1

Short-term forecasting of electricity spot prices and heat

demand

Michael Obersteiner, Michael Obersteiner,

Institute for Advance StudiesInstitute for Advance Studies

AustriaAustria

2

People

•• J.J. HlouskovaHlouskova•• S.S. KossmeierKossmeier•• A.A. SchnablSchnabl•• Z.Z. ChladnaChladna•• R. AltR. Alt•• M.M. JeckleJeckle•• J.J. Crespo CuaremaCrespo Cuarema

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3

Overview

•• Electricity sport price modelElectricity sport price model•• Heat demand modelHeat demand model•• Real Option model for unit commitmentReal Option model for unit commitment

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Importance of forecast in the market•• Good forecasts & simple DM ruleGood forecasts & simple DM rule•• Bad forecast & Ferrari DM ruleBad forecast & Ferrari DM rule

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5

Features of electricity spot pricesbehavior

•• Mean reversionMean reversion•• Time of day effectTime of day effect•• Weekend/weekday effectWeekend/weekday effect•• Seasonal effectsSeasonal effects•• Time varying volatility and volatility Time varying volatility and volatility

clusteringclustering•• Extreme valuesExtreme values

SourceSource: : IHS, 2003.IHS, 2003.

6

Average hourly LPX electricity spot prices

0

5

1 0

1 5

2 0

2 5

3 0

3 5

4 0

4 5

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4

H o u r

Euro

/MW

h

W e e k d a yW e e k e n d

4

7

Descriptive statistics for LPX electr. spot prices, June 16, 2000 - October 15, 2001

Hour Mean St. Dev. Skewness Kurtosis1 15.01 4.04 0.077 2.9602 13.25 4.03 -0.038 2.5743 12.29 4.04 -0.004 2.6504 11.88 4.08 0.010 2.5705 12.18 4.23 -0.147 2.6206 13.19 4.38 -0.434 2.7857 15.62 5.43 -0.601 2.6948 20.43 8.11 -0.028 2.7349 23.52 8.89 0.348 3.50010 25.75 9.26 0.861 5.35911 28.30 10.01 1.105 5.62312 34.87 16.59 2.758 19.95013 28.34 10.07 3.526 36.81514 25.84 9.14 1.201 8.46415 23.31 8.19 0.783 4.68716 21.44 7.08 0.567 4.43517 20.37 6.51 0.603 4.24718 21.52 9.54 6.412 88.92019 22.25 7.69 1.329 6.31120 22.04 7.03 1.683 12.33321 20.90 5.53 1.360 9.29022 19.60 4.25 1.340 13.20023 19.29 3.65 0.641 7.14024 16.86 4.05 -0.135 3.388

Whole sample 20.33 9.50 2.370 23.500

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Mean and variance of jumps and jump probabilities for specific hours

Hour mean variance jump prob.1 7.19 172.69 0.0082 no jumps3 no jumps4 no jumps5 no jumps6 no jumps7 no jumps8 no jumps9 29.60 19.72 0.010

10 36.88 119.85 0.00811 39.74 54.90 0.01212 75.85 1258.28 0.01413 68.45 2128.27 0.00614 41.72 495.72 0.00615 29.04 40.44 0.01416 28.79 13.19 0.00817 23.79 7.45 0.01018 82.87 5859.03 0.00419 31.50 77.43 0.01020 29.03 200.77 0.01221 25.52 65.78 0.01022 17.92 75.60 0.01223 19.17 67.63 0.00424 7.93 182.66 0.008

Whole sample 36.41 17.30 0.018

5

9

LPX price from 1:00, Oct. 9, 2001 - 24:00, Oct. 15, 2001 (1st out-of-sample period)

0

5

1 0

1 5

2 0

2 5

3 0

3 5

4 0

4 5

5 0

1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103

109

115

121

127

133

139

145

151

157

163

H o u rs

LPX

Pric

e (E

uro/

MW

h)

10

LPX price from 1:00, Aug. 27, 2001 - 24:00, Sep. 2, 2001 (2nd out-of-sample period)

