134 research outputs found
A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment
We present a preferential attachment growth model to obtain the distribution
of number of units in the classes which may represent business firms
or other socio-economic entities. We found that is described in its
central part by a power law with an exponent which depends on
the probability of entry of new classes, . In a particular problem of city
population this distribution is equivalent to the well known Zipf law. In the
absence of the new classes entry, the distribution is exponential. Using
analytical form of and assuming proportional growth for units, we derive
, the distribution of business firm growth rates. The model predicts that
has a Laplacian cusp in the central part and asymptotic power-law tails
with an exponent . We test the analytical expressions derived using
heuristic arguments by simulations. The model might also explain the
size-variance relationship of the firm growth rates.Comment: 19 pages 6 figures Applications of Physics in Financial Analysis,
APFA
Scale-Dependent Price Fluctuations for the Indian Stock Market
Classic studies of the probability density of price fluctuations for
stocks and foreign exchanges of several highly developed economies have been
interpreted using a {\it power-law} probability density function with exponent values , which are outside the
L\'evy-stable regime . To test the universality of this
relationship for less highly developed economies, we analyze daily returns for
the period Nov. 1994--June 2002 for the 49 largest stocks of the National Stock
Exchange which has the highest volume of trade in India. We find that
decays as an {\it exponential} function with a
characteristic decay scales for the negative tail and
for the positive tail, which is significantly different
from that observed for developed economies. Thus we conclude that the Indian
stock market may belong to a universality class that differs from those of
developed countries analyzed previously.Comment: 7 pages, 8 figure
The Power (Law) of Indian Markets: Analysing NSE and BSE trading statistics
The nature of fluctuations in the Indian financial market is analyzed in this
paper. We have looked at the price returns of individual stocks, with
tick-by-tick data from the National Stock Exchange (NSE) and daily closing
price data from both NSE and the Bombay Stock Exchange (BSE), the two largest
exchanges in India. We find that the price returns in Indian markets follow a
fat-tailed cumulative distribution, consistent with a power law having exponent
, similar to that observed in developed markets. However, the
distributions of trading volume and the number of trades have a different
nature than that seen in the New York Stock Exchange (NYSE). Further, the price
movement of different stocks are highly correlated in Indian markets.Comment: 10 pages, 7 figures, to appear in Proceedings of International
Workshop on "Econophysics of Stock Markets and Minority Games"
(Econophys-Kolkata II), Feb 14-17, 200
Statistical Properties of Business Firms Structure and Growth
We analyze a database comprising quarterly sales of 55624 pharmaceutical
products commercialized by 3939 pharmaceutical firms in the period 1992--2001.
We study the probability density function (PDF) of growth in firms and product
sales and find that the width of the PDF of growth decays with the sales as a
power law with exponent . We also find that the average
sales of products scales with the firm sales as a power law with exponent
. And that the average number products of a firm scales
with the firm sales as a power law with exponent . We
compare these findings with the predictions of models proposed till date on
growth of business firms
The foreign exchange market: return distributions, multifractality, anomalous multifractality and Epps effect
We present a systematic study of various statistical characteristics of
high-frequency returns from the foreign exchange market. This study is based on
six exchange rates forming two triangles: EUR-GBP-USD and GBP-CHF-JPY. It is
shown that the exchange rate return fluctuations for all the pairs considered
are well described by the nonextensive statistics in terms of q-Gaussians.
