229 research outputs found
A statistical analysis of product prices in online markets
We empirically investigate fluctuations in product prices in online markets
by using a tick-by-tick price data collected from a Japanese price comparison
site, and find some similarities and differences between product and asset
prices. The average price of a product across e-retailers behaves almost like a
random walk, although the probability of price increase/decrease is higher
conditional on the multiple events of price increase/decrease. This is quite
similar to the property reported by previous studies about asset prices.
However, we fail to find a long memory property in the volatility of product
price changes. Also, we find that the price change distribution for product
prices is close to an exponential distribution, rather than a power law
distribution. These two findings are in a sharp contrast with the previous
results regarding asset prices. We propose an interpretation that these
differences may stem from the absence of speculative activities in product
markets; namely, e-retailers seldom repeat buy and sell of a product, unlike
traders in asset markets.Comment: 5 pages, 5 figures, 1 table, proceedings of APFA
On pricing of interest rate derivatives
At present, there is an explosion of practical interest in the pricing of
interest rate (IR) derivatives. Textbook pricing methods do not take into
account the leptokurticity of the underlying IR process. In this paper, such a
leptokurtic behaviour is illustrated using LIBOR data, and a possible
martingale pricing scheme is discussed.Comment: 9 pages, 13 figure
Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation
A detailed study is presented for a large class of uncoupled continuous-time
random walks (CTRWs). The master equation is solved for the Mittag-Leffler
survival probability. The properly scaled diffusive limit of the master
equation is taken and its relation with the fractional diffusion equation is
discussed. Finally, some common objections found in the literature are
thoroughly reviewed.Comment: Preprint version of an already published paper. 8 page
Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation
We present a numerical method for the Monte Carlo simulation of uncoupled
continuous-time random walks with a Levy alpha-stable distribution of jumps in
space and a Mittag-Leffler distribution of waiting times, and apply it to the
stochastic solution of the Cauchy problem for a partial differential equation
with fractional derivatives both in space and in time. The one-parameter
Mittag-Leffler function is the natural survival probability leading to
time-fractional diffusion equations. Transformation methods for Mittag-Leffler
random variables were found later than the well-known transformation method by
Chambers, Mallows, and Stuck for Levy alpha-stable random variables and so far
have not received as much attention; nor have they been used together with the
latter in spite of their mathematical relationship due to the geometric
stability of the Mittag-Leffler distribution. Combining the two methods, we
obtain an accurate approximation of space- and time-fractional diffusion
processes almost as easy and fast to compute as for standard diffusion
processes.Comment: 7 pages, 5 figures, 1 table. Presented at the Conference on Computing
in Economics and Finance in Montreal, 14-16 June 2007; at the conference
"Modelling anomalous diffusion and relaxation" in Jerusalem, 23-28 March
2008; et
Cliophysics: Socio-political Reliability Theory, Polity Duration and African Political (In)stabilities
Quantification of historical sociological processes have recently gained
attention among theoreticians in the effort of providing a solid theoretical
understanding of the behaviors and regularities present in sociopolitical
dynamics. Here we present a reliability theory of polity processes with
emphases on individual political dynamics of African countries. We found that
the structural properties of polity failure rates successfully capture the risk
of political vulnerability and instabilities in which 87.50%, 75%, 71.43%, and
0% of the countries with monotonically increasing, unimodal, U-shaped and
monotonically decreasing polity failure rates, respectively, have high level of
state fragility indices. The quasi-U-shape relationship between average polity
duration and regime types corroborates historical precedents and explains the
stability of the autocracies and democracies.Comment: 4 pages, 3 figures, 1 tabl
Emerging properties of financial time series in the “Game of Life”
We explore the spatial complexity of Conway’s “Game of Life,” a prototypical cellular automaton by means of a geometrical procedure generating a two-dimensional random walk from a bidimensional lattice with periodical boundaries. The one-dimensional projection of this process is analyzed and it turns out that some of its statistical properties resemble the so-called stylized facts observed in financial time series. The scope and meaning of this result are discussed from the viewpoint of complex systems. In particular, we stress how the supposed peculiarities of financial time series are, often, overrated in their importance
Interplay between telecommunications and face-to-face interactions - a study using mobile phone data
In this study we analyze one year of anonymized telecommunications data for
over one million customers from a large European cellphone operator, and we
investigate the relationship between people's calls and their physical
location. We discover that more than 90% of users who have called each other
have also shared the same space (cell tower), even if they live far apart.
Moreover, we find that close to 70% of users who call each other frequently (at
least once per month on average) have shared the same space at the same time -
an instance that we call co-location. Co-locations appear indicative of
coordination calls, which occur just before face-to-face meetings. Their number
is highly predictable based on the amount of calls between two users and the
distance between their home locations - suggesting a new way to quantify the
interplay between telecommunications and face-to-face interactions
Inferring hidden Markov models from noisy time sequences: a method to alleviate degeneracy in molecular dynamics
We present a new method for inferring hidden Markov models from noisy time
sequences without the necessity of assuming a model architecture, thus allowing
for the detection of degenerate states. This is based on the statistical
prediction techniques developed by Crutchfield et al., and generates so called
causal state models, equivalent to hidden Markov models. This method is
applicable to any continuous data which clusters around discrete values and
exhibits multiple transitions between these values such as tethered particle
motion data or Fluorescence Resonance Energy Transfer (FRET) spectra. The
algorithms developed have been shown to perform well on simulated data,
demonstrating the ability to recover the model used to generate the data under
high noise, sparse data conditions and the ability to infer the existence of
degenerate states. They have also been applied to new experimental FRET data of
Holliday Junction dynamics, extracting the expected two state model and
providing values for the transition rates in good agreement with previous
results and with results obtained using existing maximum likelihood based
methods.Comment: 19 pages, 9 figure
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