This empirical paper compares the accuracy of 12 time series methods for short-term (dayahead) spot price forecasting in auction-type electricity markets. The methods considered include standard autoregression (AR) models, their extensions -spike preprocessed, threshold and semiparametric autoregressions (i.e. AR models with nonparametric innovations), as well as, mean-reverting jump diffusions. The methods are compared using a time series of hourly spot prices and system-wide loads for California and a series of hourly spot prices and air temperatures for the Nordic market. We find evidence that (i) models with system load as the exogenous variable generally perform better than pure price models, while this is not necessarily the case when air temperature is considered as the exogenous variable, and that (ii) semiparametric models generally lead to better point and interval forecasts than their competitors, more importantly, they have the potential to perform well under diverse market conditions.

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-ofsample 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. * The authors are grateful to Dick van Dijk and two anonymous referees for insightful comments and suggestions. This work was supported in part by KBN grant 4-T10B-030-25 (to Misiorek).

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The essence of the Value-at-Risk (VaR) and Expected Shortfall (ES) computations is estimation of low quantiles in the portfolio return distributions. Hence, the performance of market risk measurement methods depends on the quality of distributional assumptions on the underlying risk factors. This chapter is intended as a guide to heavy-tailed models for VaR-type calculations. We first describe stable laws and their lighter-tailed generalizations, the so-called truncated and tempered stable distributions. Next we study the class of generalized hyperbolic laws, which-like tempered stable distributions-can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Then we discuss copulas, which enable us to construct a multivariate distribution function from the marginal (possibly different) distribution functions of n individual asset returns in a way that takes their dependence structure into account. This dependence structure may be no longer measured by correlation, but by other adequate functions like rank correlation, comonotonicity or tail dependence. Finally, we provide numerical examples.