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An ongoing rapid development in single particle tracking techniques has opened new possibilities for analysis of particles dynamics inside living cells. Assuming that the motion is governed by a fractional Brownian motion, we have generated a synthetic video resembling a real one from an experimental video of G-proteins and coupled with them receptors inside living cells. Next, we applied Brownian bridge method to study two fundamental analysis tasks on trajectory data: segmentation and classification in context of experimental data. We have shown that, depending on the method of dealing with missing data, the obtained results might vary significantly, obviously influencing the final conclusions.

Solar flares are large explosions in the sun’s atmosphere. They can damage satellites and overload electrical systems. To manage that risk, finding methods of efficiently predicting future events is very important. In this paper we introduce a full-Sun flare prediction method based on the Hidden Markov modelling with two hidden states. We concentrate on the soft X-ray emission data near the minimum of solar cycle and consider two different driving dynamics for both states, namely the independent identically distributed (IID) random variables and the autoregressive (AR) processes, the latter introducing a memory structure. We compare prediction performance for the IID and AR approaches and also with a naive prediction equal to the last observation. The solar X-flux dynamics is predicted by using the day-ahead forecasts. We calculate point and interval forecasts and perform relevant statistical tests to choose the best method. It appears that the AR approach is clearly superior to the IID and naive both by means of point and interval forecasts. Moreover, it can well detect the higher state which can lead to very strong energy releases. Significant development of the model would be necessary to forecast solar flares over an entire solar cycle.

We present a systematic statistical analysis of the recently measured individual trajectories of fluorescently labeled telomeres in the nucleus of living human cells. The experiments were performed in the U2OS cancer cell line. We propose an algorithm for identification of the telomere motion. By expanding the previously published data set, we are able to explore the dynamics in six time orders, a task not possible earlier. As a result, we establish a rigorous mathematical characterization of the stochastic process and identify the basic mathematical mechanisms behind the telomere motion. We find that the increments of the motion are stationary, Gaussian, ergodic, and even more chaotic—mixing. Moreover, the obtained memory parameter estimates, as well as the ensemble average mean square displacement reveal subdiffusive behavior at all time spans. All these findings statistically prove a fractional Brownian motion for the telomere trajectories, which is confirmed by a generalized p-variation test. Taking into account the biophysical nature of telomeres as monomers in the chromatin chain, we suggest polymer dynamics as a sufficient framework for their motion with no influence of other models. In addition, these results shed light on other studies of telomere motion and the alternative telomere lengthening mechanism. We hope that identification of these mechanisms will allow the development of a proper physical and biological model for telomere subdynamics. This array of tests can be easily implemented to other data sets to enable quick and accurate analysis of their statistical characteristics.

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.

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.