A look into the future of electricity (spot) price forecasting

A look into the future of electricity (spot) price forecasting Rafa l Weron Institute of Organization and Management Wroc law University of Technology, Poland 28 April 214 Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 1 / 25

Introduction: Bibliometrics of electricity price forecasting Electricity price forecasting (EPF) publications 213 212 211 21 29 28 27 26 25 24 23 22 21 2 <2 Articles Proceedings papers 1 2 3 4 5 Number of WoS indexed publications 213 212 211 21 29 28 27 26 25 24 23 22 21 2 <2 Articles Reviews, book chapters Conference papers 2 4 6 8 Number of Scopus indexed publications Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 2 / 25

Introduction: Bibliometrics of electricity price forecasting EPF journal articles and citations to those articles Number of WoS indexed articles and citations 3 25 2 15 1 5 Journal articles Citations ( 2) 2 22 24 26 28 21 212 Number of Scopus indexed articles and citations 5 45 4 35 3 25 2 15 1 5 Journal articles Citations ( 2) 2 22 24 26 28 21 212 Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 3 / 25

Introduction: Bibliometrics of electricity price forecasting Ten most popular journals IEEE Transactions on Power Systems Electric Power Systems Research Int. J. Electrical Power & Energy Systems Energy Conversion and Management Energy Economics IET Generation Transmission & Distribution International Journal of Forecasting Applied Energy Energy Policy IEEE Transactions on Smart Grid Neural network & time series Neural network only Time series only Other methods 5 1 15 2 25 3 35 Number of articles (2 213) Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 4 / 25

Introduction: What and how are we forecasting? The electricity spot price Day d 2 Day d 1 Day d Bidding for day d 1 Bidding for day d 24 hours (48 half-hours) of day d 1 24 hours (48 half-hours) of day d Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 5 / 25

Introduction: What and how are we forecasting? Forecasting horizons Short-term From a few minutes up to a few days ahead Of prime importance in day-to-day market operations Medium-term From a few days to a few months ahead Balance sheet calculations, risk management, derivatives pricing Inflow of finance solutions Long-term Lead times measured in months, quarters or even in years Investment profitability analysis and planning Beyond the scope of this review Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 6 / 25

Introduction: What and how are we forecasting? A taxonomy of modeling approaches Electricity price models Multi-agent Fundamental Reduced-form Statistical Computational intelligence Cournot- Nash framework Parameter rich fundamental Jumpdiffusions Similar-day, exponential smoothing Feed-forward neural networks Supply function equilibrium Parsimonious structural Markov regimeswitching Regression models Recurrent neural networks Strategic productioncost AR, ARX-type Fuzzy neural networks Agent-based Threshold AR Support vector machines GARCH-type Hybrid Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 7 / 25

Agenda A look into the future of EPF 1 Fundamental price drivers and input variables Modeling and forecasting the trend-seasonal components The reserve margin and spike forecasting 2 Beyond point forecasts probabilistic forecasts 3 Combining forecasts Point forecasts Probabilistic forecasts 4 Multivariate factor models 5 The need for an EPF-Competition A universal test ground Guidelines for evaluating forecasts Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 8 / 25

1. Fundamental price drivers and input variables Modeling the trend-seasonal components Standard approach decompose a time series of prices P t into the long-term trend-seasonal component (LTSC) T t, the short-term seasonal component (STSC) s t, and the remaining variability, error or stochastic component X t The hourly/weekly STSC is usually captured by autoregression & dummies forecasting is straightforward Annual seasonality is present in spot prices, but in most cases the LTSC is dominated by a more irregular cyclic component Due to fuel prices, economic growth, long-term weather trends See e.g. Janczura et al. (213), Nowotarski et al. (213b) Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 9 / 25

1. Fundamental price drivers and input variables Modeling the LTSC Nord Pool spot price [EUR/MWh] 15 1 5 Spot price Wavelet based LTSC Sine Monthly dummies 1 2 3 4 5 6 7 Days [1.1.212 31.1.213] Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 1 / 25

