136 research outputs found
Copulas and time series with long-ranged dependences
We review ideas on temporal dependences and recurrences in discrete time
series from several areas of natural and social sciences. We revisit existing
studies and redefine the relevant observables in the language of copulas (joint
laws of the ranks). We propose that copulas provide an appropriate mathematical
framework to study non-linear time dependences and related concepts - like
aftershocks, Omori law, recurrences, waiting times. We also critically argue
using this global approach that previous phenomenological attempts involving
only a long-ranged autocorrelation function lacked complexity in that they were
essentially mono-scale.Comment: 11 pages, 8 figure
The travelling salesman problem on randomly diluted lattices: results for small-size systems
If one places N cities randomly on a lattice of size L, we find that the
normalized optimal travel distances per city in the Euclidean and Manhattan
metrics vary monotonically with the city concentration p. We have studied such
optimal tours for visiting all the cities using a branch and bound algorithm,
giving exact optimized tours for small system sizes (N<100). Extrapolating the
results for N tending to infinity, we find that the normalized optimal travel
distances per city in the Euclidean and Manhattan metrics both equal unity for
p=1, and they reduce to about 0.74 and 0.94, respectively, as p tends to zero.
Although the problem is trivial for p=1, it certainly reduces to the standard
TSP on continuum (NP-hard problem) for p tending to zero. We did not observe
any irregular behaviour at any intermediate point. The crossover from the
triviality to the NP-hard problem seems to occur at p=1.Comment: 7 pages, 4 figures. Revised version with changes in text and figures
(to be published in Euro. Phys. Jour. B
Statistical mechanics of money: How saving propensity affects its distribution
We consider a simple model of a closed economic system where the total money
is conserved and the number of economic agents is fixed. In analogy to
statistical systems in equilibrium, money and the average money per economic
agent are equivalent to energy and temperature, respectively. We investigate
the effect of the saving propensity of the agents on the stationary or
equilibrium money distribution.The equilibrium probablity distribution of money
becomes the usual Gibb's distribution, characteristic of non-interacting
agents, when the agents do not save. However with saving, even for local or
individual self-interest, the dynamics become cooperative and the resulting
asymmetric Gaussian-like stationary distribution acquires global ordering
properties. Intriguing singularities are observed in the stationary money
distribution in the market, as function of the ``marginal saving propensity''
of the agents.Comment: 9 pages, 5 figures. Revised version with major changes in the text
and figures (to appear in Euro. Phys. Jour. B
Market application of the percolation model: Relative price distribution
We study a variant of the Cont-Bouchaud model which utilizes the perco lation
approach of multi-agent simulations of the stock market fluctuations. Here,
instead of considering the relative price change as the difference of the total
demand and total supply, we consider the relative price change to be
proportiona l to the ``relative'' difference of demand and supply (the ratio of
the difference in total demand and total supply to the sum of the total demand
and total supply). We then study the probability distribution of the price
changes.Comment: Int. J. Mod. Phys. C 13, Jan 200
The Euclidean travelling salesman problem: Frequency distribution of neighbours for small-size systems
We have studied numerically the frequency distribution of the n-th
neighbour along the optimal tour in the Euclidean travelling salesman problem
for N cities, in dimensions d=2 and d=3. We find there is no significant
dependence of on either the number of cities N or the dimension d.Comment: 6 pages, 3 figures. To be published in Int. J. Mod. Phys.
The near-extreme density of intraday log-returns
The extreme event statistics plays a very important role in the theory and
practice of time series analysis. The reassembly of classical theoretical
results is often undermined by non-stationarity and dependence between
increments. Furthermore, the convergence to the limit distributions can be
slow, requiring a huge amount of records to obtain significant statistics, and
thus limiting its practical applications. Focussing, instead, on the closely
related density of "near-extremes" -- the distance between a record and the
maximal value -- can render the statistical methods to be more suitable in the
practical applications and/or validations of models. We apply this recently
proposed method in the empirical validation of an adapted financial market
model of the intraday market fluctuations
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