News might trigger jump arrivals in financial time series. The “bad” news and “good” news seem to have distinct impact. In the research, a double exponential jump distribution is applied to model downward and upward jumps. Bayesian double exponential jump-diffusion model is proposed. Theorems stated in the paper enable estimation of the model’s parameters, detection of jumps and analysis of jump frequency. The methodology, founded upon the idea of latent variables, is illustrated with simulated data.

The safety of mining operations in hard coal mines must be constantly developed and improved. There is ongoing multi-directional research focused at best recognition of the phenomenon associated with the properties of the coal-gas system and its connections with mining and geological conditions. This article presents the results of sorption experiments on coals from the Upper Silesian Coal Basin, which are characterized by varying degrees of coalification. One of the parameters that describes the kinetics of methane sorption, determining and providing valuable information about gas hazard and in particular the risk of gas and rock outbursts, is the effective diffusion coefficient De. It is derived from the solution of Fick’s second law using many simplifying assumptions. Among them is the assumption that the carbon matrix consists of only one type of pore – micropores. In fact, there are quite often at least two different mechanisms, which are connected to each other, related to the diffusion of methane from the microporous matrix and flows occurring in voids and macropores. This article presents both the unipore and bidisperse models and a set of comparisons which fit them to experimental curves for selected coals. For some samples the more complex bidisperse model gave much better results than the classic unipore one. The supremacy of the bidisperse model could be associated with the differences in the coal structure related to the coalification degree. Initial results justify further analyses on a wider set of coals using the methodology developed in this paper.

A Bayesian stochastic volatility model with a leverage effect, normal errors and jump component with the double exponential distribution of a jump value is proposed. The ready to use Gibbs sampler is presented, which enables one to conduct statistical inference. In the empirical study, the SVLEDEJ model is applied to model logarithmic growth rates of one month forward gas prices. The results reveal an important role of both jump and stochastic volatility components.

In the paper we present and apply a Bayesian jump-diffusion model and stochastic volatility models with jumps. The problem of how to classify an observation as a result of a jump is addressed, under the Bayesian approach, by introducing latent variables. The empirical study is focused on the time series of gas forward contract prices and EUA futures prices. We analyse the frequency of jumps and relate the moments in which jumps occur to calendar effects or political and economic events and decisions. The calendar effects explain many jumps in gas contract prices. The single jump is identified in the EUA futures prices under the SV-type models. The jump is detected on the day the European Parliament voted against the European Commission’s proposal of backloading. The Bayesian results are compared with the outcomes of selected non-Bayesian techniques used for detecting jumps.