text: We find empirical evidence that mean-reverting jump processes are not statistically adequate to model electricity spot price spikes but independent, signed sums of such processes are statistically adequate. Further we demonstrate a change in the composition of these sums after a major economic event. This is achieved by developing a Markov Chain Monte Carlo (MCMC) procedure for Bayesian model calibration and a Bayesian assessment of model adequacy (posterior predictive checking). In particular we determine the number of signed mean-reverting jump components required in the APXUK and EEX markets, in time periods both before and after the recent global financial crises. Statistically, consistent structural changes occur across both markets, with a reduction of the intensity and size, or the disappearance, of positive price spikes in the later period. All code and data are provided to enable replication of results.
  @cite_5: This paper discusses practical Bayesian estimation of stochastic volatility models based on OU processes with marginal Gamma laws. Estimation is based on a parameterization which is derived from the Rosinski representation, and has the advantage of being a non-centered parameterization. The parameterization is based on a marked point process, living on the positive real line, with uniformly distributed marks. We define a Markov chain Monte Carlo (MCMC) scheme which enables multiple updates of the latent point process, and generalizes single updating algorithm used earlier. At each MCMC draw more than one point is added or deleted from the latent point process. This is particularly useful for high intensity processes. Furthermore, the article deals with superposition models, where it discuss how the identifiability problem inherent in the superposition model may be avoided by the use of a Markov prior. Finally, applications to simulated data as well as exchange rate data are discussed.
  @cite_3: Continuous-time stochastic volatility models are becoming an increasingly popular way to describe moderate and high-frequency financial data. Barndorff-Nielsen and Shephard (2001a) proposed a class of models where the volatility behaves according to an Ornstein–Uhlenbeck (OU) process, driven by a positive Levy process without Gaussian component. These models introduce discontinuities, or jumps, into the volatility process. They also consider superpositions of such processes and we extend that to the inclusion of a jump component in the returns. In addition, we allow for leverage effects and we introduce separate risk pricing for the volatility components. We design and implement practically relevant inference methods for such models, within the Bayesian paradigm. The algorithm is based on Markov chain Monte Carlo (MCMC) methods and we use a series representation of Levy processes. MCMC methods for such models are complicated by the fact that parameter changes will often induce a change in the distribution of the representation of the process and the associated problem of overconditioning. We avoid this problem by dependent thinning methods. An application to stock price data shows the models perform very well, even in the face of data with rapid changes, especially if a superposition of processes with different risk premiums and a leverage effect is used.
  @cite_2: We develop Markov chain Monte Carlo methodology for Bayesian inference for non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes. The approach introduced involves expressing the unobserved stochastic volatility process in terms of a suitable marked Poisson process. We introduce two specific classes of Metropolis-Hastings algorithms which correspond to different ways of jointly parameterizing the marked point process and the model parameters. The performance of the methods is investigated for different types of simulated data. The approach is extended to consider the case where the volatility process is expressed as a superposition of Ornstein-Uhlenbeck processes. We apply our methodology to the US dollar-Deutschmark exchange rate. Copyright 2004 Royal Statistical Society.
summary: In related contexts, MCMC has been applied to fit continuous-time stochastic volatility models to financial time series, where the price is a diffusion process whose volatility is a latent mean reverting jump process or the sum of a number of such processes (called a superposition model). In this line of research a missing data methodology is employed whereby the observed process is augmented with one or more latent marked Poisson processes and the MCMC procedure generates posterior samples in this high dimensional augmented state space. Examples include @cite_2 , @cite_3 and @cite_5 . Since energy prices additionally exhibit jumps directly in their paths, MCMC has been applied to extensions of these models in which a diffusion process with stochastic volatility is superposed with a jump process, see in the context of electricity and for gas prices. Technically the latter two papers estimate a discrete approximation of the models whereas in this study we pursue inference for continuous time models.