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 γ 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.

Single-particle tracking (SPT) has become a popular tool to study the intracellular transport of molecules in living cells. Inferring the character of their dynamics is important, because it determines the organization and functions of the cells. For this reason, one of the first steps in the analysis of SPT data is the identification of the diffusion type of the observed particles. The most popular method to identify the class of a trajectory is based on the mean-square displacement (MSD). However, due to its known limitations, several other approaches have been already proposed. With the recent advances in algorithms and the developments of modern hardware, the classification attempts rooted in machine learning (ML) are of particular interest. In this work, we adopt two ML ensemble algorithms, i.e., random forest and gradient boosting, to the problem of trajectory classification. We present a new set of features used to transform the raw trajectories data into input vectors required by the classifiers. The resulting models are then applied to real data for G protein-coupled receptors and G proteins. The classification results are compared to recent statistical methods going beyond MSD.

In this paper, we deal with a problem of local damage detection in bearings in the presence of a high-energy impulsive noise. Such a problem was identified during diagnostics of bearings in raw materials crusher. Unfortunately, classical approaches cannot be applied due to the impulsive character of the noise. In this paper we propose, a procedure that cancels out impulsive noise rather than extracts signal of interest. The methodology is based on the regime switching model with two regimes: first corresponding to high-energy noncyclic impulses and second to the rest of the signal. We apply the proposed technique to a simulated signal as well as to the real one. Effectiveness of the method is presented graphically using time series, time-frequency spectrogram, and classical envelope analysis. The obtained results indicate efficiency of the method in impulsive noise cancellation and improve the ability to detect a damage.