Related papers: Small scale behavior of financial data

Prices of commodities or assets produce what is called time-series. Different kinds of financial time-series have been recorded and studied for decades. Nowadays, all transactions on a financial market are recorded, leading to a huge amount…

Many stochastic time series can be modelled by discrete random walks in which a step of random sign but constant length $\delta x$ is performed after each time interval $\delta t$. In correlated discrete time random walks (CDTRWs), the…

We establish new results for estimation and inference in financial durations models, where events are observed over a given time span, such as a trading day, or a week. For the classical autoregressive conditional duration (ACD) models by…

Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the…

A general approach to a broad class of asymptotic problems related to long-time influence of small perturbations, of both deterministic and stochastic type, is presented in the paper. The main characteristic of this influence is a limiting…

We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…

Turbulent flows in three dimensions are characterized by the transport of energy from large to small scales through the energy cascade. Since the small scales are the result of the nonlinear dynamics across the scales, they are often…

We show that recent stock market fluctuations are characterized by the cumulative distributions whose tails on short, minute time scales exhibit power scaling with the scaling index alpha > 3 and this index tends to increase quickly with…

We revisit the statistics of extremes and records of symmetric random walks with stochastic resetting, extending earlier studies in several directions. We put forward a diffusive scaling regime (symmetric step length distribution with…

We find a nonlinear dependence between an indicator of the degree of multiscaling of log-price time series of a stock and the average correlation of the stock with respect to the other stocks traded in the same market. This result is a…

A most debated topic of the last years is whether simple statistical physics models can explain collective features of social dynamics. A necessary step in this line of endeavour is to find regularities in data referring to large scale…

Using frequency distributions of daily closing price time series of several financial market indexes, we investigate whether the bias away from an equiprobable sequence distribution found in the data, predicted by algorithmic information…

The methods of statistical physics of open systems are used for describing the time dependence of economic characteristics (income, profit, cost, supply, currency etc.) and their correlations with each other. Nonlinear equations (analogies…

Large variations in stock prices happen with sufficient frequency to raise doubts about existing models, which all fail to account for non-Gaussian statistics. We construct simple models of a stock market, and argue that the large…

Being able to predict the occurrence of extreme returns is important in financial risk management. Using the distribution of recurrence intervals---the waiting time between consecutive extremes---we show that these extreme returns are…

We study the distributions of event-time returns and clock-time returns at different microscopic timescales using ultra-high-frequency data extracted from the limit-order books of 23 stocks traded in the Chinese stock market in 2003. We…

The fluctuations are termed mesoscopic, when their typical size is essentially larger then the average distance between the nearest neighbors, while being much smaller than the overall system size. Since the features of mesoscopic…

Empirical analyses of ordinal outcomes using repeated cross-sectional data rely on marginal distributions, leaving the joint distribution unobserved and the sources of distributional change unidentified. This paper develops a framework to…

Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…

Earlier we showed that the fine structure of the spectrum of amplitude variations in the results of measurements of the processes of different nature (in other words, the fine structure of the dispersion of results or the pattern of the…