dcca cross correlation coefficient quantifying level of cross correlation abstract in this paper a new coefficient is proposed with the objective of quantifying the level of cross correlation between nonstationary time series this cross correlation coefficient is defined in terms of the dfa method and the dcca method the implementation of this cross correlation coefficient will be illustrated with selected time series

multifractal detrended cross correlation analysis for two nonstationary signals we propose a method called multifractal detrended cross correlation analysis to investigate the multifractal behaviors in the power law cross correlations between two time series or higher dimensional quantities recorded simultaneously which can be applied to diverse complex systems such as turbulence finance ecology physiology geophysics and so on the method is validated with cross correlated one and two dimensional binomial measures and multifractal random walks as an example we illustrate the method by analyzing two financial time series

symbolic dynamics of fully developed chaos iii infinite memory sequences and phase transitions abstract a special type of dynamical phase transitions which arises in a particular one dimensional fully developed chaotic iterated map is studied by means of a symbolic dynamics exact analytical expressions for the probabilities of words are found on both sides of the critical value making it possible to give a statistical description of the critical behaviour at the phase transition in terms of boltzmann entropies correlation functions and generalized dimensions

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

multiscale multifractal dcca and complexity behaviors of return intervals for potts price model abstract to investigate the characteristics of extreme events in financial markets and the corresponding return intervals among these events we use a potts dynamic system to construct a random financial time series model of the attitudes of market traders we use multiscale multifractal detrended cross correlation analysis mm dcca and lempel ziv complexity lzc perform numerical research of the return intervals for two significant china s stock market indices and for the proposed model the new mm dcca method is based on the hurst surface and provides more interpretable cross correlations of the dynamic mechanism between different return interval series we scale the lzc method with different exponents to illustrate the complexity of return intervals in different scales empirical studies indicate that the proposed return intervals from the potts system and the real stock market indices hold similar statistical properties

multiscale multifractal analysis of heart rate variability recordings with a large number of occurrences of arrhythmia human heart rate variability in the form of time series of intervals between heart beats shows complex fractal properties recently it was demonstrated many times that the fractal properties vary from point to point along the series leading to multifractality in this paper we concentrate not only on the fact that the human heart rate has multifractal properties but also that these properties depend on the time scale in which the multifractality is measured this time scale is related to the frequency band of the signal we find that human heart rate variability appears to be far more complex than hitherto reported in the studies using a fixed time scale we introduce a method called multiscale multifractal analysis mma which allows us to extend the description of heart rate variability to include the dependence on the magnitude of the variability and time scale or frequency band mma is relatively immune to additive noise and nonstationarity including the nonstationarity due to inclusions into the time series of events of a different dynamics e g arrhythmic events in sinus rhythm the mma method may provide new ways of measuring the nonlinearity of a signal and it may help to develop new methods of medical diagnostics

the ferromagnetic q state potts model on three dimensional lattices a study for real values of q abstract we study the phase diagram of the ferromagnetic q state potts model on the various three dimensional lattices for integer and non integer values of q 1 our approach is based on a thermodynamically self consistent ornstein zernike approximation for the two point correlation functions we calculate the transition temperatures and when the transition is first order the jump discontinuities in the magnetization and the internal energy as well as the coordinates of the critical endpoint in external field our predictions are in very good agreement with the best available estimates from the numerical study of the region of weak first order transition we estimate the critical value qc for which the transition changes from second to first order the q 1 limit that describes the bond percolation problem is also investigated

quantifying cross correlation between ibovespa and brazilian blue chips the dcca approach abstract the objective of this paper is to demonstrate the influence of the blue chips companies in the stock market in this we apply the detrended cross correlation coefficient dcca at the sao paulo stock market ibovespa brazil initially we found that there is a positive cross correlation between these companies and the index afterwards we show that the cross correlation coefficient value depends on the time scale and the specific company blue chips thus this type of analysis lets to infer what is the most adherent company with ibovespa also in this paper we analyze in the point of view of dcca the 2008 financial crisis before after altogether the results show that there is more cross correlation between ibovespa index the blue chips after the 2008 crisis

