Several economical time series such as exchange rates US$/British Pound, USA Treasure Bonds rates and Warsaw Stock Index WIG have been investigated using the method of recurrence plots. The percentage of recurrence REC and the percentage of determinism DET have been calculated for the original and for shuffled data. We have found that in some cases the values of REC and DET parameters are about 20% lower for the surrogate data which indicates the presence of unstable periodical orbits in the considered data. A similar result has been obtained for the chaotic Lorenz model contaminated by noise. Our investigations suggest that real economical dynamics is a mixture of deterministic and stochastic chaos. We show how a simple chaotic economic model can be controlled by appropriate influence of time-delayed feedback.

Selected data from Polish and USA stock and bond markets as well as foreign-exchange data have been analysed by the use of recurrence plots and the Hurst method. It has been found that there exist significant correlations in some of analysed data chains. Values of recurrence ratios and ratios of determinism calculated from recurrence diagrams decrease significantly if one shuffles the data. The corresponding values of Hurst exponents are in the range 0.56–0.74 and they also decrease after shuffling. The lowest values of the Hurst exponent have been found for single shares at Polish stock market while the highest values are related to foreign-exchange data. The mean length of the cycle calculated from the behaviour of the Hurst exponent for Dow Jones index and S&P500 index is about 5 years while the Warsaw Stock Index WIG possesses the corresponding cycle of order of 11 months. The performed analysis shows that in the economical dynamics the main role is played by stochastic behaviour but traces of deterministic origin can be also seen.

Alternating current stimulation is a promising method for the study and treatment of various visual neurological dysfunctions as well as progressive understanding of the healthy brain. Unfortunately, due to the current stimulation artifact, problems remain in the context of analysis of the electroencephalography (EEG) signal recorded during ongoing stimulation. To address this problem, we propose the use of a simple moving average subtraction as a method for artifact elimination. This method involves the creation of a template of the stimulation artifact from EEG signal recorded during non-invasive electrical stimulation with a sinusoidal alternating current. The present report describes results of the effects of a simple moving average filtration that varies based on averaging parameters; in particular, we varied the number of sinusoidal periods per segment of the recorded signal and the number of segments used to construct an artifact template. Given the ongoing lack of a mathematical model that allows for the prediction of the “hidden” EEG signal with the alternating current stimulation artifact, we propose performing an earlier simulation that is based on the addition of artificial stimulation artifact to the known EEG signal. This solution allows for the optimization of filtering parameters with detailed knowledge about the accuracy of artifact removal. The algorithm, designed in the MATLAB environment, has been tested on data recorded from two volunteers subjected to sinusoidal transorbital alternating current stimulation. Analysis of the percentage difference between the original and filtered signal in time and frequency domain highlights the advantage of 1-period filtration.