1. 1 Lecture Plan 1145-1300 Factor models for spot electricity markets (modelling and predicting prices and price distributions). Part I. Building fundamental models for the UK, Nordpool and the EEX spot market using static and dynamic (rolling) regression. Predicting mean prices. The UK, EEX and NP spot electricity markets Linear fundamental regression models for expected electricity spot prices Testing of model specification

2. 2 The UK el-market is getting integrated with the rest of Europe (Interconnect cable Belgium-UK) Planned “Green” Cables Norway-UK 2020

3. 3 The UK Electricity Market –One of the earliest electricity markets formed in 1990 –Combined auction and spot market trading – In April 2005 the British Electricity Trading and Transmission Arrangement (BETTA) was formed and all parts of UK was included in the market –Gas, Coal. Nuclear main input but Renewables (especially wind) are getting a larger share in the future

4. 4 The UK Electricity Market –No location prices –48 half-hour prices (48 periods intra-day) –Spot market trades up to 1 hour prior to delivery both OTC and at the exchange APX/UKPX –Each day, demand forecast and reserve forecast for all the 48 periods for the next day are released by the TSO

5. 5 Data Available (48 time series)

6. 6 The German Electricity Market –The spot market for electricity is operated by EPEX SPOT in Germany, a joint venture owned by German EEX AG and the French Powernext SA –On each day of the year, EPEX SPOT operates day ahead auctions for three market areas: Germany/Austria, France and Switzerland. –In this market, we have observed a significant growth of wind and photovoltaic (PV) installations, supported by feed-in tarifs (FITs). –However, over the last years, aims were shifted from the promotion of renewable energy power plants to an enhanced electricity grid, that is capable of handling the volatile electricity generated from renewables.

7. 7 The German Spot Electricity Market –No location prices –24 half-hour prices (24 periods intra-day) –Auction market where the physical delivery of power takes place on the next day –EPEX SPOT provides also an intraday market for Germany and France. Participants in the market can buy up to 45 minutes before every hour electricity for the specific hour. This market operates 24/7 without exceptions. The electricity for the next day can be traded from 15:00 onwards.

8. 8 Data Available (24 time series)

9. 9 The Nordpool Electricity Market –One of the earliest electricity markets in Europe/World –Nord Pool Spot is one of Europe's leading power market covering Nordic and Baltic countries (+N2 –380 companies from 20 countries trade on the markets –In 2014 the turnover was 501 TWh kWh –Auction market and an intraday market (Elbas) –Hydro, Nuclear, Thermal, and Wind main input

10. 10 The Nordpool Electricity Market –Area prices –24 hourly prices –Each day/week supply and demand data are provided by NVE, Statnett, and Nordpool Spot

11. 11 Data Available (24 time series)

12. 12 Characteristics of spot electricity prices: Price distribution far from normally distributed High positive skewness Fat tails / high kurtosis Large price risk Mean reversion in prices / stationarity Time varying volatility High degree of positive serial correlation and seasonal effects Very different characteristics for different hours of the day Very different characteristics for different market areas

13. 13 Linear fundamental regression models for expected electricity spot prices Intro Simple linear regression Multiple linear regression Test of model specification

14. 14 Regression Analysis – Intro- The general equation that underlies any regression is: Observed data = Predictable component + Unpredictable component In our case we could have; Observed data of the dependent variable being the electricity spot price or log of the electricity spot price The predictable component being an regression equation generated by prices of other energy markets (e.g. coal/gas) as well as supply and demand variables The unpredictable component are residuals from our regression

15. 15 Simple Linear Regression

16. 16 Simple Linear Regression a: Intercept b: Slope Regression Line Y=a+b*X X Y The regression line in the case of an approximate linear relationship between Y and X. The slope b represent the average change in Y when X increases by one unit. The intercept a corresponds to the average value of Y when X equals 0. The error term corresponds to the distance between the regression line and the actual observations ε: Error term

17. 17 Simple Linear Regression

18. 18 Simple Linear Regression Example UK Market P38 Ln(Electricity Spot Price Period 38 t ) = a + b*Ln(Coal Price) t + e t The ln() transform stabilize the data of stationary variables and makes us able to interpret the parameters as sensitivities (e.g. b=0.81 means that 1% increase in the coal price will increase the electricity price by 0.81%)

19. 19 Simple Linear Regression Tools-Dataanalysis

20. 20 Simple Linear Regression The model is able to explain 26.2% of the variation of the p38 el-price 1% increase in the coal price will increase the p38 el price by 0.81% T values above 2.33 Indicate that the parameters are significant at 1% level

21. 21 Simple Linear Regression Example German Market H18 Ln(Electricity Spot Price Period 18 t ) = a + b*Ln(Coal Price) t + e t