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

identifying the influential nodes via eigen centrality from the differences and similarities of structure abstract one of the most important problems in complex network is the identification of the influential nodes for this purpose the use of differences and similarities of structure to enrich the centrality method in complex networks is proposed the centrality method called ecds centrality used is the eigen centrality which is based on the jaccard similarities between the two random nodes this can be described by an eigenvalues problem here we use a tunable parameter to adjust the influence of the differences and similarities comparing with the results of the susceptible infected recovered sir model for four real networks the ecds centrality could identify influential nodes more accurately than the tradition centralities such as the k shell degree and closeness centralities especially in the erdos network the kendall s tau could be reached to 0 93 when the spreading rate is 0 12 in the us airline network the kendall s tau could be reached to 0 95 when the spreading rate is 0 06

backbone exponents of the two dimensional q state potts model a monte carlo investigation we determine the backbone exponent x b of several critical and tricritical q state potts models in two dimensions the critical systems include the bond percolation the ising the q 2 sqrt 3 3 and 4 state potts and the baxter wu model and the tricritical ones include the q 1 potts model and the blume capel model for this purpose we formulate several efficient monte carlo methods and sample the probability p2 of a pair of points connected via at least two independent paths finite size scaling analysis of p2 yields x b as 0 3566 2 0 2696 3 0 2105 3 and 0 127 4 for the critical q 2 sqrt 3 1 2 3 and 4 state potts model respectively at tricriticality we obtain x b 0 0520 3 and 0 0753 6 for the q 1 and 2 potts model respectively for the critical q 0 potts model it is derived that x b 3 4 from a scaling argument we find that at tricriticality x b reduces to the magnetic exponent as confirmed by the numerical results

fluctuation behaviors of financial time series by a stochastic ising system on a sierpinski carpet lattice abstract we develop a financial market model using an ising spin system on a sierpinski carpet lattice that breaks the equal status of each spin to study the fluctuation behavior of the financial model we present numerical research based on monte carlo simulation in conjunction with the statistical analysis and multifractal analysis of the financial time series we extract the multifractal spectra by selecting various lattice size values of the sierpinski carpet and the inverse temperature of the ising dynamic system we also investigate the statistical fluctuation behavior the time varying volatility clustering and the multifractality of returns for the indices sse szse djia ixic s p500 hsi n225 and for the simulation data derived from the ising model on the sierpinski carpet lattice a numerical study of the model s dynamical properties reveals that this financial model reproduces important features of the empirical data

scaling and correlation in financial time series we discuss the results of three recent phenomenological studies focussed on understanding the distinctive statistical properties of nancial time series i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to very drastic events such as the crash of 19 october 1987 sometimes referred to as black monday the distribution of price uctuations decays with a power law tail well outside the levy stable regime and describes uctuations that dier by as much as 8 orders of magnitude in addition this distribution preserves its functional form for uctuations on time scales that dier by 3 orders of magnitude from 1 min up to approximately 10 days ii correlations in nancial time series while price uctuations themselves have rapidly decaying correlations the magnitude of uctuations measured by either the absolute value or the square of the price uctuations has correlations that decay as a power law persisting for several months iii volatility and trading activity we quantify the relation between trading activity measured by the number of transactions nt and the price change gt for a given stock over a time interval t t t we nd that nt displays long range power law correlations in time which leads to the interpretation that the long range correlations previously found for jgtj are connected to those of nt c 2000 elsevier science b v all rights reserved

volatility aggregation intensity energy futures series on stochastic finite range exclusion dynamics abstract the stochastic finite range exclusion process one of statistical physics systems is introduced to construct a new agent based financial price model to study the mechanism of market dynamics a novel volatility aggregation intensity vai time series describing the fluctuation aggregation intensity of the volatility series is developed for further investigating the nonlinear volatility behaviors in energy markets for studying the proposed vai series and the proposed price model the new york mercantile exchange energy futures data is selected and analyzed further cross correlation analysis auto correlation analysis with multiscale and multifractal detrended fluctuation analysis are applied to analyze the correlation volatility clustering and multifractal natures of the vai time series the empirical results show that the proposed model has the parallel behaviors with the authentic markets indicating that it is rational and available the new concept of vai series is of great value and can enrich the study of volatility behaviors in energy markets to some extent

crossover in the cont bouchaud percolation model for market fluctuations abstract monte carlo simulations of the cont bouchaud herding model for stock market traders show power law distributions for short times and exponential truncation for longer time intervals if they are made at the percolation threshold in two to seven dimensions

