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This paper complements a recently published study (Janczura and Weron in AStA-Adv Stat Anal 96(3):385–407, 2012) on efficient estimation of Markov regime-switching models. Here, we propose a new goodness-of-fit testing scheme for the marginal distribution of such models. We consider models with an observable (like threshold autoregressions) as well as a latent state process (like Markov regime-switching). The test is based on the Kolmogorov–Smirnov supremum-distance statistic and the concept of the weighted empirical distribution function. The motivation for this research comes from a recent stream of literature in energy economics concerning electricity spot price models. While the existence of distinct regimes in such data is generally unquestionable (due to the supply stack structure), the actual goodness-of-fit of the models requires statistical validation. We illustrate the proposed scheme by testing whether commonly used Markov regime-switching models fit deseasonalized electricity prices from the NEPOOL (US) day-ahead market.

We develop a simple test for deviations from power law tails. Actually, from the tails of any distribution. We use this test – which is based on the asymptotic properties of the empirical distribution function – to answer the question whether great natural disasters, financial crashes or electricity price spikes should be classified as dragon-kings or ‘only’ as black swans.

One of the most profound features of electricity spot prices are the price spikes. Markov regime-switching (MRS) models seem to be a natural candidate for modeling this spiky behavior. However, in the studies published so far, the goodness-of-fit of the proposed models has not been a major focus. While most of the models were elegant, their fit to empirical data has either been not examined thoroughly or the signs of a bad fit ignored. With this paper we want to fill the gap. We calibrate and test a range of MRS models in an attempt to find parsimonious specifications that not only address the main characteristics of electricity prices but are statistically sound as well. We find that the most universal and robust structure is that of an independent spike 3-regime model with heteroscedastic diffusion-type base regime dynamics and shifted spike regime distributions.

In the last decade Markov regime-switching (MRS) models have been extensively used for modeling the unique behavior of spot prices in wholesale electricity markets. This popularity stems from the models’ relative parsimony and the ability to capture the stylized facts, in particular the mean-reverting character of electricity spot prices, the regime changes implied by fundamentals, and the resulting extreme price spikes. Due to the unobservable switching mechanism, the estimation of MRS models requires inferring model parameters and state process values at the same time. The situation becomes more complicated when the individual regimes are independent from each other and at least one of them is mean-reverting. Statistical validation of such models is also nontrivial. In this paper we review the available techniques and suggest efficient tools for statistical inference of MRS models.

An important issue in fitting stochastic models to electricity spot prices is the estimation of a component to deal with trends and seasonality in the data. Unfortunately, estimation routines for the long-term and short-term seasonal pattern are usually quite sensitive to extreme observations, known as electricity price spikes. Improved robustness of the model can be achieved by (a) filtering the data with some reasonable procedure for outlier detection, and then (b) using estimation and testing procedures on the filtered data. In this paper we examine the effects of different treatments of extreme observations on model estimation and on determining the number of spikes (outliers). In particular we compare results for the estimation of the seasonal and stochastic components of electricity spot prices using either the original or filtered data. We find significant evidence for a superior estimation of both the seasonal short-term and long-term components when the data have been treated carefully for outliers. Overall, our findings point out the substantial impact the treatment of extreme observations may have on these issues and, therefore, also on the pricing of electricity derivatives like futures and option contracts. An added value of our study is the ranking of different filtering techniques used in the energy economics literature, suggesting which methods could be and which should not be used for spike identification.

We calibrate Markov regime-switching (MRS) models to mean daily spot prices from the EEX market. Our empirical study shows that (i) models with shifted spike regime distributions lead to more realistic models of electricity spot prices and that (ii) introducing heteroskedasticity in the base regime leads to better spike identification and goodness-of-fit than in MRS models with the standard mean-reverting, constant volatility dynamics.

In this paper we derive analytic formulas for electricity derivatives under assumption that electricity spot prices follow a 3-regime Markov regime-switching model with independent spikes and drops and periodic transition matrix. Since the classical derivatives pricing methodology cannot be used in the case of non-storable commodities, we employ the concept of the risk premium. The obtained theoretical results are then used for the European Energy Exchange data analysis. We calculate the risk premium in the case of the calibrated 3-regime MRS model. We find a time varying structure of the risk premium and an evidence for a negative risk premium (or positive forward premium), especially at short times before delivery. Finally, we use the obtained risk premium to calculate prices of European options written on spot, as well as, forward prices.

In this paper we discuss the calibration of models built on mean-reverting processes combined with Markov regime-switching (MRS). We propose a method that greatly reduces the computational burden induced by the introduction of independent regimes and perform a simulation study to test its efficiency. Our method allows for a 100 to over 1000 times faster calibration than in case of a competing approach utilizing probabilities of the last 10 observations. It is also more general and admits any value of gamma in the base regime dynamics. Since the motivation for this research comes from a recent stream of literature in energy economics, we apply the new method to sample series of electricity spot prices from the German EEX and Australian NSW markets. The proposed MRS models fit these datasets well and replicate the major stylized facts of electricity spot price dynamics.