Electric Spot Prices And Wind Forecasts: A Dynamic Ogy Nordic/Baltic .
Norwegian University of Science and Technology4.2%11Electric Spot Prices and Wind Forecasts: A dynamicNordic/Baltic Electricity Market Analysis using NonlinearImpulse-Response MethodologybyProfessor Per B Solibakke
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisIntroduction A dynamic daily market approach is established from the Nordic/Baltic Electricity market (NordPool). The period with available datawind forecasts is from January 2013 to May 2017. The daily wind information in MWh is shown below:8.3%22
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisIntroduction The daily electricity price information in MWh for the Nordic/Baltic Electricity market (NordPool) 2013-2017 is shown below:12.5%33
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisThe Impulse-Response MethodologyImpulse Responses for the Mean Equation:The paper applies the methodologies outlined by Gallant et al. (1993) defining one-step ahead forecast for the mean conditioned on thehistory as (for a Markovian process) (y spot price and wind forecast changes): g yt-L 1 ,.,yt E yt 1 yt-k E E yy j x E g yt-L j ,.,yt jWe write:Note that y -10 jjt j k 0 L1 x xt yt-L j ,.,yt j xti x and therefore y j for i -60, ,60 and j 0, ,5, wherex yL - 1 ,.,y0 represent the response to a negative 10% impulse. Here the responses depend upon the initial change x, which reflectsthe non-linearity.We report iy j- y , i 60,., 60 and j 0,.,5 , which represents the effects of the shocks on the trajectories of the process itself.0 jjA conditional profile can therefore be defined as:16.7%44L 1E g y t j- J ,., y t j y t-k k 0 , j 0,1,.,5 ,
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisThe Impulse-Response MethodologyImpulse Responses for the Variance Equation:Defining one-step ahead variance (volatility), is the on-step ahead forecast for the variance conditioned on the history as (y spot priceand wind forecast changes): k 0 E - y t 1 y t-k yt 1 E ψ j x E g y t-L j ,., y t j x t xWe write: E Var y t j x t j -1 x t xNote that We report k 0 x y t 1 E- y y t-kt 1 k 0 y t-k ′ Var yt 1 yt-k k 0 for j 0, ,5, where x yL - 1 ,.,y0 -10 jirepresent the volatility response to a negative 10% impulse. The responses depend upon the initial change x.j j - , i 60,., 60 and j 0,.,5 ,0 jwhich represents the effects of the shocks on the trajectories of the process itself.jThe conditional volatility profile is different from the path described by the j-step ahead square error process. Note that analyticalevaluation of the integrals in the definition of a conditional moment profile is intractable. However, evaluation is well suited to MonteCarlo integration. For simulated realisations we write (with approximation error tending to zero almost surely as R ): j-1g j x . g y j-J ,.,yj 1 / R g yR20.8%55r 1rjJ,.,y f y i 0rji 1 yy-L 1 ,.,y dy1 .dyji Sup-norm bands (confidence intervals) are constructed by bootstrapping (changing seed generates densities and impulse response samples)
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisLiterature reviewSpot Electricity Prices:Goto and Karolyi (2004), Chan and Gray (2006), Theodorou and Karyampas (2008), Bystrøm (2003) and Solibakke (2002).Higgs and Worthington (2008), Huisman and Mahieu ((2003) and Thomas et al., (2011).De Vany and Walls (1999), Higgs and Worthington (2008), Huisman and Mahieu (2003), Huisman and Kilic (2013), Haldrup and Nilsen(2006), Knittel (2005), Li and Flynn (2004), Lindstrom and Regland (2012), Mount, Ning and Cai (2006), Robinson (2000), Robinson andBaniak (2002), Rubin and Babcock (2011), Tashpulatov (2013), and Weron (2006, 2008).Chan and Gray (2006), Escribano, Pena and Villaplana (2011), Habell, Marathe and Shawky (2004), Higgs and Worthington (2005),Koopman, Ooms and Carnero (2007) and Solibakke (2002).Weron (2006, 2008), Harris (2006), Geman and Roncoroni (2006), Koopman et al. (2007) and Pilipovic (2007).Wind Forecasts:Price changes:Skytte, 1999, Morthorst, 2003 , Giabardo et al., 2009, and Traber and Kenfert, 2011Price Volatility:Green and Vasilakos (2010), Steggals et al. (2011), Woo et al. (2011), Jacobsen and Zvingilaite (2010), and Twomey and Neuhoff (2010),The Semi-Non-Parametric Methodology (background and the impulse response methodology):Robinson (1983)Engle (1982)Bollerslev (1986)Gallant & Tauchen (2010, 2014)25%66previously used for contemporaneous price – volume analysis of stocks /indices andtrading volume.
