355 research outputs found
Modeling electricity loads in California: a continuous-time approach
In this paper we address the issue of modeling electricity loads and prices
with diffusion processes. More specifically, we study models which belong to
the class of generalized Ornstein-Uhlenbeck processes. After comparing
properties of simulated paths with those of deseasonalized data from the
California power market and performing out-of-sample forecasts we conclude
that, despite certain advantages, the analyzed continuous-time processes are
not adequate models of electricity load and price dynamics.Comment: To be published in Physica A (2001): Proceedings of the NATO ARW on
Application of Physics in Economic Modelling, Prague, Feb. 8-10, 200
Relaxation under outflow dynamics with random sequential updating
In this paper we compare the relaxation in several versions of the Sznajd
model (SM) with random sequential updating on the chain and square lattice. We
start by reviewing briefly all proposed one dimensional versions of SM. Next,
we compare the results obtained from Monte Carlo simulations with the mean
field results obtained by Slanina and Lavicka . Finally, we investigate the
relaxation on the square lattice and compare two generalizations of SM, one
suggested by Stauffer and another by Galam. We show that there are no
qualitative differences between these two approaches, although the relaxation
within the Galam rule is faster than within the well known Stauffer rule.Comment: 9 figure
How effective is advertising in duopoly markets?
A simple Ising spin model which can describe the mechanism of advertising in
a duopoly market is proposed. In contrast to other agent-based models, the
influence does not flow inward from the surrounding neighbors to the center
site, but spreads outward from the center to the neighbors. The model thus
describes the spread of opinions among customers. It is shown via standard
Monte Carlo simulations that very simple rules and inclusion of an external
field -- an advertising campaign -- lead to phase transitions.Comment: 7 pages, 6 figures; v2: cosmetic change
Continuous Opinions and Discrete Actions in Opinion Dynamics Problems
A model where agents show discrete behavior regarding their actions, but have
continuous opinions that are updated by interacting with other agents is
presented. This new updating rule is applied to both the voter and Sznajd
models for interaction between neighbors and its consequences are discussed.
The appearance of extremists is naturally observed and it seems to be a
characteristic of this model.Comment: 10 pages, 4 figures, minor changes for improved clarit
Time dependence of the survival probability of an opinion in a closed community
The time dependence of the survival probability of an opinion in a closed
community has been investigated in accordance with social temperature by using
the Kawasaki-exchange dynamics based on previous study in Ref. [1]. It is shown
that the survival probability of opinion decays with stretched exponential law
consistent with previous static model. However, the crossover regime in the
decay of the survival probability has been observed in this dynamic model
unlike previous model. The decay characteristics of both two regimes obey to
stretched exponential.Comment: Revised version of the paper (9 page, 5 Figures). Submitted to Int.
J. Mod. Phys.
Black swans or dragon kings? A simple test for deviations from the power law
We develop a simple test for deviations from power law tails, which is based
on the asymptotic properties of the empirical distribution function. We use
this test to answer the question whether great natural disasters, financial
crashes or electricity price spikes should be classified as dragon kings or
'only' as black swans
Entropy of the Nordic electricity market: anomalous scaling, spikes, and mean-reversion
The electricity market is a very peculiar market due to the large variety of
phenomena that can affect the spot price. However, this market still shows many
typical features of other speculative (commodity) markets like, for instance,
data clustering and mean reversion. We apply the diffusion entropy analysis
(DEA) to the Nordic spot electricity market (Nord Pool). We study the waiting
time statistics between consecutive spot price spikes and find it to show
anomalous scaling characterized by a decaying power-law. The exponent observed
in data follows a quite robust relationship with the one implied by the DEA
analysis. We also in terms of the DEA revisit topics like clustering,
mean-reversion and periodicities. We finally propose a GARCH inspired model but
for the price itself. Models in the context of stochastic volatility processes
appear under this scope to have a feasible description.Comment: 16 pages, 7 figure
Universal relaxation function in nonextensive systems
We have derived the dipolar relaxation function for a cluster model whose
volume distribution was obtained from the generalized maximum Tsallis
nonextensive entropy principle. The power law exponents of the relaxation
function are simply related to a global fractal parameter and for
large time to the entropy nonextensivity parameter . For intermediate times
the relaxation follows a stretched exponential behavior. The asymptotic power
law behaviors both in the time and the frequency domains coincide with those of
the Weron generalized dielectric function derived from an extension of the Levy
central limit theorem. They are in full agreement with the Jonscher
universality principle. Moreover our model gives a physical interpretation of
the mathematical parameters of the Weron stochastic theory and opens new paths
to understand the ubiquity of self-similarity and power laws in the relaxation
of large classes of materials in terms of their fractal and nonextensive
properties.Comment: Two figures. Submitted for publicatio
Charged particle dynamics in the presence of non-Gaussian L\'evy electrostatic fluctuations
Full orbit dynamics of charged particles in a -dimensional helical
magnetic field in the presence of -stable L\'evy electrostatic
fluctuations and linear friction modeling collisional Coulomb drag is studied
via Monte Carlo numerical simulations. The L\'evy fluctuations are introduced
to model the effect of non-local transport due to fractional diffusion in
velocity space resulting from intermittent electrostatic turbulence. The
probability distribution functions of energy, particle displacements, and
Larmor radii are computed and showed to exhibit a transition from exponential
decay, in the case of Gaussian fluctuations, to power law decay in the case of
L\'evy fluctuations. The absolute value of the power law decay exponents are
linearly proportional to the L\'evy index . The observed anomalous
non-Gaussian statistics of the particles' Larmor radii (resulting from outlier
transport events) indicate that, when electrostatic turbulent fluctuations
exhibit non-Gaussian L\'evy statistics, gyro-averaging and guiding centre
approximations might face limitations and full particle orbit effects should be
taken into account.Comment: 5 pages, 5 figures. Accepted as a letter in Physics of Plasma
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