Analysis of dayahead electricity data

1
Analysis of day-ahead electricity data

• Zita Marossy Márk Szenes (ColBud)
• MANMADE workshop
• January 21, 2008

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Topics

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

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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

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Persistence analysis

• Calculating the Hurst exponent of prices
• Without differencing the time series
• Hurst exponent classical usage
• (with differencing the time series first)
• gt 0.5 persistent process
• High return shock followed by high return
• 0.5 random walk
• Return is white noise
• lt 0.5 antipersistent process (mean reversion)
• Hurst exponent without differencing
• gt 0.5 persistent process
• High price followed by high price Are high
  prices persistent?
• 0.5 white noise
• lt 0.5 antipersistent process

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Hurst exponent estimation results
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Price distribution

• Two estimated distributions
• Lévy
• Generalized extreme value

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Comparison

• Kolmogorov test
• Test statistic
• Lévy 0.0141
• GEV 0.0262
• Mean of absolute differences
• Lévy 8.0710-4
• GEV 7.1810-4

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Seasonality

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

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Need for new seasonal filter

• The type of distribution changes

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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

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Empirical results

• Figures periodogram of
• ACF (orig prices)
• ACF (filtered data)
• Intraweekly filtering
• successful

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Estimated GEV parameters
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Distributions with high scale param
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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

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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

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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

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TAR (Threshold AR)

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