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisEmpirical Model AnalysisStationarity for price and wind forecast changesFor both series we adjust for systematic location and scale effects in both mean and volatility. x b uStep 1 (mean): Regress, where x consists of calendar variables (trends, day of week, week number, calendarseparation variable, Eastern and other sub-periods.u 2Step 2 (variance): For the residuals û we regress u 2 x g . We form x g giving us a series with mean zero and unit varianceegiven x (calendar variables).The series a b (u e xg ) is taken as the adjusted series. a and b are chosen so the unit of measurement of the adjusted series is thesame as that of the original series.For the b and g parameters for these two simple regressions, I refer to the manuscript.29.2%77
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisEmpirical Model AnalysisStationary Electricity Spot Price changes (time series)Stationary Wind Forecast changes (time series)Adjusted Log Spot Price MovementsAdjusted Log W ind Forecast sted Log Wind Forecast 10010120308020Theoretical QuantilesTheoretical QuantilesKernelStudent's 204060Quantiles of ADJUSTED LOG SPOT PRICE8820NormalLogis ticNormalStudent's tLogistic-30-20-1001020Quantiles of ADJUSTED LOG W INDNormalStudent's tLogis tic30
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisEmpirical Model Analysis An unconditional electricity price and wind forecast scatterplot for the Nordic/Baltic Electricity market (NordPool) 2013-2017:37.5%99
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisEmpirical Model AnalysisThe Semi-Non-Parametric Model (SNP) specification is (7,1f,1f,1,4,0,0,0) :Table 3 Bivariate SNP model: System Price and Wind Forecast Movements41.7%1010A BIC-optimal bivariate model for the mean and volatility (parametric) and hermite functions (higher order terms) to capture departuresfrom that parametric model.
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisEmpirical Model AnalysisThe bivariate SNP Model specification is (7,1f,1f,1,4,0,0,0): A conditional Scatter plot:45.8%1111
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisEmpirical Model AnalysisThe bivariate SNP Model specification is (7,1f,1f,1,4,0,0,0) properties: Conditional Volatility and Price – Wind Forecast Correlation45.8%1212
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisEmpirical Model AnalysisThe bivariate SNP Model specification is (7,1f,1f,1,4,0,0,0) properties (cont.): Leverage Effects and Bivariate Unconditional Densities50%1313
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisEmpirical Model AnalysisThe bivariate SNP Model specification is (7,1f,1f,1,4,0,0,0) properties (cont.): bivariate conditional density plots (matrix)Wind Forecast e-30Changes-20-10-5-3-101351020304054.2%601414A suggested negative densitycorrelation121520
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisImpulse Response AnalysisThere are NO wind mean responses from spot price changes (important for model acceptance)58.3%1515
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisImpulse Response AnalysisThere are NEGLECTIBLE wind variance responses from spot price changes; low wind suggests higher uncertainty around future wind62.5%1616
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisImpulse Response AnalysisStep-Ahead Spot Price Mean Responses from Spot Price and Wind Forecast Change Impulses:66.7%1717
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisImpulse Response AnalysisStep-Ahead Spot Price Mean Responses from Spot Price and Wind Forecast Change Impulses:70.8%1818
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisImpulse Response AnalysisStep-Ahead Spot Price Volatility Responses from Spot Price and Wind Forecast Change Impulses:75%1919
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisImpulse Response AnalysisStep-Ahead Spot Price Volatility Responses from Spot Price and Wind Forecast Change Impulses:79.2%2020
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisImpulse Response AnalysisStep-Ahead Spot Price and Wind Forecast Co-variance Responses from Spot Price and Wind Forecast Change Impulses83.3%2121
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisImpulse Response AnalysisStep-Ahead Spot Price and Wind Forecast Co-variance Responses from Spot Price and Wind Forecast Change Impulses87.5%2222
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisImpulse Response AnalysisOne-step Ahead Spot Price Mean Response Forecasting from Spot Price and Wind Forecast Change Co-variance91.7%2323
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisImpulse Response AnalysisOne-step Ahead Spot Price Volatility Response Forecasting from Spot Price and Wind Forecast Change Co-variance95.8%2424
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response AnalysisStationarity and Electricity Market Price and Wind Forecast adjustmentsSummary A bivariate impulse response analysis for the Baltic/Nordic Electricity system The time series analysis requires stationary series using calendar and trend adjustments for interpretations /validity A Semi-Non-Parametric model (mean, volatility and higher moments adjustments) is dynamically estimated (daily) One-step Ahead spot price and price – wind covariance analysis Dynamically sort spot price change and volatility over one-step-ahead covariance A methodology for one-step ahead spot, forward/futures and derivatives market positioning. Note, variance and co-variance are latent (non-observable). A model is therefore needed for explicit variance/co-variance measures fordynamic market positioning.100%2525
Spot Electricity Prices and Wind Forecasts. Dynamic Impulse-Response Analysis Stationary Electricity Spot Price changes (time series) Stationary Wind Forecast changes (time series) 0 0 0 0 10 20 30 . A suggested negative density correlation 54.2%. 1515 Impulse Response Analysis Spot Electricity Prices and Wind Forecasts. Dynamic Impulse .
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negative non-linear covariance between spot prices and wind forecasts movements in the Nordic/Baltic electricity . Spot electricity prices exhibit high volatility, strong mean reversion3, frequent spikes and seasonal patterns4 and differs from region to region (Li and Flynn, 2004). Moreover, Goto and Karolyi (2004) find mean-reversion effect .
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