arXiv subjects

A. Bahraminasab

Publications and source records attributed to A. Bahraminasab.

10 recordsLinked to original sources

arXiv2007

Uncertainty in the Fluctuations of the Price of Stocks

We report on a study of the Tehran Price Index (TEPIX) from 2001 to 2006 as an emerging market that has been affected by several political crises during the recent years, and analyze the non-Gaussian probability density function (PDF) of the log returns of the stocks' prices. We show that while the average of the index did not fall very much over the time period of the study, its day-to-day fluctuations strongly increased due to the crises. Using an approach based on multiplicative processes with a detrending procedure, we study the scale-dependence of the non-Gaussian PDFs, and show that the temporal dependence of their tails indicates a gradual and systematic increase in the probability of the appearance of large increments in the returns on approaching distinct critical time scales over which the TEPIX has exhibited maximum uncertainty.

q-fin.ST↗

arXiv2007

Why does the Standard GARCH(1,1) model work well?

The AutoRegressive Conditional Heteroskedasticity (ARCH) and its generalized version (GARCH) family of models have grown to encompass a wide range of specifications, each of them is designed to enhance the ability of the model to capture the characteristics of stochastic data, such as financial time series. The existing literature provides little guidance on how to select optimal parameters, which are critical in efficiency of the model, among the infinite range of available parameters. We introduce a new criterion to find suitable parameters in GARCH models by using Markov length, which is the minimum time interval over which the data can be considered as constituting a Markov process. This criterion is applied to various time series and results support the known idea that GARCH(1,1) model works well.

physics.data-an↗

arXiv2006

Stochastic $ϕ^4-$Theory in the Strong Coupling Limit

The stochastic $ϕ^4$-theory in $d-$dimensions dynamically develops domain wall structures within which the order parameter is not continuous. We develop a statistical theory for the $ϕ^4$-theory driven with a random forcing which is white in time and Gaussian-correlated in space. A master equation is derived for the probability density function (PDF) of the order parameter, when the forcing correlation length is much smaller than the system size, but much larger than the typical width of the domain walls. Moreover, exact expressions for the one-point PDF and all the moments $<ϕ^n>$ are given. We then investigate the intermittency issue in the strong coupling limit, and derive the tail of the PDF of the increments $ϕ(x_2) - ϕ(x_1)$. The scaling laws for the structure functions of the increments are obtained through numerical simulations. It is shown that the moments of field increments defined by, $C_b=< |ϕ(x_2)-ϕ(x_1)|^b>$, behave as $|x_1-x_2|^{ξ_b}$, where $ξ_b=b$ for $b\leq 1$, and $ξ_b=1$ for $b\geq1$

cond-mat.other↗

arXiv2006

Level Crossing Analysis of Burgers Equation in 1+1 Dimensions

We investigate the average frequency of positive slope $ν_α^{+}$, crossing the velocity field $u(x)- \bar u = α$ in the Burgers equation. The level crossing analysis in the inviscid limit and total number of positive crossing of velocity field before creation of singularities are given. The main goal of this paper is to show that this quantity, $ν_α^{+}$, is a good measure for the fluctuations of velocity fields in the Burgers turbulence.

cond-mat.stat-mech↗

arXiv2006

Exact Analysis of Level-Crossing Statistics for (d+1)-Dimensional Fluctuating Surfaces

We carry out an exact analysis of the average frequency $ν_{αx_i}^+$ in the direction $x_i$ of positive-slope crossing of a given level $α$ such that, $h({\bf x},t)-\bar{h}=α$, of growing surfaces in spatial dimension $d$. Here, $h({\bf x},t)$ is the surface height at time $t$, and $\bar{h}$ is its mean value. We analyze the problem when the surface growth dynamics is governed by the Kardar-Parisi-Zhang (KPZ) equation without surface tension, in the time regime prior to appearance of cusp singularities (sharp valleys), as well as in the random deposition (RD) model. The total number $N^+$ of such level-crossings with positive slope in all the directions is then shown to scale with time as $t^{d/2}$ for both the KPZ equation and the RD model.

