We model the time series of the S&P500 index by a combined process, the AR+GARCH process, where AR denotes the autoregressive process which we use to account for the short-range correlations in the index changes and GARCH denotes the generalized autoregressive conditional heteroskedastic process...

We model the power-law stability in distribution of returns for S&P500 index by the GARCH process which we use to account for the long memory in the variance correlations. Precisely, we analyze the distributions corresponding to temporal aggregation of the GARCH process, i.e., the sum of n GARCH...

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...

We present a preferential attachment growth model to obtain the distribution P(K) of number of units K in the classes which may represent business firms or other socio-economic entities. We found that P(K) is described in its central part by a power law with an exponent amp;#966; = 2+b/(1amp;#8722;b)...

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 z = 3. Because of data limitations, previous...

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 power-law probability density function P(g) ∼ g−( 1) with exponent values 2, which are outside the L´evy-stable regime 0 ...

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...

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...

We introduce a model of proportional growth to explain the distribution Pg(g) of business-firm growth rates. The model predicts that Pg(g) is exponential in the central part and depicts an asymptotic power-law behavior in the tails with an exponent z=3. Because of data limitations, previous...

Price fluctuations of commodities like cotton and wheat are thought to display probability distributions of returns that follow a L\'evy stable distribution. Recent analysis of stocks and foreign exchange markets show that the probability distributions are not L\'evy stable, a plausible result...