Efficiently Estimated Mean and Volatility Characteristics for the Nordic Spot Electric Power Market

Abstract

ABSTRACT This paper investigates the conditional mean and volatility characteristics of the Nordic Spot electric power market. The investigation is motivated by the fact that the system price is the underlying instrument for several derivatives in the electric power market, the variance-covariance matrix may be applied for value at risk calculations and consumption patterns may suggest extensive predictability in mean and volatility. An adjustment procedure shows that the raw data series show strong day, month and scaling effects. The applied BIC efficient ARMA-GARCH-in-Mean specifications for the adjusted time show close to zero drift and an autocorrelation pattern for the conditional mean, suggesting consumption patterns. As expected, the in-Mean parameter is redundant and clearly significant ARCH and GARCH effects in the conditional volatility process. All specification tests reject data dependence in the residuals. Our results therefore suggest that a BIC efficient ARMA-GARCH lag specification seems to model the market dynamics adequately. JEL: C22, C52 Keywords: Electric power market; System price; Consumption pattern; Conditional heteroscedasticity, Supply and demand curves I. INTRODUCTION This paper studies the characteristics of the conditional mean and volatility of daily price changes of the so-called System Price for the Nordic spot electric power market. The spot market is a Nordic contract market where electric power is traded on a daily basis for delivery the following day, with full obligation to pay. The prices are fixed on the basis of all participants' collected purchase and sale requests. The System Price is the balance price for the aggregated supply and demand graphs; i.e. the price is fixed at the market equilibrium. Hence, our investigation is an empirical investigation of the dynamics of the so-called system price series. The motivation is based on the fact that the price series is the underlying instrument for several derivatives in the electric power market. A first glance inspection of the series suggests a consumption pattern in the mean and a very high, changing and mean reverting volatility. Consequently, the electric power market may benefit strongly for a higher understanding of both mean and volatility characteristics. The consumption pattern may show serial correlation in the mean, which may suggest predictability in the mean process. Moreover, when valuing derivatives in financial markets, forecasts of volatilities and correlations over the whole life of the derivative are usually required. The system price change series seems to show several extreme observations. The distribution may therefore show signs of heavy tails suggesting leptokurtosis in the time series. The deviation from the normal distribution may be an important factor to account for when valuing options especially. Finally, as the mean-variance analysis we perform can calculate the whole variance-covariance matrices, value at risk calculations may be employed. We employ elaborate specification test statistics for model misspecifications. Insignificant test statistics suggest appropriate specifications and consequently an appropriate model for exogenous variable analyses in both the mean and the latent volatility series. The empirical investigation is performed allowing serial correlation and changing volatility models. Specifically, we apply an ARMA-GARCH-in-Mean lag specification (1), where the ARMA lag specification models the mean and the GARCH lag specification models the latent volatility process. The in-Mean specification models total (residual) risk mean effects. Then lags are Bayes Information Criterion (BIC) (Schwartz, 1978) preferred in both mean and volatility. Hence, the ARMA-GARCH specification pertains to model the first observed series characteristics. Consequently, the changing volatility model seems therefore to be an obvious candidate as the stochastic volatility specification fails to find a BIC preferred model. …

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