1. Fundamental price drivers and input variables Adequate seasonal decomposition is important! 1 5 Wavelet based: α=9.6, β=.48, (α/β=2.), σ=6.17, µ=71.98, γ=.13, λ=.1 Simulated stochastic component (X t ) 1 5 1 5 1 2 3 4 5 6 7 Sine: α=1.7, β=.6, (α/β=17.11), σ=2.75, µ=1.52, γ=26.96, λ=.11 1 2 3 4 5 6 7 Monthly dummies: α=1.11, β=.6, (α/β=2.13), σ=2.7, µ=1.49, γ=23.75, λ=.14 1 2 3 4 5 6 7 Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 11 / 25

1. Fundamental price drivers and input variables The reserve margin and spike forecasting Reserve margin, also called surplus generation, relates the available capacity (generation, supply), C t, and the demand (load), D t, at a given moment in time t The traditional engineering notion: RM = C t D t Some authors prefer to work with dimensionless ratios: ρ t = Dt C t or the so-called capacity utilization CU = 1 Dt C t Consider ρ(t 1, t 2 ) = D(t 1,t 2 ) C(t 1,t 2 ) calculated at time t 1 (e.g. today) for an upcoming period t 2 D(t 1, t 2 ) is the National Demand Forecast (Indicated Demand) C(t 1, t 2 ) is the predicted Generation Capacity (Indicated Generation, see www.bmreports.com) See Cartea et al. (29), Maryniak and Weron (214) Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 12 / 25

1. Fundamental price drivers and input variables ρ(t 1, t 2 ) for 23-5 (top) and 26-12 (bottom) #spikes CF 2 15 1 5 τ=2d τ=1w τ=2w P(spike CF ρ).8.6.4.2 τ=2d τ=1w τ=2w.7.8.9 1 ρ(t τ,t).7.8.9 1 ρ(t τ,t) P(spike RSC ρ).6.4.2 τ=2d τ=1w τ=2w P(spike ρ).4.3.2.1 RSC RFP CF.7.8.9 1 ρ(t τ,t).7.8.9 1 ρ(t 2D,t) Anderson and Davison (28): ρ = 85% is the industrial standard warranting a safe functioning of the power system Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 13 / 25

2. Beyond point forecasts Probabilistic forecasts Interval forecasts (only 1 articles) Zhang et al. (23), Zhang and Luh (25), Misiorek et al. (26), Weron and Misiorek (28), Zhao et al. (28), Serinaldi (211), Gonzalez et al. (212), Wu et al. (213), Khosravi et al. (213a,b) In only one paper formal statistical tests for coverage are conducted conditional coverage of Christoffersen (1998) Density forecasts (only 2/3 articles) Serinaldi (211) forecasts the distribution of electricity prices, but computes and discusses only the PI Huurman et al. (212) perform density forecasting of Nord Pool spot prices and use the test of Berkowitz (21) Jonsson et al. (214) generate prediction densities of day-ahead electricity prices in Western Denmark, but do not test them Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 14 / 25

3. Combining forecasts Forecast combinations, forecast/model averaging The idea goes back to the 196s Electricity demand or transmission congestion forecasting (Bunn, 1985a; Bunn and Farmer, 1985; Løland et al., 212; Smith, 1989; Taylor, 21; Taylor and Majithia, 2) Only recently for EPF: Bordignon et al. (213), Nowotarski et al. (213a), Nowotarski and Weron (214) and Raviv et al. (213) In the AI world : committee machines or ensemble averaging Guo and Luh (24) combine a RBF network (23 inputs and six clusters) and a MLP (55 inputs and eight hidden neurons) to compute daily average on-peak electricity price for New England Forecast combinations and committee machines seem to evolve independently, with researchers from both groups not being aware of the parallel developments! Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 15 / 25

3. Combining forecasts To combine or not to combine? NP Price [EUR/MWh] WMAE i min(wmae i ) 15 12 9 6 3 Individual forecasts (weeks 1 34) Combined forecasts (weeks 5 34) 8.8.212 5.6.213 31.12.213 Hours [8.8.212 31.12.213] 3 2 1 Individual models Simple CLS LAD 5 1 15 2 25 3 34 Weeks [5.6.213 31.12.213] Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 16 / 25

