Vygintas Gontis

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We present a simple point process model of 1/f(beta) noise, covering different values of the exponent beta . The signal of the model consists of pulses or events. The interpulse, interevent, interarrival, recurrence, or waiting times of the signal are described by the general Langevin equation with the multiplicative noise and stochastically diffuse in some(More)
We are looking for the agent-based treatment of the financial markets considering necessity to build bridges between microscopic, agent based, and macroscopic, phenomenological modeling. The acknowledgment that agent-based modeling framework, which may provide qualitative and quantitative understanding of the financial markets, is very ambiguous emphasizes(More)
A simple analytically solvable model exhibiting a 1/f spectrum in an arbitrarily wide frequency range was recently proposed by Kaulakys and Meškauskas (KM). Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is Brownian fluctuations of the average intervent time between subsequent pulses of the pulse sequence. We(More)
We investigate the volatility return intervals in the NYSE and FOREX markets. We explain previous empirical findings using a model based on the interacting agent hypothesis instead of the widely-used efficient market hypothesis. We derive macroscopic equations based on the microscopic herding interactions of agents and find that they are able to reproduce(More)
We introduce the stochastic multiplicative point process modelling trading activity of financial markets. Such a model system exhibits power-law spectral density S(f) ∝ 1/f , scaled as power of frequency for various values of β between 0.5 and 2. Furthermore, we analyze the relation between the power-law autocorrelations and the origin of the power-law(More)
We investigate large changes, bursts, of the continuous stochastic signals, when the exponent of multiplicativity is higher than one. Earlier we have proposed a general nonlinear stochastic model which can be transformed into Bessel process with known first hitting (first passage) time statistics. Using these results we derive PDF of burst duration for the(More)
We propose the point process model as the Poissonian-like stochastic sequence with slowly diffusing mean rate and adjust the parameters of the model to the empirical data of trading activity for 26 stocks traded on NYSE. The proposed scaled stochastic differential equation provides the universal description of the trading activities with the same parameters(More)
We present examples of agent-based and stochastic models of competition and business processes in economics and finance. We start from as simple as possible models, which have microscopic, agent-based, versions and macroscopic treatment in behavior. Microscopic and macroscopic versions of herding model proposed by Kirman and Bass diffusion of new products(More)