There exist some small quantitative variations in the nonextensivity
q-parameter values for different exchange rates and this can be related to the
importance of a given exchange rate in the world's currency trade. Temporal
correlations organize the series of returns such that they develop the
multifractal characteristics for all the exchange rates with a varying degree
of symmetry of the singularity spectrum f(alpha) however. The most symmetric
spectrum is identified for the GBP/USD. We also form time series of triangular
residual returns and find that the distributions of their fluctuations develop
disproportionately heavier tails as compared to small fluctuations which
excludes description in terms of q-Gaussians. The multifractal characteristics
for these residual returns reveal such anomalous properties like negative
singularity exponents and even negative singularity spectra. Such anomalous
multifractal measures have so far been considered in the literature in
connection with the diffusion limited aggregation and with turbulence. We find
that market inefficiency on short time scales leads to the occurrence of the
Epps effect on much longer time scales. Although the currency market is much
more liquid than the stock markets and it has much larger transaction
frequency, the building-up of correlations takes up to several hours - time
that does not differ much from what is observed in the stock markets. This may
suggest that non-synchronicity of transactions is not the unique source of the
observed effect
Effect of Celluclast 1.5L on the Physicochemical Characterization of Gold Kiwifruit Pectin
The effects of Celluclast 1.5L concentration on the physicochemical characterization of gold kiwifruit pectin was evaluated. Varying the enzyme concentration affected the pectin yield and pectin physicochemical properties. The viscosity of extracted pectin was largely dependent on the enzyme concentration. Celluclast 1.5L with medium concentration exhibited the highest viscosity. Varying the enzyme concentration also influenced the molecular weight distribution. High molecular weight (Mw) pectin (1.65 × 106 g/mol) was obtained when the medium concentration was used. Overall, the study clearly reflects the importance of taking into consideration the amount of cellulytic enzyme added in order to determine the final quality of pectin
Multifractal Properties of Price Fluctuations of Stocks and Commodities
We analyze daily prices of 29 commodities and 2449 stocks, each over a period
of years. We find that the price fluctuations for commodities have
a significantly broader multifractal spectrum than for stocks. We also propose
that multifractal properties of both stocks and commodities can be attributed
mainly to the broad probability distribution of price fluctuations and
secondarily to their temporal organization. Furthermore, we propose that, for
commodities, stronger higher order correlations in price fluctuations result in
broader multifractal spectra.Comment: Published in Euro Physics Letters (14 pages, 5 figures
The components of empirical multifractality in financial returns
We perform a systematic investigation on the components of the empirical
multifractality of financial returns using the daily data of Dow Jones
Industrial Average from 26 May 1896 to 27 April 2007 as an example. The
temporal structure and fat-tailed distribution of the returns are considered as
possible influence factors. The multifractal spectrum of the original return
series is compared with those of four kinds of surrogate data: (1) shuffled
data that contain no temporal correlation but have the same distribution, (2)
surrogate data in which any nonlinear correlation is removed but the
distribution and linear correlation are preserved, (3) surrogate data in which
large positive and negative returns are replaced with small values, and (4)
surrogate data generated from alternative fat-tailed distributions with the
temporal correlation preserved. We find that all these factors have influence
on the multifractal spectrum. We also find that the temporal structure (linear
or nonlinear) has minor impact on the singularity width of the
multifractal spectrum while the fat tails have major impact on ,
which confirms the earlier results. In addition, the linear correlation is
found to have only a horizontal translation effect on the multifractal spectrum
in which the distance is approximately equal to the difference between its DFA
scaling exponent and 0.5. Our method can also be applied to other financial or
physical variables and other multifractal formalisms.Comment: 6 epl page
Quantitative features of multifractal subtleties in time series
Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the
Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of
multifractality in the time series. Series fluctuating according to a qGaussian
distribution, both uncorrelated and correlated in time, are used. For the
uncorrelated series at the border (q=5/3) between the Gaussian and the Levy
basins of attraction asymptotically we find a phase-like transition between
monofractal and bifractal characteristics. This indicates that these may solely
be the specific nonlinear temporal correlations that organize the series into a
genuine multifractal hierarchy. For analyzing various features of
multifractality due to such correlations, we use the model series generated
from the binomial cascade as well as empirical series. Then, within the
temporal ranges of well developed power-law correlations we find a fast
convergence in all multifractal measures. Besides of its practical significance
this fact may reflect another manifestation of a conjectured q-generalized
Central Limit Theorem
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