Volume 10, Issue 3 - Nonlinear Analysis of Electricity Prices

The functioning of electricity markets has experienced increasing complexity as a result of deregulation in recent years. Consequently this affects the multilateral price behaviour across regions with physical exchange of power. It has been documented elsewhere that features such as long memory and regime switching reflecting congestion and non-congestion periods are empirically relevant and hence are features that need to be taken into account when modeling price behavior. In the present paper we further elaborate on the co-existence of long memory and regime switches by focusing on the effect that the direction of possible congestion episodes has on the price dynamics. Under non-congestion prices are identical. The direction of possible congestion is identified by the region with excess demand of power through the sign of price differences and hence three different states can be considered: Non-congestion and congestion periods with excess demand in the one or the other region. Using data from the Nordic power exchange, Nord Pool, we find that the price dynamics and long memory features of the price series generally are rather different across the different states. Also, there is evidence of fractional cointegration at some grid points when conditioning on the states.

In this paper we assess the short-term forecasting power of different time series models in the electricity spot market. In particular we calibrate AR/ARX (''X'' stands for exogenous/fundamental variable -– system load in our study), AR/ARX-GARCH, TAR/TARX and Markov regime-switching models to California Power Exchange (CalPX) system spot prices. We then use them for out-of-sample point and interval forecasting in normal and extremely volatile periods preceding the market crash in winter 2000/2001. We find evidence that (i) non-linear, threshold regime-switching (TAR/TARX) models outperform their linear counterparts, both in point and interval forecasting, and that (ii) an additional GARCH component generally decreases point forecasting efficiency. Interestingly, the former result challenges a number of previously published studies on the failure of non-linear regime-switching models in forecasting.

Due to its non-storable nature, electricity is a commodity with probably the most volatile spot prices, exemplified by occasional spikes. Appropriate pricing, portfolio, and risk management models have to incorporate these characteristics, and the spikes in particular. We investigate the nature of power spikes in a number of different markets. We test what time-series model is best able to capture the dynamics of these disruptive spot prices. We use regime-switching models to infer whether the price spikes should be treated as abnormal and independent deviations from the ‘normal’ price dynamics or whether they form an integral part of the price process. We test the time-series models on day-ahead markets in Europe and the US. We find that regime-switch models are better able to capture the market dynamics than a GARCH(1,1) or Poisson jump model. We also find clear differences between the markets and attribute part of the differences to the share of hydro-power in the total supply stack: hydro-power serves as an indirect means to store electricity, which has a dampening effect on spikes.

This study investigates the extent to which predicted electricity spot prices from a statistical model, along with consensus forecasts issued by the Australian Financial Market Association (AFMA), provide unbiased price estimates of a forward contract price over a specified time to expiration. The statistical model is a regime switching time series model which is based on the dynamics of the market mechanism. To evaluate a price estimate, two criteria are utilized in order to conclude appropriateness for use in the marking-to-market process. First is the requirement that the predicted prices converge to the spot price at expiration of a hedging contract. The second criterion refers to the mis-pricing due to the price estimates over the days leading up to the contract expiration. Over the data period under consideration, the ranking of alternatives for generating price predictions is clear. On both criteria the Stevenson (2001) model is preferred. Of significance is the lack of support for the consensus (market) prices. They do not converge to the spot price at equilibrium and, further, they generate a considerable overvaluation of the risk management portfolio.

This paper uses hourly electricity prices and MW hour demand for Alberta, Canada over the deregulated period after 1996 to test for randomly modulated periodicity. In doing so, we apply the signal coherence spectral analysis to the time series of hourly spot prices and megawatt-hours (MWh) demand from 1/1/1996 to 12/7/2003 using the FORTRAN 95 program developed by Hinich (2000). We detect relatively steady weekly and daily cycles in demand but very unstable cycles in prices.

We model electricity futures prices using a seasonal forward curve model, quantifying seasonalities by a deterministic seasonal forward premium. Stochastic features of the futures prices are contained in the stochastic forward premium: a quantity analogous to the well-known convenience yield. The model parameters are estimated from the historical data of IPE electricity futures prices and the spark spread, and electricity forward curves are deseasonalized to reveal their underlying stochastic structure. We apply principal component analysis to the deseasonalized forward curves and develop trading strategies using indicators based on these principal components.

We investigate the presence of significant electricity forward risk premia, using data from three major continental European energy markets - German, Dutch and French. We introduce the risk premium in the framework of a standard electricity spot/forward unobserved factor model, and derive the implied forward price behaviour. We then assess the term-structure and time-evolution of the risk premia for each of the markets.

This paper presents an analytic approximation for the pricing dynamics of spark spread options in terms of Fourier transforms. We propose to model the spark spread, that is, the price difference of electricity and gas, directly using a mean-reverting model with diffusion and jumps. The model is analyzed empirically, and shown to fit observed data in the UK reasonably well. The main advantage with the model is that the spark spread of electricity and gas forwards, being forwards with delivery over periods, can be priced analytically. The price dynamics for different spark spread options with electricity and gas forwards as underlying, is analytically derived through Fourier transforms. These pricing expressions allow for efficient numerical valuations via the fast Fourier transform technique.

Predictions of future weather conditions play an important role in pricing weather derivatives. In many instances, the dates for which we require predictions are well beyond the point where physical forecasts have any skill. Under these circumstances, predictions are generated from statistical models of historic data. This paper derives conditions for which the predictive performance in regression is improved by ignoring or shrinking the contribution from some of the explanatory variables. We suggest methods for estimating the degree of shrinkage required in practice. We illustrate our methods using surface temperature data from fifteen stations in the United States.

In this paper we specify and estimate a multivariate GARCH-M model of natural gas and electricity price changes, and test for causal relationships between natural gas and electricity price changes and their volatilities, using data over the deregulated period from January 1, 1996 to November 9, 2004 from Alberta's (deregulated) spot power and natural gas markets. The model allows for the possibilities of spillovers and asymmetries in the variance-covariance structure for natural gas and electricity price changes, and also for the separate examination of the effects of the volatility of anticipated and unanticipated changes in natural gas and electricity prices.