0

2 0

4 0

6 0

8 0

1 0 0

1 2 0

1 4 0

1 6 0

1 8 0

2 0 0

1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103

109

115

121

127

133

139

145

151

157

163

H o u r s

LPX

Pric

e (E

uro/

MW

h)

6

11

Model 1: Mean reverting process

( )

( )

∫−

−

−−

−

=

=−=

++=

↓

=+−=

t

t

tst

ttt

sdWe

ee

pp

pptdWdttptdp

1

)(

10

110

0

)(

,1

version timediscreteexact

)0(),()()(

ση

βµα

ηβα

σµκ

κ

κκ

12

Model 2: Mean reverting process with time-varying mean

( )

( ]( ) ( )

( ) [ ]

∑

∑ ∑

∑

∑ ∑

++

++=

++=

↓

+∈+

+∈+−∈=

=+−=

=

−

=

monthttrendmonthtmonth

i daydaytdayitit

tttt

monthtrendmonth

i daydayti

trendd

ddh

pp

tcmonthtc

daytciilct

pptdWdttpttdp

αα

ααα

ηβα

µ

σµκ

,

24

1,,

11

24

1

0

version timediscreteexact

1

1,11)(

,)0(),()()()(

7

13

Model 3: ARMA model with time-varying intercept

∑∑ ∑

∑ ∑

+++=

++=

+=

=

= =−−

monthttrendmonthtmonth

i daydaytdayitit

t

p

i

q

iitititit

ttt

trenddddh

N

p

ααααα

σε

εθεηρη

ηα

,

24

1,,

21 1

),0(~

ARMA models – traditional time series approach to modeling electricity prices

14

One week ahead forecasts for the 1st osp for M3 when modeling each hour separately

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106

113

120

127

134

141

148

155

162

H o u r s

Euro

/MW

h

L P X P r ic eF o r e c a s t sF o r e c a s t s + f s eF o r e c a s t s - f s e

8

15

One week ahead forecasts for the 2nd osp for M3 when modeling each hour separately

0

2 0

4 0

6 0

8 0

1 0 0

1 2 0

1 4 0

1 6 0

1 8 0

2 0 0

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106

113

120

127

134

141

148

155

162

H o u r s

Euro

/MW

h L P X P r ic eF o re c a s t sF o re c a s t s + f s eF o re c a s t s - f s e

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Model 4: E-Garch model

( ) ( )

0effect leverage inverse),0(~

loglog

2

1

1

1

121

2

>→

+++=−

−

−

−−

γσε

σεγ

σετσδωσ

tt

t

t

t

ttt

N

• volatility clustering• positive price shocks increase volatility more than

negative shocks of the same magnitude –inverse leverage effect

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Jump-diffusion process

( )

jttt

jjtt

tt

jj

pp

pN

pNtqtW

Ntq

tdqtdWdttpttdp

µλβα

λσσµβα

λσβα

σµλ

σµκ

η

η

++=

↓

+++

−+

Φ

−Φ−

Φ++−=

−

−

−

11

2211t

211t

2

ˆˆas dconstructe are model jump""for forecasts The

prob. with),(~p

1 prob. with),(~ptindependenmutually are and)(),( :Assumption

size jump the),(~intensity withprocess Poisson)(

)()()()()(

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Summary of the models

For For ii=1,2,3,4:=1,2,3,4:•• MMii.1 .1 –– model model ii with no jumpswith no jumps•• MMii.2 .2 –– model model ii with jumpswith jumps•• MMii..jjaa –– model model ii with or without a jump deals with the with or without a jump deals with the

whole sample (hourly frequency)whole sample (hourly frequency)•• MMii..jjbb –– model model ii with or without a jump deals with with or without a jump deals with

each hour separately (24 models based on daily each hour separately (24 models based on daily frequency)frequency)

•• M4 M4 –– EE--GarchGarch model (deals only with the whole model (deals only with the whole sample)sample)

