We analyze the multifractal spectra of daily foreign exchange rates for Japan, Hong-Kong, Korea, and Thailand with respect to the United States Dollar from 1991 to 2005. We find that the return time series show multifractal spectrum features for all four cases. To observe the effect of the Asian currency crisis, we also estimate the multifractal spectra of limited series before and after the crisis. We find that the Korean and Thai foreign exchange markets experienced a significant increase in multifractality compared to Hong-Kong and Japan. We also show that the multifractality is stronge related to the presence of high values of returns in the series.
Data transfer is one of the main functions of the Internet. The Internet consists of a large number of interconnected subnetworks or domains, known as Autonomous Systems. Due to privacy and other reasons the information about what route to use to reach devices within other Autonomous Systems is not readily available to any given Autonomous System. The Border Gateway Protocol is responsible for discovering and distributing this reachability information to all Autonomous Systems. Since the topology of the Internet is highly dynamic, all Autonomous Systems constantly exchange and update this reachability information in small chunks, known as routing control packets or Border Gateway Protocol updates. Motivated by scalability and predictability issues with the dynamics of these updates in the quickly growing Internet, we conduct a systematic time series analysis of Border Gateway Protocol update rates. We find that Border Gateway Protocol update time series are extremely volatile, exhibit long-term correlations and memory effects, similar to seismic time series, or temperature and stock market price fluctuations. The presented statistical characterization of Border Gateway Protocol update dynamics could serve as a ground truth for validation of existing and developing better models of Internet interdomain routing.
Different definitions of links in climate networks may lead to considerably different network topologies. We construct a network from climate records of surface level atmospheric temperature in different geographical sites around the globe using two commonly used definitions of links. Utilizing detrended fluctuation analysis, shuffled surrogates and separation analysis of maritime and continental records, we find that one of the major influences on the structure of climate networks is due to the auto-correlation in the records, that may introduce spurious links. This may explain why different methods could lead to different climate network topologies.
We study, using simulations the dynamical properties of complex ferromagnetic granular materials. The system of grains is modeled by a disordered two-dimensional lattice in which the grains are embedded, while the magnitude and direction of the easy axis are random. Using the monte-carlo method we track the dynamics of the magnetic moments of the grains. We observe a transition of the system from a macroscopic blocked (ferromagnetic) phase at low temperature in which the grains magnetic moment do not flip to the other direction to an unblocked (superparamagnetic) phase at high temperature in which the magnetic moment is free to rotate. Our results suggest that this transition exhibits the characteristics of a second order phase transition such as the appearance of a giant cluster of unblocked grains which is fractal at the critical temperature, a peak in the size of the second largest cluster at the same temperature and a power law distribution of cluster sizes near the criticality.
We construct and analyze climate networks based on daily satellite measurements of temperatures and geopotential heights. We show that these networks are stable during time and are similar over different altitudes. Each link in our network is stable with typical 15% variability. The entire hierarchy of links is about 80% consistent during time. We show that about half of this stability is due to the spatial 2D embedding of the network, and half is due to physical coupling mechanisms. The network stability of equatorial regions is found to be lower compared to the stability of a typical network in non-equatorial regions.
We introduce a contrarian opinion (CO) model in which a fraction p of contrarians within a group holds a strong opinion opposite to the opinion held by the rest of the group. At the initial stage, stable clusters of two opinions, A and B exist. Then we introduce contrarians which hold a strong B opinion into the opinion A group. Through their interactions, the contrarians are able to decrease the size of the largest A opinion cluster, and even destroy it. We see this kind of method in operation, e.g when companies send free new products to potential customers in order to convince them to adopt the product and influence others. We study the CO model, using two different strategies, on both ER and scale-free networks. In strategy I, the contrarians are positioned at random. In strategy II, the contrarians are chosen to be the highest degrees nodes. We find that for both strategies the size of the largest A cluster decreases to zero as p increases as in a phase transition. At a critical threshold value p_c the system undergoes a second-order phase transition that belongs to the same universality class of mean field percolation. We find that even for an ER type model, where the degrees of the nodes are not so distinct, strategy II is significantly more effctive in reducing the size of the largest A opinion cluster and, at very small values of p, the largest A opinion cluster is destroyed.
We study the daily trading volume volatility of 17,197 stocks in the U.S. stock markets during the period 1989--2008 and analyze the time return intervals $tau$ between volume volatilities above a given threshold q. For different thresholds q, the probability density function P_q(tau) scales with mean interval <tau> as P_q(tau)=<tau>^{-1}f(tau/<tau>) and the tails of the scaling function can be well approximated by a power-law f(x)~x^{-gamma}. We also study the relation between the form of the distribution function P_q(tau) and several financial factors: stock lifetime, market capitalization, volume, and trading value. We find a systematic tendency of P_q(tau) associated with these factors, suggesting a multi-scaling feature in the volume return intervals. We analyze the conditional probability P_q(tau|tau_0) for $tau$ following a certain interval tau_0, and find that P_q(tau|tau_0) depends on tau_0 such that immediately following a short/long return interval a second short/long return interval tends to occur. We also find indications that there is a long-term correlation in the daily volume volatility. We compare our results to those found earlier for price volatility.
We construct and analyze a climate network which represents the interdependent structure of the climate in different geographical zones and find that the network responds in a unique way to El-Ni~{n}o events. Analyzing the dynamics of the climate network shows that when El-Ni~{n}o events begin, the El-Ni~{n}o basin partially loses its influence on its surroundings. After typically three months, this influence is restored while the basin loses almost all dependence on its surroundings and becomes textit{autonomous}. The formation of an autonomous basin is the missing link to understand the seemingly contradicting phenomena of the afore--noticed weakening of the interdependencies in the climate network during El-Ni~{n}o and the known impact of the anomalies inside the El-Ni~{n}o basin on the global climate system.
We study the cascading dynamics immediately before and immediately after 219 market shocks. We define the time of a market shock T_{c} to be the time for which the market volatility V(T_{c}) has a peak that exceeds a predetermined threshold. The cascade of high volatility aftershocks triggered by the main shock is quantitatively similar to earthquakes and solar flares, which have been described by three empirical laws --- the Omori law, the productivity law, and the Bath law. We analyze the most traded 531 stocks in U.S. markets during the two-year period 2001-2002 at the 1-minute time resolution. We find quantitative relations between (i) the main shock magnitude M equiv log V(T_{c}) occurring at the time T_{c} of each of the 219 volatility quakes analyzed, and (ii) the parameters quantifying the decay of volatility aftershocks as well as the volatility preshocks. We also find that stocks with larger trading activity react more strongly and more quickly to market shocks than stocks with smaller trading activity. Our findings characterize the typical volatility response conditional on M, both at the market and the individual stock scale. We argue that there is potential utility in these three statistical quantitative relations with applications in option pricing and volatility trading.
Equity activity is an essential topic for financial market studies. To explore its statistical regularities, we comprehensively examine the trading value, a measure of the equity activity, of the 3314 most-traded stocks in the U.S. equity market and find that (i) the trading values follow a log-normal distribution; (ii) the standard deviation of the growth rate of the trading value obeys a power-law with the initial trading value, and the power-law exponent beta=0.14. Remarkably, both features hold for a wide range of sampling intervals, from 5 minutes to 20 trading days. Further, we show that all the 3314 stocks have long-term correlations, and their Hurst exponents H follow a normal distribution. Furthermore, we find that the Hurst exponent depends on the size of the company. We also show that the relation between the scaling in the growth rate and the long-term correlation is consistent with beta=1-H, similar to that found recently on human interaction activity by Rybski and collaborators.
