Estimating the Volatility of Electricity Prices: The Case of the
England and Wales Wholesale Electricity Market
Sherzod Tashpulatov
Recent Advances in Changepoint Analysis
Centre for Research in Statistical Methodology
Warwick, 26-28 March 2012
General Introduction
Liberalization of Electricity Industry
Fig. 1: Structure of a Network Industry before and after Liberalization
Core Products
Core Products
Core Products
Core Products
Vertically
Intergrated
Structure
Network Infrastructure
Customer Service
Provision
Customer Service
Provision
Network
Infrastructure
Customer Service
Provision
Customer Service
Provision
(a) Vertically Integrated Case
Customer Service
Provision
Customer Service
Provision
(b) Vertically Separated Case
2
General Introduction
Liberalization of Electricity Industry
Fig. 2: Description of the Electricity Industry in Great Britain
Producers
National Power
PowerGen
.........
AES
EdF
Scottish Power and
Scottish
Nuclear Power
Scottish Hydro-Electric
Network Infrastucture
and Wholesale Market
(both operated by the
National Grid Company
in England and Wales)
Network Infrastructure
Network Infrastructure
ELECTRICITY POOL
Retail Suppliers
Regional Electricity
Companies (12 RECs)
Other Licensed Suppliers
Customers
Small Customers
“Franchise Market”
Large Customers
“Competitive Market”
England & Wales
(Scotland)
Scottish Power and
Scottish Hydro-Electric
Small Customers
“Franchise Market”
Large Customers
“Competitive Market”
Exporters
3
Other Licensed
Suppliers
General Introduction
Liberalization of Electricity Industry
• The Key Question to Analyze Liberalization
1. hi
• Do liberalized markets drive price volatility?
• Case Study
1. hi
• Wholesale electricity market in England and Wales
4
General Introduction
Liberalization of Electricity Industry
• Motivation
Fig. 3: Daily Electricity Prices (April 1, 1990 – March 26, 2001)
70
1600
Daily SMP
1200
50
Frequency
Daily Electricity Prices (£/MWh)
Mean
Min
Max
Std. Dev.
Obs.
1400
60
40
30
£/MWh
20.97
7.23
65.61
5.79
4013
1000
800
600
20
400
10
0
0
200
0
0
500 1000 1500 2000 2500 3000 3500 4000 4500
10
20
30
40
50
Daily Electricity Prices (£/MWh)
Trading Days
5
60
70
General Introduction
Liberalization of Electricity Industry
Institutional Changes and Regulatory Reforms
Creation of
Wholesale
Electricity
Market
End of Coal
Contracts
Regime 1
April 1, 1990
Start of
Price-Cap
Regulation
Regime 2
End of
Price-Cap
Regulation
Pre-Regime 4
Regime 3
April 1, 1993 April 1, 1994
April 1, 1996
Divestment 1
Pre-Regime 4
Divestment 2
Regime 4
July 1996
6
Restructure of
Wholesale
Electricity
Market
Regime 5
July 1999
March 26, 2001
.
Estimating the Volatility of Electricity Prices: The Case of the
England and Wales Wholesale Electricity Market
7
Paper
Estimating the Volatility of Electricity Prices
• Motivation
Policy Importance
• Price fluctuations:
– uncertainty about revenues and costs
– higher electricity prices for consumers
Research Question
• How did the institutional changes and regulatory reforms affect the dynamics of
electricity prices during the liberalization process?
Research Approach
• stationarity and seasonality
• AR-ARCH model with a smoothly time-varying intercept term
8
Paper
Estimating the Volatility of Electricity Prices
• Literature Review
1. hi
• Crespo et al. (2004)
Hourly prices from the Leipzig Power Exchange (Jun. 16, 2000 - Oct. 15, 2001)
AR, ARMA models: separate studies of each hour yielded better forecasts
• Guthrie and Videbeck (2007)
30-min prices from the New Zealand Electricity Market (Nov. 1, 1996 – Apr. 30,
2005)
Half-hourly trading periods naturally fall into 5 groups, which can be studied
separately using a periodic AR model
• Huisman et al. (2007)
The Amsterdam Power Exchange (APX), the European Energy Exchange (EEX;
Germany), and the Paris Power Exchange (PPX) for the year 2004
Hourly electricity prices are treated as a panel in which hours represent
cross-sectional units and days represent the time dimension. SUR is applied
9
Paper
Estimating the Volatility of Electricity Prices
• Literature Review (cont.)