22. 22 Simple Linear Regression Example German Market H18 Ln(Electricity Spot Price Period 18 t ) = a + b*Ln(Coal Price) t + e t

23. 23 Simple Linear Regression Example Nordpool Market H18 Ln(Electricity Spot Price Period 18 t ) = a + b*Ln(Coal Price) t + e t

24. 24 Simple Linear Regression Example Nordpool Market H18 Ln(Electricity Spot Price Period 18 t ) = a + b*Ln(Coal Price) t + e t

25. 25 Multiple Linear Regression Let X 1,X 2,….,X k denote k different independent variables whose relationship with a response variable Y is to be investigated A Multiple Linear Regression may be written as: Y=α +β 1 *X 1 + β 2 *X 2 +…..+β k *X k +ε Y: Dependent variable X 1,X 2 +…..+X k : Independent variables ε: Error term that is uncorrelated to all regressors

26. 26 Multiple Regression Analysis Parameters are here found by matrix algebra The parameters are estimated with X (the data matrix of the independent variables) and y (the column of the data for the dependent variable): u is the here the errors (the deviation from the model prediction and the real data)

27. 27 Multiple Linear Regression Example UK P38 Ln(Electricity Spot Price Period 38 t ) = a + b 1 *Ln(coal price) t + b 2 *Ln(gas price) t + b 3 *Ln(co2 price) t + b 4 *Ln(demand forecast) t + b 5 *Ln(reserve margin forecast) t + e t

28. 28 Multiple Linear Regression Tools-Dataanalysis

29. 29 Multiple Linear Regression UK P38 The explanatory power has gone from 26.2% to 70.4% 1% increase in the coal price will now increase the p38 el price 0.55% (not 0.81%) after controlling for the effect of all the other variables (this is a partial or conditional effect versus the direct effect me measured under simple regression)

30. 30 Model Prediction, Real Data, and the Residuals UK P38 Although rather good explanatory power, the spikes are not captured properly with the model! The residuals / errors are not normally distributed independent white noise which we assume in linear regression models

31. 31 Regression Model Specification Tests Test of model assumptions should always be performed: Residuals e t in the regression should be: 1)Normally distributed 2)Not correlated with the explanatory variables / cross correlated. 3)Not correlated over time / serial correlated 4)Have a constant variance 5)In addition, the model should be linear Violation of these assumptions could lead to wrong estimates of T, and F values and hence affect the hypothesis testing and model evaluation. Slides of formal tests 1)-5) with Excel Spreadsheets can be provided by the lecturer if you are interested.

32. 32 Multiple Linear Regression EEX H18 Solar production can be 0 and prices can be 0 or negative in EEX. We therefore do not use log transform of these variables.

33. 33 Multiple Linear Regression EEX H18

34. 34 Multiple Linear Regression NP H18

35. 35 Multiple Linear Regression NP H18

36. 36 Rolling Regression Parameter values/sensitivities might not be stable over time E.g. the impact of wind in Germany has changed due to increased importance in the imput mix Static regression assumes constant parameter values Rolling regression allows for changing values of parameters

37. 37 Rolling Regression Example EEX H18 Estimate 300 days rolling regression That is we move the estimation window forward based on the last 300 days observations We can use the array function LINEST() in Excel for this purpose All the betas do now change according to different data input (some more than others)

38. 38 Rolling Regression Example EEX H18

39. 39 Rolling Regression Example EEX H18

40. 40 Rolling Regression Example UK P38

41. 41 Rolling Regression Example NP H18

42. 42 Fundamental analysis of electricity spot price formation in UK Forthcoming paper Energy Journal 2015

43. 43 Fundamental analysis of the German electricity spot price formation Paper Energy Policy, 73(2014)196–210

44. 44 Fundamental analysis of the NP electricity spot price formation I Forthcoming Journal of Energy and Development 2015

45. 45 Fundamental analysis of the NP electricity spot price formation II Working paper

46. 46 Analysis of time varying sensitivities energy futures prices Forthcoming Opec Energy Review 2015

47. 47 Analysis of time varying sensitivities energy futures prices Forthcoming Opec Energy Review 2015

48. 48 Analysis of time varying sensitivities energy futures prices Opec Energy Review 2010, June, 82-106

49. 49 Analysis of time varying sensitivities energy futures prices Journal of Energy Markets,1,3, Fall2008, 37-68

50. 50 From the data, develop static and dynamic multifactor regression models for UK, Germany, and Nordpool using the other hours./periods (1,2,3,….) Note that certain supply/demand variables are linked to the specific hour/periods while other determinants are not How does the sensitivities change with? Hours Markets Over time Exercises