ABSTRACT
The concept of entropy is not uniquely relevant to the statistical mechanics but, among others, it can play pivotal role in the analysis of a time series, particularly the stock market data. In this area, sudden events are especially interesting as they describe abrupt data changes with potentially long-lasting effects. Here, we investigate the impact of such events on the entropy of financial time series. As a case study, we assume data of the Polish stock market, in the context of its main cumulative index, and discuss it for the finite time periods before and after outbreak of the 2022 Russian invasion of Ukraine. This analysis allows us to validate the entropy-based methodology in assessing changes in the market volatility, as driven by the extreme external factors. We show that some qualitative features of such market variations can be well captured in terms of the entropy. In particular, the discussed measure appears to highlight differences between data of the two considered timeframes in agreement with the character of their empirical distributions, which is not always the case in terms of the conventional standard deviation. Moreover, the entropy of cumulative index averages, qualitatively, the entropies of composing assets, suggesting capability for describing interdependencies between them. The entropy is also found to exhibit signatures of the upcoming extreme events. To this end, the role of recent war in shaping the current economic situation is briefly discussed.
ABSTRACT
In the framework of the mimetic approach, we study the [Formula: see text] gravity with the Lagrange multiplier constraint and the scalar potential. We introduce field equations for the discussed theory and overview their properties. By using the general reconstruction scheme we obtain the power law cosmology model for the [Formula: see text] case as well as the model that describes symmetric bounce. Moreover, we reconstruct model, unifying both matter dominated and accelerated phases, where ordinary matter is neglected. Using inverted reconstruction scheme we recover specific [Formula: see text] function which give rise to the de-Sitter evolution. Finally, by employing the perfect fluid approach, we demonstrate that this model can realize inflation consistent with the bounds coming from the BICEP2/Keck array and the Planck data. We also discuss the holographic dark energy density in terms of the presented [Formula: see text] theory. Thus, it is suggested that the introduced extension of the mimetic regime may describe any given cosmological model.
ABSTRACT
Recently introduced [Formula: see text] theory is generalized by adding dependence on the arbitrary scalar field [Formula: see text] and its kinetic term [Formula: see text], to explore non-minimal interactions between geometry, scalar and matter fields in context of the Gauss-Bonnet theories. The field equations for the resulting [Formula: see text] theory are obtained and show that particles follow non-geodesic trajectories in a perfect fluid surrounding. The energy conditions in the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime are discussed for the generic function [Formula: see text]. As an application of the introduced extensions, using the reconstruction techniques we obtain functions that satisfy common cosmological models, along with the equations describing energy conditions for the reconstructed [Formula: see text] gravity. The detailed discussion of the energy conditions for the de Sitter and power-law spacetimes is provided in terms of the fixed kinetic term i.e. in the [Formula: see text] case. Moreover, in order to check viability of the reconstructed models, we discuss the energy conditions in the specific cases, namely the [Formula: see text] and [Formula: see text] approaches. We show, that for the appropriate choice of parameters and constants, the energy conditions can be satisfied for the discussed scenarios.
