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

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

Main results Persistence analysis  Underlying variable: price, not price change  Results: H = (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

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

Modeling prices, not price changes 1. The price process has no unit root, there is no need to differentiate the time series 2. Electricity can not be stored: ‘return’ has no direct meaning 3. By differencing we cause spurious patterns in ACF:

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

Hurst exponent: estimation results MethodEstimated Hurst exponent Aggregated variance0.872 Differenced aggregated variance0.702 Aggregated absolute values/means0.924 Fractal dimension (Higuchi)0.967 Residuals of regression (Peng)0.811 R/S0.835 Periodogram0.891 Modified periodogram0.770 Wavelet0.839

Price distribution Two estimated distributions:  Lévy  Generalized extreme value

Comparison Kolmogorov test: Test statistic:  Lévy:  GEV: Mean of absolute differences:  Lévy: 8.07*10 -4  GEV: 7.18*10 -4

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

Need for new seasonal filter The type of distribution changes

Suggested filter ‘GEV filter’ 1. Separately estimate a GEV distribution for each hour and day i: F1(i) 2. Transform the prices: F 2 -1 F 1,i (x) F 2 : lognormal cdf (parameters: entire distribution) 3. Model the prices of filtered data 4. Forecast 5. Transform the forecasts back into GEV

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

Estimated GEV parameters

Distributions with high scale param

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

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

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

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