3. Combining forecasts To combine or not to combine? Summary statistics for 6 individual and 3 averaging methods: WMAE is the mean value of WMAE for a given model (with standard deviation in parentheses), # best is the number of weeks a given averaging method performs best in terms of WMAE, and finally m.d.f.b. is the mean deviation from the best model in each week. The out-of-sample test period covers 3 weeks (5.6.213 31.12.213). Individual models Forecast combinations AR TAR SNAR MRJD NAR FM Simple CLS LAD WMAE 5.3 5.7 4.77 4.98 4.88 5.36 4.47 4.29 4.92 (3.4) (3.53) (3.26) (3.17) (1.62) (3.17) (2.87) (1.88) (2.41) # best 1 3 4 1 2 4 8 6 1 m.d.f.b. 1.1 1.5.75.96.86 1.34.45.27.89 Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 17 / 25

3. Combining forecasts Combining interval/density EPF only one paper Nowotarski and Weron (214) propose a new method for constructing PI, which utilizes the concept of quantile regression (QR) and a pool of point forecasts of individual models Empirical PI from combined forecasts do not yield gains QR-based PI are more accurate than those of the benchmark (AR) and the best individual model (SNAR) Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 18 / 25

4. Multivariate factor models Factor models All hourly prices P kt, k = 1,..., 24, co-move and depend on a small set of common factors F t = [F 1t,..., F Nt ] The individual series P kt can be modeled as a linear function of N principal components F t and stochastic residuals ν kt : P kt = Λ k F t + ν kt, (1) where the loads (or loadings) Λ k = [Λ k1,..., Λ kn ] describe the relation between the factors F t and the panel variables P kt See e.g. Bai (23), Stock and Watson (22) It is natural to assume that the common factors follow a VAR(p) model, see e.g. Maciejowska and Weron (214) Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 19 / 25

4. Multivariate factor models Forecasting PJM Dominion Hub daily spot prices Using the information contained in hourly prices Spot price [USD/MWh] Loadings 4 3 2 1 Out of sample test period 2 4 6 8 1 12 14 16 18 2 Days [1.1.28 31.12.212] 4 2 2 4 L1 L2 L3 Hourly prices 4 8 12 16 2 24 Hours Relative RMSE 1.2 1.98 Average daily price AR AR24 FM.96 2 4 6 Forecasting horizon [Days] Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 2 / 25

4. Multivariate factor models Factor models and EPF Applications of multivariate models to EPF are very recent Chen et al. (28), Härdle and Trück (21) In the last two years, an increased inflow of multivariate EPF papers can be observed Garcia-Martos et al. (212), Peña (212), Vilar et al. (212), Elattar (213), Miranian et al. (213), Wu et al. (213) The idea originating in macroeconometrics of using disaggregated data for forecasting of aggregated variables Liebl (213), Maciejowska and Weron (213, 214), Raviv et al. (213) Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 21 / 25

5. The need for an EPF-Competition The need for an EPF-Competition Many of the published results seem to contradict each other Misiorek et al. (26) report a very poor forecasting performance of a MRS model, while Kosater and Mosler (26) reach opposite conclusions for a similar MRS model but a different market and mid-term forecasting horizons On the other hand, Heydari and Siddiqui (21) find that a regime-switching model does not capture price behavior correctly in the mid-term Cross-category comparisons are even less conclusive and more biased Typically advanced statistical techniques are compared with simple AI methods, see e.g. Conejo et al. (25a), and vice versa, see e.g. Amjady (26) Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 22 / 25

5. The need for an EPF-Competition A universal test ground This calls for a comprehensive and thorough study involving 1 the same datasets 2 the same robust error evaluation procedures 3 statistical testing of the significance of the outperformance of one model by another Like the Makridakis or M-Competitions for economic forecasting Global Energy Forecasting Competition 214 includes a price forecasting track this year, see www.drhongtao.com/gefcom Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 23 / 25

5. The need for an EPF-Competition Guidelines for evaluating forecasts A selection of the better performing measures weighted-mae, like the weekly-weighted WMAE seasonal MASE (Mean Absolute Scaled Error) RMSSE (Root Mean Square Scaled Error) should be used exclusively or in conjunction with the more popular ones (MAPE, RMSE) Statistical testing for the significance of the difference in forecasting accuracy of the models The Diebold and Mariano (1995) test; for uses and abuses see Diebold (213) The model confidence set approach of Hansen et al. (211) Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 24 / 25

The end Bibliography Based on an invited paper prepared for the International Journal of Forecasting. A restricted working paper version is available for download from: http://ideas.repec.org/p/wuu/wpaper/hsc142.html Rafa l Weron (WUT) A look into the future... 28.4.214, U.Paris-Dauphine 25 / 25