↓↓Comparing the forecasting abilities of 14 modelsComparing the forecasting abilities of 14 models

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Forecast error statistics

( )

hours) (168 week one 1h :horizonForecast

ˆ1

1:(MAE) Error Absolute Mean

ˆ1

1

:(RMSE) Error Square Root Mean

2

=+

−+

−+

∑

∑

+

=

+

=

hS

Sttt

hS

Sttt

pph

pph

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Forecast performance tested on the 1st ospM odel 168 169 170 171

R M SEM 1.1a 7 .625 7.637 7.653 7.685M 1.2a 7 .637 7.642 7.656 7.696M 1.1b 4 .638 4.854 4.879 4.931M 1.2b 4 .604 4.840 4.868 4.924M 2.1a 4 .261 4.273 4.292 4.324M 2.2a 4 .381 4.395 4.419 4.464M 2.1b 3 .876 4.114 4.407 4.608M 2.2b 3 .893 4.081 4.204 4.232M 3.1a 3 .796 3.803 3.812 3.822M 3.2a 4 .585 4.588 4.614 4.659M 3.1b 3.325 3.554 3.739 3.808M 3.2b 3 .375 3.732 3.901 3.940M 4.1a 5 .788 - - -M 4.2a 5 .577 - - -

M AEM 1.1a 6 .162 6.183 6.205 6.242M 1.2a 6 .192 6.203 6.221 6.261M 1.1b 3 .362 3.578 3.624 3.672M 1.2b 3 .321 3.566 3.608 3.658M 2.1a 3 .285 3.299 3.319 3.353M 2.2a 3 .440 3.456 3.482 3.529M 2.1b 2 .966 3.121 3.434 3.666M 2.2b 2 .779 2.868 2.972 2.984M 3.1a 2 .953 2.962 2.976 2.987M 3.2a 3 .656 3.660 3.693 3.743M 3.1b 2.383 2.510 2.637 2.674M 3.2b 2 .415 2.573 2.711 2.731M 4.1a 4 .487 - - -M 4.2a 3 .938 - - -

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21

Forecast performance tested on the 2nd ospM odel 168 169 170 171

RM SEM 1.1a 20.803 20.797 20.797 20.796M 1.2a 20.705 20.686 20.679 20.677M 1.1b 18.718 18.531 18.458 18.411M 1.2b 18.614 18.419 18.345 18.300M 2.1a 17.777 17.777 17.777 17.782M 2.2a 17.916 17.916 17.915 17.920M 2.1b 15.886 15.838 15.796 15.780M 2.2b 16.232 16.199 16.219 16.249M 3.1a 16.836 16.834 16.833 16.836M 3.2a 18.454 18.450 18.442 18.449M 3.1b 15.012 14.943 14.930 14.927M 3.2b 15.744 15.675 15.655 15.659M 4.1a 18.775 - - -M 4.2a 19.190 - - -

M AEM 1.1a 9.322 9.334 9.353 9.353M 1.2a 9.303 9.301 9.313 9.310M 1.1b 8.274 7.939 7.907 7.830M 1.2b 8.237 7.891 7.857 7.780M 2.1a 6.770 6.768 6.765 6.776M 2.2a 6.711 6.714 6.718 6.720M 2.1b 5.308 5.139 5.052 5.037M 2.2b 5.777 5.755 5.918 6.041M 3.1a 6.750 6.744 6.741 6.752M 3.2a 7.681 7.672 7.666 7.678M 3.1b 5.194 5.166 5.364 5.491M 3.2b 5.316 5.252 5.378 5.478M 4.1a 8.257 - - -M 4.2a 8.215 - - -

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Heat demand features

•• Time of day effectTime of day effect•• Weekend/weekday effectWeekend/weekday effect•• Seasonal effectsSeasonal effects•• Time varying volatilityTime varying volatility

