This document discusses using singular spectrum analysis (SSA) to model electricity prices. SSA decomposes time series data into trend, periodic, and noise components. The author applies SSA to French electricity prices, trading volumes, and consumption data. SSA shows the price trends are better correlated with consumption data than with trading volumes. The author proposes a model where the short-range price components are a function of short-range consumption components and noise, providing a physically-based way to link prices and consumption for scenario testing and analysis.

1. CERNA, Centre d’économie industrielle Ecole Nationale Supérieure des Mines de Paris - 60, bld St Michel - 75272 Paris cedex 06 - France Téléphone : (33) 01 40 51 91 26 - E-mail : Nicolas.Rouveyrollis@ensmp.fr,Alain.Galli@ensmp.fr Using Singular Spectrum Analysis to Model Electricity Prices Nicolas Rouveyrollis & Alain Galli Presented at ETE Workshop Leuven, 15-16 Sept 2005

3. Modelling Electricity Prices First Step: Split prices into two components. a) Part with physical meaning b) Stochastic noise Ex. Lucia & Schwartz (2000) like a classical signal/noise decomposition.

5. Component <=> % total information Singular Spectrum Analysis Works directly in the time domain Ref: Broomhead & King (1986) addition SSA

6. Part 1 X=Trajectory Matrix SSA - Description of the Method X(t 1 ), X(t 2 ), …, X(t i+1 ), X(t i+2 ),,…, X(t i+M+1 ),…, X(t N ), M

7. Part 1 X=Trajectory Matrix Univariate SSA - Description of the Method As in PC compute eigenvalues and eigenvectors of C But different because the trajectory matrix X explicitly includes temporal correlations

10. Powernext Base Load Log of Baseload

11. Daily Volumes for Powernext

12. Daily French Consumption From RTE –web site

13. SSA on Powernext (prices & volumes) and French consumption First 10 eigenvalues

14. SSA on Powernext (prices & volumes) and French consumption Components Components Volume Consumption Ln(Spot) Components % Var % Var % Var Trend cp1,cp2 56.68 cp1,cp2 60.01 cp3 6.89 Weekly periodicity ? ? cp3-cp10 24.95 cp1,cp2, cp4-cp10 42.16 Residual cp3-cp200 43.32 cp11-cp200 15.04 Cp11-cp200 50.94

15. SSA Illustration

16. SSA Illustrations Residual Ln(Spot)

17. SSA Illustrations Residual Consumption

18. SSA Illustrations Residual Volume

21. Volume =D - 1 Barlow’s Approach Physical Limit Sell (Volume) ) g ( Volume

23. Log Prices Volume The random component for prices is not explained by Powernext volumes Drawback of Barlow’s Approach to the French market

24. The random component for prices is better explained by consumption data Alternative Approach to the French market

26. Focusing on the short range components for Comsumption & Log prices 01-03-2002 to 31-03-2004 Strong correlation

27. Real Estimate An alternative model Short range component of logprices =f(short range component of consumption,Noise ) 28-11-2001 to 31-03-2004 Promising Approach

30. Any questions?