Analysis of day-ahead electricity data

1. Analysis of day-ahead electricity data Zita Marossy & Márk Szenes (ColBud) MANMADE workshop January 21, 2008

2. Topics • Stylized facts of electricity price data • Modeling variable: price • Autocorrelation structure • Persistence • Price distribution • Seasonality • Time series modeling • Neural network • SETAR

3. Main results • Persistence analysis • Underlying variable: price, not price change • Results: H = 0.7-0.97 (0.8) • Price distribution • Generalized extreme value distribution vs. Lévy distribution • Design of a seasonal filter • Filtering the intra-weekly seasonality • Performance evaluation of an ANN model • Reasonable for short-run forecasts • SETAR model for determining price spikes • Data: EEX, hourly day-ahead prices

4. Autocorrelation structure • Seasonality • Effect of intra-weekly seasonality is strong • AC decays slowly

5. Modeling prices, not price changes • The price process has no unit root, there is no need to differentiate the time series • Electricity can not be stored: ‘return’ has no direct meaning • By differencing we cause spurious patterns in ACF:

6. Persistence analysis • Calculating the Hurst exponent of prices • Without differencing the time series • Hurst exponent – classical usage (with differencing the time series first): • > 0.5 persistent process • High ‘return’ shock followed by high ‘return’ • = 0.5 random walk • ‘Return’ is white noise • < 0.5 antipersistent process (mean reversion) • Hurst exponent – without differencing • > 0.5 persistent process • High price followed by high price = Are high prices persistent? • = 0.5 white noise • < 0.5 antipersistent process

7. Hurst exponent: estimation results

8. Price distribution • Two estimated distributions: • Lévy • Generalized extreme value

9. Comparison • Kolmogorov test: • Test statistic: • Lévy: 0.0141 • GEV: 0.0262 • Mean of absolute differences: • Lévy: 8.07*10-4 • GEV: 7.18*10-4

10. Seasonality • Seasonality: • intradaily • Weekly • Spectral decomposition • Periodogram of prices • Periodogram of ACF • Filtering • Median or average week • Differencing • Moving average technique

11. Need for new seasonal filter • The type of distribution changes

12. Suggested filter • ‘GEV filter’ • Separately estimate a GEV distribution for each hour and day i: F1(i) • Transform the prices: F2-1F1,i(x) F2: lognormal cdf (parameters: entire distribution) • Model the prices of filtered data • Forecast • Transform the forecasts back into GEV

13. Empirical results • Figures: periodogram of • ACF (orig prices) • ACF (filtered data) • Intraweekly filtering • successful

14. Estimated GEV parameters

15. Distributions with high scale param

16. Conclusion • Different hours of week behave differently • There are a few hours with fatter tails • These are more sensitive to price spikes • We can model fat tails and forecasting separately

17. Performance evaluation of an ANN • Short term price forecasting (few hours to days) • ANN: simple but flexible tool • Architecture: standard feedforward type • Layers: 168 – 15 – 1 • Input: historical data • Training set: 42 days • Prediction horizon: from 1 hour to 1 week

18. Performance evaluation of an ANN • Measuring error by MAPE • Testing against naive method • Averaged over 50 runs: 50 consecutive weeks from Nov. 2005 to Nov. 2006 • Results: • NN performs well in day-ahead forecasting • But it fails to compete with naive method in wider time horizon • Improvements: • Exogenous variables

19. TAR (Threshold AR) • SETAR • Aim: • Identifying the limit (C) between high and low prices • 2 state SETAR model • On daily price • Threshold: 44.26