original series are compared◆ As a result, the two-step forecast is generally more accurate than the direct forecast,and the logarithmic series model is more accurate than the original series model
Comparison of prediction error (mean absolute value error: MAE)

14

Forecast error verification: density forecast◆ For density forecast, (ii) log series vs. original series and (iii) QR vs. GARCH are compared◆ As a result, in general, the log series model is more accurate than the original seriesmodel, and the QR is more accurate than the GARCH
Comparison of density forecast accuracy (Pinball Loss: PL)* "OLS + G" means OLS and GARCH.
The price density is forecasted by
combining these models.
15

Effect of improving forecast accuracy by weather forecast◆ When the weather forecast is incorporated, the prediction error is reduced mainly inthe summer compared to when the weather forecast is not incorporated
Monthly density forecast error (PL) comparison

16

Application to arbitrage strategy in the forward market◆ Compare two arbitrage strategies: trading based on OLS forecasts and QR forecasts◆ The QR forecasting strategy incorporates quantile forecasts into trading decisions,allowing traders to trade according to their risk tolerance
Strategy using QR forecast

Strategy using OLS forecast
Density

𝑆𝑡 : spot price density(e.g. 10 percentile strategy)

Density

𝐹𝑡 : forward price(observed)

PricePrice

Case ①: long forward

Case ②: short forward

𝑆መ𝑡
Expected value (average value) is forecastedCase ①:long forward

10%
𝑆መ𝑡

Case ②:
do nothing

90%
𝑆መ𝑡

Case ③:
short forwardQuantiles are forecasted

17

Profit and loss risk brought about by arbitrage◆ Risk of loss: lower with quantile prediction (QR) strategy than with OLS◆ Profit: Higher with OLS➔ Trade-off between risk reduction and return capture◆ In the JEPX forward market, there is an arbitrage opportunity of about 10% of the priceProfit and loss risk brought about by arbitrage (by bidding strategy / 3 areas / 2 loads)

18

Arbitrage profit with and without weather forecast◆ Compared arbitrage profits by QR/OLS strategy with and without weather forecasting◆ Arbitrage profit increased by 1.5 to 3.3 times with the use of weekly weather forecasts
Arbitrage profit with and without weather forecast (by bidding strategy / 3 areas / 2 loads)

w/ Weather forecast
w/o Weather forecast

19Summary◆ This study proposed “forecasting methods for the weekly average JEPX spot price”
and “arbitrage trading strategies in the JEPX forward market”◆ We constructed several models and verified the forecast accuracy of the weekly
average spot price and found the following results:➢ Two-step models using actual temperatures as a mediator have higher
forecast accuracy than models that use forecasted temperatures directly➢ Log-series models have higher forecast accuracy than price-series models➢ QR, which can model any distribution shape, has higher forecast accuracy
than GARCH, which assumes a normal distribution◆ The use of weekly weather forecasts contributes significantly to both "improving
forecast accuracy" and "earning profits from forward contracts."◆ The value of weather information can be increased through modeling ingenuity, yielding
gains of 1.5 to 3.3 times in the case of JEPX forward arbitrage20