cond-mat.stat-mech↗

arXiv2006

Characteristic Angular Scales in Cosmic Microwave Background Radiation

We investigate the stochasticity in temperature fluctuations in the cosmic microwave background (CMB) radiation data from {\it Wilkinson Microwave Anisotropy Probe}. We show that the angular fluctuations of the temperature is a Markov process with a {\it Markov angular scale}, $Θ_{\rm Markov}=1.01^{+0.09}_{-0.07}$. We characterize the complexity of the CMB fluctuations by means of a Fokker-Planck or Langevin equation and measure the associated Kramers-Moyal coefficients for the fluctuating temperature field $T(\hat n)$ and its increment, $ΔT =T(\hat n_1) - T(\hat n_2)$. Through this method we show that temperature fluctuations in the CMB has fat tails compared to a Gaussian distribution.

astro-ph↗

arXiv2005

Dynamics of the Markov Time Scale of Seismic Activity May Provide a Short-Term Alert for Earthquakes

We propose a novel method for analyzing precursory seismic data before an earthquake that treats them as a Markov process and distinguishes the background noise from real fluctuations due to an earthquake. A short time (on the order of several hours) before an earthquake the Markov time scale $t_M$ increases sharply, hence providing an alarm for an impending earthquake. To distinguish a false alarm from a reliable one, we compute a second quantity, $T_1$, based on the concept of extended self-similarity of the data. $T_1$ also changes strongly before an earthquake occurs. An alarm is accepted if {\it both} $t_M$ and $T_1$ indicate it {\it simultaneously}. Calibrating the method with the data for one region provides a tool for predicting an impending earthquake within that region. Our analysis of the data for a large number of earthquakes indicate an essentially zero rate of failure for the method.

physics.geo-ph↗

arXiv2005

Zero tension Kardar-Parisi-Zhang equation in (d+1)- Dimensions

The joint probability distribution function (PDF) of the height and its gradients is derived for a zero tension $d+1$-dimensional Kardar-Parisi-Zhang (KPZ) equation. It is proved that the height`s PDF of zero tension KPZ equation shows lack of positivity after a finite time $t_{c}$. The properties of zero tension KPZ equation and its differences with the case that it possess an infinitesimal surface tension is discussed. Also potential relation between the time scale $t_{c}$ and the singularity time scale $t_{c, ν\to 0}$ of the KPZ equation with an infinitesimal surface tension is investigated.

nlin.CD↗

arXiv2005

Intermittency of Height Fluctuations and Velocity Increment of The Kardar-Parisi-Zhang and Burgers Equations with infinitesimal surface tension and Viscosity in 1+1 Dimensions

The Kardar-Parisi-Zhang (KPZ) equation with infinitesimal surface tension, dynamically develops sharply connected valley structures within which the height derivative is not continuous. We discuss the intermittency issue in the problem of stationary state forced KPZ equation in 1+1--dimensions. It is proved that the moments of height increments $C_a = < | h (x_1) - h (x_2) |^a > $ behave as $ |x_1 -x_2|^{ξ_a}$ with $ξ_a = a$ for length scales $|x_1-x_2| << σ$. The length scale $σ$ is the characteristic length of the forcing term. We have checked the analytical results by direct numerical simulation.

physics.flu-dyn↗

arXiv2004

Mid-Infrared Radiation as a Short-Term Earthquake Precursor

Recently it has been found by F. Freund that the granite under high pressure undergoes a phase transition from insulator to a p-type semiconductor. This phase transition is a key concept to understanding pre-earthquake phenomena. This effect accompanies with the radiation of the granite in the mid-infrared region. we were able to predict the recent earthquake in the south of Iran by monitoring this radiation.

physics.geo-ph↗