1. hi
• Conejo et al. (2005)
PJM interconnection data for the year 2002
Dynamic modeling is preferred to seasonal differencing
• Garcia et al. (2005)
Spanish and California electricity markets (Sept. 1, 1999 - Nov. 30, 2000; Jan. 1,
2000 - Dec. 31, 2000)
GARCH model outperforms a general ARIMA model when volatility and price spikes
are present
• Bosco et al. (2007)
Daily prices from the Italian wholesale electricity market
Periodic AR-GARCH methodology
10
Paper
Estimating the Volatility of Electricity Prices
• Seasonality: Time Domain Analysis
1
1
0.8
0.8
0.6
0.6
0.4
0.4
PACF
ACF
Fig. 4: Correlogram for Daily Electricity Prices
0.2
0.2
0
0
-0.2
-0.2
-0.4
0
200
400
Lag
600
800
-0.4
0
1000
11
200
400
Lag
600
800
1000
Paper
Estimating the Volatility of Electricity Prices
• Seasonality: Frequency Domain Analysis
Fig. 5: Periodogram for Daily Electricity Prices
6000
5000
|F (i ωk )|
4000
3000
2000
1000
0
0
2π/7
ωk
12
4π/7
6π/7
Paper
Estimating the Volatility of Electricity Prices
• Regression Model
pricet
ht
=
=
a0 +
α0 +
P
X
i=1
p
X
i=1
νt
=
εt
√
ht
ai pricet−i + zt0 · γ + εt
(1)
αi ε2t−i + zt0 · δ
(2)
∼ GED,
(3)
where zt is a vector of additional explanatory variables including the sine/cosine
periodic functions and regime dummy variables.
• Methodological findings:
1. • The sine/cosine periodic functions allow better modeling weekly seasonality
• + and − shocks from the previous week are found to asymmetrically affect
volatility
13
Paper
Estimating the Volatility of Electricity Prices
• Diagnostics of standardized residuals
100%
100%
90%
90%
80%
80%
70%
70%
60%
60%
p-value
p-value
Fig. 6: Ljung-Box Q-Test for Standardized Residuals ν̂t and νˆt2
50%
50%
40%
40%
30%
30%
20%
20%
10%
10%
0%
0
25
50
75
100
125
150
175
0%
200
Lag
0
25
50
75
100
Lag
14
125
150
175
200
Paper
Estimating the Volatility of Electricity Prices
• Distribution of standardized residuals
Fig. 7: Standard Normal Distribution and Distribution of Standardized Residuals ν̂t
0.6
0.5
β = 2; N (0, 1)
β = 1.273
Density
0.4
0.3
0.2
0.1
0
-3
-2
0
-1
15
1
2
3
Paper
Estimating the Volatility of Electricity Prices
• Results
140%
700%
120%
600%
Intercept Term (% change)
Intercept Term (% change)
Fig. 8: Impact of the Institutional Changes and Regulatory Reforms on Price and
Volatility Dynamics
100%
80%
60%
40%
20%
500%
400%
300%
200%
100%
0%
Regime 1 Regime 2 Regime 3 Pre-Reg 4 Regime 4 Regime 5
0%
Regime 1 Regime 2 Regime 3 Pre-Reg 4 Regime 4 Regime 5
(a) Mean Equation
(b) Conditional Volatility Equation
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Paper
Estimating the Volatility of Electricity Prices
• Contributions and conclusion
• Methodological contribution
1. • Application of the sine and cosine periodic functions allow better modeling
weekly seasonality
• + and − shocks from the previous week are found to asymmetrically affect
volatility
• Policy contribution
1. • The price-cap regulation and first series of divestments are found to result in
opposite directions for the movement in the price level and volatility
• During the last regime period it was possible to simultaneously decrease prices
and volatility
17
h
Thank You
Paper
Estimating the Volatility of Electricity Prices
• Seasonality: Frequency Domain Analysis
The Fourier transform of a real-valued function p(t) on the domain [0, T ] is defined as
F (i ω) = F{p(t)} =
ZT
p(t) · e−iωt dt
0
−1
TP
−1
TP
−iωk t |F (i ωk )| ≈ pt · e
pt · (cos ωk t − i sin ωk t) =
=
t=0
t=0
T −1
TP
−1
P
=
pt · cos ωk t − i
pt · sin ωk t =
t=0
t=0
= |(pt , cos ωk t) − i (pt , sin ωk t)| −→ max
ωk
where ωk =
k
N −1
· 2π
and k = 0, 1, 2, . . . , N − 1
19