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23

Heat demand vs. outside temperature

-15

-10

-5

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300 350 400 450

24

Average hourly heat demand

150

160

170

180

190

200

210

220

230

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour

MW

Weekday Weekend

13

25

Descriptive statistics for heat demand, October 10, 2000 - April 30, 2001

Hour Mean St. Dev. Skewness Kurtosis1 158.12 55.90 0.19 2.552 157.38 58.00 0.21 2.483 158.25 60.23 0.28 2.584 164.10 62.88 0.19 2.495 177.64 69.14 0.09 2.426 204.21 76.35 -0.01 2.447 214.51 76.25 -0.02 2.558 216.96 75.51 0.04 2.689 211.28 72.69 0.16 2.89

10 202.55 71.14 0.23 2.6911 193.32 69.62 0.27 2.6212 185.08 67.51 0.31 2.7313 179.46 66.92 0.27 2.5314 175.60 67.62 0.32 2.6415 174.93 68.95 0.33 2.5216 175.57 69.47 0.28 2.5417 177.71 70.17 0.22 2.5018 183.24 71.60 0.17 2.4619 186.73 70.49 0.10 2.4420 189.16 68.98 0.09 2.4921 189.93 66.70 0.03 2.5122 183.11 61.70 0.09 2.6123 168.26 55.91 0.14 2.6024 158.04 53.44 0.25 2.62

Whole sample 182.71 69.35 0.27 2.68

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Descriptive statistics for the first differences of heat demand, Oct. 10, 2000 – Apr. 30, 2001

Hour Mean St. Dev. Skewness Kurtosis1 0.20 30.91 0.01 3.192 0.17 32.49 0.01 3.573 0.21 32.80 -0.20 3.594 0.21 33.60 -0.09 3.805 0.25 39.50 0.59 6.886 0.33 42.55 0.45 4.217 0.39 45.19 0.29 3.648 0.34 44.39 0.21 3.469 0.30 41.33 0.07 3.27

10 0.25 41.46 0.21 4.4511 0.19 40.64 0.48 5.6912 0.10 36.33 -0.08 3.5913 0.02 37.60 0.18 4.0514 0.01 38.45 0.14 4.1715 0.02 38.66 0.30 4.2116 0.01 36.24 0.33 4.4917 0.00 33.58 0.31 4.1018 0.01 33.92 0.20 3.8419 0.01 33.59 0.34 3.7920 0.01 31.86 0.24 4.0821 0.03 29.83 0.17 3.7622 0.03 29.71 -0.07 4.1023 0.03 27.86 -0.13 3.6424 0.05 27.27 -0.05 3.18

Whole sample 0.00 15.48 -0.13 12.14

14

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Summary of the modelsD escrip tion o f th e m od el Ab brev ia tio n

G lo ba l m o delsno tem peratu re

A R M A on H D M 1A R M A on log H D M 2S A R M A on H D M 3

w ith tem peratu reA R M A X on H D M 4A R M A X on log H D M 5S A R M A X on H D M 6S A R IM A X on H D M 7non-linea r S A R IM A X on H Dw ith s truc tura l tem pera tu re o f lag 0 M 8non-linea r S A R IM A X on H Dw ith s truc tura l tem pera tu re o f lags 0 and 1 M 9S A R IM A X on log H D M 10non-linea r S A R IM A X on log H Dw ith s truc tura l tem pera tu re o f lag 0 M 11non-linea r S A R IM A X on log H Dw ith s truc tura l tem pera tu re o f lags 0 and 1 M 12

S eparab le m o delsno tem peratu re

A R M A on H D M 13A R M A on log H D M 14A R IM A on H D M 15A R IM A on log H D M 16tim e varying coe ffic ien t m ode l on H D M 17

w ith tem peratu reA R M A X on H D M 18A R M A X on log H D M 19A R IM A X on H D M 20A R IM A X on log H D M 21non-linea r A R IM A X on H Dw ith s truc tura l tem pera tu re o f lag 0 M 22non-linea r A R M A X on H Dw ith s truc tura l tem pera tu re o f lag 0 M 23tim e varying coe ffic ien t m ode l on H D M 24

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Forecast performance tested on 10-23 April 2001

