Related papers: Multiplicative point process as a model of trading…
In this paper we explain the wild fluctuations of financial prices from the intrinsic amplifying feedback of speculative supply and demand. Formally, we show that an asset return follows a multiplicative random growth with exogenous input,…
Stock price changes occur through transactions, just as diffusion in physical systems occurs through molecular collisions. We systematically explore this analogy and quantify the relation between trading activity - measured by the number of…
Intermittent transitions, associated with critical dynamics and characterized by power-law distributions, are commonly observed during sleep. These critical behaviors are evident at the microscopic level through neuronal avalanches and at…
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…
Complex systems comprise a large number of interacting elements, whose dynamics is not always a priori known. In these cases -- in order to uncover their key features -- we have to turn to empirical methods, one of which was recently…
The origin of the low-frequency noise with power spectrum $1/f^\beta$ (also known as $1/f$ fluctuations or flicker noise) remains a challenge. Recently, the nonlinear stochastic differential equations for modeling $1/f^\beta$ noise have…
We analyze the sequence of time intervals between consecutive stock trades of thirty companies representing eight sectors of the U. S. economy over a period of four years. For all companies we find that: (i) the probability density function…
We consider Feller mean-reverting square-root diffusion, which has been applied to model a wide variety of processes with linearly state-dependent diffusion, such as stochastic volatility and interest rates in finance, and neuronal and…
This paper presents a method for forecasting limit order book durations using a self-exciting flexible residual point process. High-frequency events in modern exchanges exhibit heavy-tailed interarrival times, posing a significant challenge…
Protein concentration in a living cell fluctuates over time due to noise in growth and division processes. From extensive single-cell experiments by using E. coli strains with different promoter strength (over two orders of magnitude) and…
Motivated by how transaction amount constrain trading volume and price volatility in stock market, we, in this paper, study the relation between volume and price if amount of transaction is given. We find that accumulative trading volume…
It is widely accepted that there is strong persistence in the volatility of financial time series. The origin of the observed persistence, or long-range memory, is still an open problem as the observed phenomenon could be a spurious effect.…
.Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments…
Using empirical data from a social media site (Twitter) and on trading volumes of financial securities, we analyze the correlated human activity in massive social organizations. The activity, typically excited by real-world events and…
Many human-related activities show power-law decaying interevent time distribution with exponents usually varying between 1 and 2. We study a simple task-queuing model, which produces bursty time series due to the nontrivial dynamics of the…
Time series datasets often contain heterogeneous signals, composed of both continuously changing quantities and discretely occurring events. The coupling between these measurements may provide insights into key underlying mechanisms of the…
We replicate a renewal process at random times, which is equivalent to nesting two renewal processes, or considering a renewal process subject to stochastic resetting. We investigate the consequences on the statistical properties of the…
In the study of complex networks (systems), the scaling phenomenon of flow fluctuations refers to a certain power-law between the mean flux (activity) $<F_i>$ of the $i$th node and its variance $\sigma_i$ as $\sigma_i \propto < F_{i} >…
We study the activity, i.e., the number of transactions per unit time, of financial markets. Using the diffusion entropy technique we show that the autocorrelation of the activity is caused by the presence of peaks whose time distances are…
This article present a continuous cascade model of volatility formulated as a stochastic differential equation. Two independent Brownian motions are introduced as random sources triggering the volatility cascade. One multiplicatively…