arXiv subjects

Kaushik Matia

Publications and source records attributed to Kaushik Matia.

9 recordsLinked to original sources

arXiv2006

A Generalized Preferential Attachment Model for Business Firms Growth Rates: I. Empirical Evidence

We introduce a model of proportional growth to explain the distribution $P(g)$ of business firm growth rates. The model predicts that $P(g)$ is Laplace in the central part and depicts an asymptotic power-law behavior in the tails with an exponent $ζ=3$. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. We test the model at different levels of aggregation in the economy, from products, to firms, to countries, and we find that the its predictions are in good agreement with empirical evidence on both growth distributions and size-variance relationships.

physics.data-an↗

arXiv2005

The Growth of Business Firms: Theoretical Framework and Empirical Evidence

We introduce a model of proportional growth to explain the distribution of business firm growth rates. The model predicts that the distribution is exponential in the central part and depicts an asymptotic power-law behavior in the tails with an exponent 3. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. In this article, we test the model at different levels of aggregation in the economy, from products to firms to countries, and we find that the model's predictions agree with empirical growth distributions and size-variance relationships.

physics.data-an↗

arXiv2005

A Generalized Preferential Attachment Model for Complex Systems

Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the steady influx of new classes. We investigate how the distribution depends on the initial conditions and changes from a pure exponential form for zero influx of new classes to a power law with an exponential cutoff form when the influx of new classes is substantial. We apply the model to study the growth dynamics of pharmaceutical industry.

physics.soc-ph↗

arXiv2005

Scaling Phenomena in the Growth Dynamics of Scientific Output

We analyze a set of three databases at different levels of aggregation (i) a database of approximately $10^6$ publications of 247 countries in the period between 1980--2001. (ii) A database of 508 academic institutions from European Union (EU) and 408 institutes from USA in the 11 year period between during 1991--2001. (iii) A database comprising of 2330 Flemish authors in the period 1980--2000. At all levels of aggregation we find that the mean annual growth rates of publications is independent of the number of publications of the various units involved. We also find that the standard deviation of the distribution of annual growth rates decays with the number of publications as a power law with exponent $\approx 0.3$. These findings are consistent with those of recent studies of systems such as the size of R&D funding budgets of countries, the research publication volumes of US universities, and the size of business firms.

physics.soc-ph↗

arXiv2005

Statistical Properties of Demand Fluctuation in the Financial Market

We examine the out-of-equilibrium phase reported by Plerou {\it et. al.} in Nature, {\bf 421}, 130 (2003) using the data of the New York stock market (NYSE) between the years 2001 --2002. We find that the observed two phase phenomenon is an artifact of the definition of the control parameter coupled with the nature of the probability distribution function of the share volume. We reproduce the two phase behavior by a simple simulation demonstrating the absence of any collective phenomenon. We further report some interesting statistical regularities of the demand fluctuation of the financial market.

physics.soc-ph↗

arXiv2005

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 $β= 0.20 \pm 0.01$. We also find that the average sales of products scales with the firm sales as a power law with exponent $α= 0.57 \pm 0.02$. And that the average number products of a firm scales with the firm sales as a power law with exponent $γ= 0.42 \pm 0.02$. We compare these findings with the predictions of models proposed till date on growth of business firms.

physics.soc-ph↗

arXiv2003

Multifractal Properties of Price Fluctuations of Stocks and Commodities

We analyze daily prices of 29 commodities and 2449 stocks, each over a period of $\approx 15$ 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.

cond-mat.stat-mech↗

arXiv2003

Scale-Dependent Price Fluctuations for the Indian Stock Market

Classic studies of the probability density of price fluctuations $g$ for stocks and foreign exchanges of several highly developed economies have been interpreted using a {\it power-law} probability density function $P(g) \sim g^{-(α+1)}$ with exponent values $α> 2$, which are outside the Lévy-stable regime $0 < α< 2$. 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 $P(g)$ decays as an {\it exponential} function $P(g) \sim \exp(-βg)$ with a characteristic decay scales $β= 1.51 \pm 0.05$ for the negative tail and $β= 1.34 \pm 0.04$ 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.

cond-mat.stat-mech↗

arXiv2002

Non-Lévy Distribution of Commodity Price Fluctuations

Price fluctuations of commodities like cotton and wheat are thought to display probability distributions of returns that follow a Lévy stable distribution. Recent analysis of stocks and foreign exchange markets show that the probability distributions are not Lévy stable, a plausible result since commodity markets have quite different features than stock markets. We analyze daily returns of 29 commodities over typically 20 years and find that the distributions of returns decay as power laws with exponents $α$ which have values $α> 2$, outside the Lévy-stable domain. We also find that the amplitudes of the returns display long-range time correlations, like stocks, while the returns themselves are uncorrelated for time lags $\approx$ 2 days, much larger than for stocks ($\approx$ 4 min).

cond-mat.stat-mech↗