Model Forecast horizon: 3 days Forecast horizon: 7 daysRMSE - average MAE - average RMSE - last MAE - last RMSE - average MAE - average RMSE - last MAE - last

M1 33.40 28.44 21.16 17.45 44.69 39.40 26.81 22.70M2 33.28 28.32 20.51 16.34 46.27 41.32 25.66 21.27M3 27.26 22.58 26.92 20.31 32.19 26.47 29.44 23.27M4 17.06 12.64 11.14 8.29 19.02 13.81 16.37 10.65M5 19.32 14.87 13.16 10.05 21.32 15.99 16.64 11.40M6 16.98 13.03 14.31 11.85 19.20 14.74 17.30 13.03M7 15.17 11.31 13.02 11.17 16.20 12.04 13.51 8.86M8 14.31 10.51 11.00 8.74 16.29 12.44 13.45 8.87M9 14.28 10.47 11.00 8.76 16.04 12.12 13.65 9.09M10 16.68 12.51 10.80 8.79 18.90 14.28 14.72 9.26M11 15.81 11.77 11.24 9.05 17.87 13.54 14.51 9.44M12 15.68 11.63 11.25 9.07 17.44 13.04 14.50 9.39M13 30.30 24.88 22.39 18.82 34.09 28.44 20.12 16.26M14 29.68 24.25 25.30 20.42 33.04 26.87 20.31 16.11M15 33.50 26.98 39.72 33.19 39.96 29.97 44.57 36.01M16 29.74 24.27 30.72 24.14 33.22 27.08 23.15 18.27M17 29.70 24.40 21.13 16.69 32.70 26.37 21.89 17.29M18 16.10 12.39 14.92 12.88 16.42 12.36 16.70 12.61M19 16.03 12.47 13.50 11.31 16.28 12.35 15.23 11.13M20 16.87 12.94 16.12 13.53 17.59 13.08 16.96 12.35M21 19.30 14.76 15.17 13.12 20.60 15.65 17.19 13.15M22 17.30 13.38 16.13 13.00 18.68 14.18 17.24 12.85M23 16.61 12.52 14.07 11.92 17.64 13.13 15.98 11.91M24 19.05 15.16 14.07 11.96 20.39 16.19 17.48 13.52

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3-days ahead forecasts of heat demand by M9 (21-23 April, 2001)

0

50

100

150

200

250

300

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71

Hour

MW

Heat DemandHeat Demand - ForecastsHD_f + 2*fseHD_f - 2*fse

30

1-week ahead forecasts of heat demand by M9 (17-23 April, 2001)

0

50

100

150

200

250

300

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101

106

111

116

121

126

131

136

141

146

151

156

161

166

Hour

MW

Heat DemandHeat Demand - ForecastsHD_f + 2*fseHD_f - 2*fse

16

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Background

•• OptimizeOptimize Corporate Portfolio according to Corporate Portfolio according to the standard finance toolsthe standard finance tools

•• Unit commitment Unit commitment pathpath--dependent dependent American OptionAmerican Option

•• Fwd Monte Carlo simulation andFwd Monte Carlo simulation and bwdbwddynamic programmingdynamic programming

•• Operational ConstraintsOperational Constraints

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Indifference Loci

0

5

10

15

20

25

30

35

40

45

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48

turn onturn offLPX

17

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Implementation

•• ROM for CHPROM for CHP•• ROM for P & Ancillary ServicesROM for P & Ancillary Services

•• Next on CHP & AS & Carbon priceNext on CHP & AS & Carbon price

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Validation of Real Option Approach•• Computationally intensiveComputationally intensive

•• Linear in complexityLinear in complexity•• Flexible to include new products or Flexible to include new products or

technical constraintstechnical constraints

18

35

Main conclusion

•• Good forecasts are an important assetGood forecasts are an important asset•• Flexibility [buy Flexibility [buy –– sell; multiple outputs] sell; multiple outputs]

increases profits increases profits •• Assess assets and positions like a financial Assess assets and positions like a financial

companycompany