Related papers: Asymmetric Tsallis distributions for modelling fin…
We provide an update of the overview of imprints of Tsallis nonextensive statistics seen in a multiparticle production processes. They reveal an ubiquitous presence of power law distributions of different variables characterized by the…
The non-extensive statistical mechanics has been applied to describe a variety of complex systems with inherent correlations and feedback loops. Here we present a dynamical model based on previously proposed static model exhibiting in the…
The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation…
We analyze the Standard & Poor's 500 stock market index from the last 22 years. The probability density function of price returns exhibits two well-distinguished regimes with self-similar structure: the first one displays strong…
The distribution of the return intervals $\tau$ between volatilities above a threshold $q$ for financial records has been approximated by a scaling behavior. To explore how accurate is the scaling and therefore understand the underlined…
In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the…
Several works have observed heavy-tailed behavior in the distributions of returns in different markets, which are observable indicators of underlying complex dynamics. Such prior works study return distributions that are marginalized across…
Stylized facts of empirical assets log-returns $Z$ include the existence of (semi) heavy tailed distributions $f_Z(z)$ and a non-linear spectrum of Hurst exponents $\tau(\beta)$. Empirical data considered are daily prices of 10 large…
This paper builds a model of high-frequency equity returns by separately modeling the dynamics of trade-time returns and trade arrivals. Our main contributions are threefold. First, we characterize the distributional behavior of…
We study the distribution of fluctuations over a time scale $\Delta t$ (i.e., the returns) of the S&P 500 index by analyzing three distinct databases. Database (i) contains approximately 1 million records sampled at 1 min intervals for the…
Symmetries play a conspicuous role in the large-scale behavior of critical systems. While in equilibrium they allow to classify asymptotics into different universality classes, out of equilibrium they can emerge, some times unexpectedly, as…
The q-Gaussians are discussed from the point of view of variance mixtures of normals and exchangeability. For each q< 3, there is a q-Gaussian distribution that maximizes the Tsallis entropy under suitable constraints. This paper shows that…
Standard quantitative models of the stock market predict a log-normal distribution for stock returns (Bachelier 1900, Osborne 1959), but it is recognised (Fama 1965) that empirical data, in comparison with a Gaussian, exhibit leptokurtosis…
The observable outputs of many complex dynamical systems consist in time series exhibiting autocorrelation functions of great diversity of behaviors, including long-range power-law autocorrelation functions, as a signature of interactions…
Tsallis statistics (or q-statistics) in nonextensive statistical mechanics is a one-parameter description of correlated states. In this paper we use a translated entropic index: $1 - q \to q$ . The essence of this translation is to improve…
We establish an analogy between the motion of spring whose mass increases linearly with time and volatile stock markets dynamics within an economic model based on simple temporal demand and supply functions [J. Phys. A: Math. Gen. 33, 3637…
We derive and study quasicanonical Gibbs distribution function which is characterized by the thermostat with finite number of particles (quasithermostat). We show that this naturally leads to Tsallis nonextensive statistics and…
In the present work, we have found that the phenomenological Tsallis distribution (which nowadays is largely used to describe the transverse momentum distributions of hadrons measured in $pp$ collisions at high energies) is consistent with…
The modelling of financial markets presents a problem which is both theoretically challenging and practically important. The theoretical aspects concern the issue of market efficiency which may even have political implications…
Superstatistics are superpositions of different statistics relevant for driven nonequilibrium systems with spatiotemporal inhomogeneities of an intensive variable (e.g., the inverse temperature). They contain Tsallis statistics as a special…