cross correlations between volume change and price change in finance one usually deals not with prices but with growth rates r defined as the difference in logarithm between two consecutive prices here we consider not the trading volume but rather the volume growth rate r the difference in logarithm between two consecutive values of trading volume to this end we use several methods to analyze the properties of volume changes r and their relationship to price changes r we analyze 14 981 daily recordings of the standard and poor s s p 500 index over the 59 year period 1950 2009 and find power law cross correlations between r and r by using detrended cross correlation analysis dcca we introduce a joint stochastic process that models these cross correlations motivated by the relationship between r and r we estimate the tail exponent of the probability density function p r r 1 for both the s p 500 index as well as the collection of 1819 constituents of the new york stock exchange composite index on 17 july 2009 as a new method to estimate we calculate the time intervals q between events where r q we demonstrate that q the average of q obeys q q we find 3 furthermore by aggregating all q values of 28 global financial indices we also observe an approximate inverse cubic law

simulation of potts models with real q and no critical slowing down a monte carlo algorithm is proposed to simulate the ferromagnetic q state potts model for any real qg0 a single update is a random sequence of disordering and deterministic moves one for each link of the lattice a disordering move attributes a random value to the link regardless of the state of the system while in a deterministic move this value is a state function the relative frequency of these moves depends on the two parameters q and ensuremath beta 1 kt the algorithm is not affected by critical slowing down and the dynamical critical exponent z is exactly vanishing we simulate in this way a three dimensional potts model in the range 2lql3 for estimating the critical value q c where the thermal transition changes from second order to first order and find q c 2 620 ifmmode pm else textpm fi 0 005

congruence topologies on the mapping class group abstract let s be the pure mapping class group of a connected orientable surface s of negative euler characteristic for c a class of finite groups let 1 s c be the pro c completion of the fundamental group of s the c congruence completion s c of s is the profinite completion induced by the embedding s out 1 s c in this paper we begin a systematic study of such completions for different c we show that the combinatorial structure of the profinite groups s c closely resemble that of s a fundamental question is how c congruence completions compare with pro c completions even though in general e g for c the class of finite solvable groups s c is not even virtually a pro c group we show that for z 2 c g s 2 and s open there is a natural epimorphism from the c congruence completion s 2 c of the abelian level of order 2 to its pro c completion s 2 c in particular this is an isomorphism for the class of finite groups and for the class of 2 groups moreover in these two cases the result also holds for a closed surface

scaling and memory of intraday volatility return intervals in stock markets we study the return interval tau between price volatilities that are above a certain threshold q for 31 intraday data sets including the standard and poor s 500 index and the 30 stocks that form the dow jones industrial index for different threshold q the probability density function pq tau scales with the mean interval tau as formula see text similar to that found in daily volatilities since the intraday records have significantly more data points compared to the daily records we could probe for much higher thresholds and still obtain good statistics we find that the scaling function f x is consistent for all 31 intraday data sets in various time resolutions and the function is well approximated by the stretched exponential f x similar to e ax gamma with gamma 0 38 0 05 and a 3 9 0 5 which indicates the existence of correlations we analyze the conditional probability distribution pq tau tau0 for tau following a certain interval tau0 and find pq tau tau0 depends on tau0 which demonstrates memory in intraday return intervals also we find that the mean conditional interval tau tau0 increases with tau0 consistent with the memory found for pq tau tau0 moreover we find that return interval records in addition to having short term correlations as demonstrated by pq tau tau0 have long term correlations with correlation exponents similar to that of volatility records

return interval distribution of extreme events and long term memory the distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines it is well known that many physical processes in nature and society display long range correlations hence in the last few years considerable research effort has been directed towards studying the distribution of return intervals for long range correlated time series based on numerical simulations it was shown that the return interval distributions are of stretched exponential type in this paper we obtain an analytical expression for the distribution of return intervals in long range correlated time series which holds good when the average return intervals are large we show that the distribution is actually a product of power law and a stretched exponential form we also discuss the regimes of validity and perform detailed studies on how the return interval distribution depends on the threshold used to define extreme events

dynamic relationship between chinese rmb exchange rate index and market anxiety a new perspective based on mf dcca abstract this paper employs multifractal detrended cross correlation analysis mf dcca to study the cross correlations between the chinese rmb exchange rate index and market anxiety using data from june 21 2010 to december 28 2018 cross correlation statistics and coefficients verify the existence of cross correlations and the mf dcca method quantitatively confirms the presence of multifractality between the chinese rmb index and market anxiety for both the long and short term the results of the rolling window analysis reveal that cross correlation scaling exponents of the chinese rmb index and market anxiety are sensitive to external shocks