Youngki Lee

Scaling the volatility of GDP growth rates

Abstract The distribution of shocks to GDP growth rates is found to be exponential rather than normal. Their standard deviation scales with GDPβ where β=−0.15±0.03. These macroeconomic results place restrictions on the microeconomic structure of interactions between agents.

Common scaling patterns in intertrade times of U. S. stocks

We analyze the sequence of time intervals between consecutive stock trades of thirty companies representing eight sectors of the U.S. economy over a period of 4 yrs. For all companies we find that: (i) the probability density function of intertrade times may be fit by a Weibull distribution, (ii) when appropriately rescaled the probability densities of all companies collapse onto a single curve implying a universal functional form, (iii) the intertrade times exhibit power-law correlated behavior within a trading day and a consistently greater degree of correlation over larger time scales, in agreement with the correlation behavior of the absolute price returns for the corresponding company, and (iv) the magnitude series of intertrade time increments is characterized by long-range power-law correlations suggesting the presence of nonlinear features in the trading dynamics, while the sign series is anticorrelated at small scales. Our results suggest that independent of industry sector, market capitalization and average level of trading activity, the series of intertrade times exhibit possibly universal scaling patterns, which may relate to a common mechanism underlying the trading dynamics of diverse companies. Further, our observation of long-range power-law correlations and a parallel with the crossover in the scaling of absolute price returns for each individual stock, support the hypothesis that the dynamics of transaction times may play a role in the process of price formation.

Weighted Scale-Free Network in Financial Correlations

While many scale-free (SF) networks have been introduced recently for complex systems, most of them are binary random graphs. Here we introduce a weighted SF network in associated with the cross-correlations in stock price changes among the S&P 500 companies, where all vertices (companies) are fully connected and each edge has nonuniform weight given by the covariance between the two returns connected, normalized by their volatilities. Influence-strength (IS) is defined as the sum of the weights on the edges incident upon a given vertex. Then the IS distribution in its absolute magnitude | q | exhibits a SF behavior, P I (| q |)∼| q | -η with the exponent η≈1.8(1).

Power-law distribution of family names in Japanese societies

We study the frequency distribution of family names. From a common data base, we count the number of people who share the same family name. This is the size of the family. We find that (i) the total number of different family names in a society scales as a power law of the population, (ii) the total number of family names of the same size decreases as the size increases with a power law and (iii) the relation between size and rank of a family name also shows a power law. These scaling properties are found to be consistent for five different regional communities in Japan.

Scale-invariant truncated Lévy process

We develop a scale-invariant truncated Levy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits Levy stability for the distribution, and hence shows scaling properties as commonly observed in empirical data; it has the advantage that all moments are finite and so accounts for the empirical scaling of the moments. To test the potential utility of the STL process, we analyze financial data.

Flow between two sites on a percolation cluster

We study the flow of fluid in porous media in dimensions d=2 and 3. The medium is modeled by bond percolation on a lattice of L(d) sites, while the flow front is modeled by tracer particles driven by a pressure difference between two fixed sites (wells) separated by Euclidean distance r. We investigate the distribution function of the shortest path connecting the two sites, and propose a scaling ansatz that accounts for the dependence of this distribution (i) on the size of the system L and (ii) on the bond occupancy probability p. We confirm by extensive simulations that the ansatz holds for d=2 and 3. Further, we study two dynamical quantities: (i) the minimal traveling time of a tracer particle between the wells when the total flux is constant and (ii) the minimal traveling time when the pressure difference is constant. A scaling ansatz for these dynamical quantities also includes the effect of finite system size L and off-critical bond occupation probability p. We find that the scaling form for the distribution functions for these dynamical quantities for d=2 and 3 is similar to that for the shortest path, but with different critical exponents. Our results include estimates for all parameters that characterize the scaling form for the shortest path and the minimal traveling time in two and three dimensions; these parameters are the fractal dimension, the power law exponent, and the constants and exponents that characterize the exponential cutoff functions.

Systems with Correlations in the Variance: Generating Power-Law Tails in Probability Distributions

We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated L{e}vy distribution. For both (i) and (ii), we find that due to the correlations in the variance, the process ``dynamically generates power-law tails in the distributions, whose exponents can be controlled through the way the correlations in the variance are introduced. For (ii), we find that the process can extend a truncated distribution {it beyond the truncation cutoff}, which leads to a crossover between a L{e}vy stable power law and the present ``dynamically-generated power law. We show that the process can explain the crossover behavior recently observed in the

Predicting oil recovery using percolation

S&P500

Scaling of the Distribution of Shortest Paths in Percolation

stock index.

Applications of statistical physics to the oil industry: predicting oil recovery using percolation theory

One particular practical problem in oil recovery is to predict the time to breakthrough of a fluid injected in one well and the subsequent decay in the production rate of oil at another well. Because we only have a stochastic view of the distribution of rock properties we need to predict the uncertainty in the breakthrough time and post-breakthrough behaviour in order to calculate the economic risk. In this paper we use percolation theory to predict (i) the distribution of the chemical path (shortest path) between two points (representing well pairs) at a given Euclidean separation and present a scaling hypothesis for this distribution which is confirmed by numerical simulation, (ii) the distribution of breakthrough times which can be calculated algebraically rather than by very time consuming direct numerical simulation of large numbers of realisations.