scaling and memory in the non poisson process of limit order cancelation abstract the order submission and cancelation processes are two crucial aspects in the price formation of stocks traded in order driven markets we investigate the dynamics of order cancelation by studying the statistical properties of inter cancelation durations defined as the waiting times between consecutive order cancelations of 22 liquid stocks traded on the shenzhen stock exchange of china in year 2003 three types of cancelations are considered including cancelation of any limit orders of buy limit orders and of sell limit orders we find that the distributions of the inter cancelation durations of individual stocks can be well modeled by weibulls for each type of cancelation and the distributions of rescaled durations of each type of cancelations exhibit a scaling behavior for different stocks complex intra day patterns are also unveiled in the inter cancelation durations the detrended fluctuation analysis dfa and the multifractal dfa show that the inter cancelation durations possess long term memory and multifractal nature which are not influenced by the intra day patterns no clear crossover phenomenon is observed in the detrended fluctuation functions with respect to the time scale these findings indicate that the cancelation of limit orders is a non poisson process which has potential worth in the construction of order driven market models

long range power law correlations in stock returns abstract this study investigates long range power law correlations in us uk japanese german french and spanish stock markets using daily data and applying a recently developed residual analysis termed detrended fluctuation analysis dfa we quantify correlations for the returns absolute value of returns and square of returns the results show that there is little evidence of long range correlations in returns but there is strong evidence of long range correlation in absolute and squared returns for the absolute returns a cross over of approximately 41 days is found

the scattering of sound by two semi infinite parallel staggered plates ii evaluation of the velocity potential for an incident plane wave and an incident duct mode in a recent paper abrahams wickham showed how to exactly solve the diffraction problem for two parallel semi infinite plates that are arranged to form a duct the edges of the plates are misaligned so that the geometry is asymmetric with respect to the central line of the duct in this paper we examine in detail the effect of this asymmetry on the field radiated from the duct when a fundamental travelling mode is excited within it and the scattered field when a plane wave is excited at infinity to evaluate the field in either case it is first necessary to solve the integral equations derived in our paper here we show how this is effected using the expansion theorem also enunciated in that paper this solution is then used to calculate a number of physically interesting quantities such as the variation of the energy capture by the duct when irradiated by an incident plane wave as the stagger is increased and the asymmetric radiation pattern from an incident duct mode the numerical computations are checked using an energy balance argument and finally a simple heuristic approximation is given for the scattering problem that in many situations accurately reproduces the essential physical characteristics of the solution

self similarity and network perspective of the chinese fund market abstract by testing 88 different funds of the chinese fund market cfm we find fractal behavior and long range correlations in the return series which are insensitive to the kind of funds meanwhile a power law relationship between the deviation d of prices and the hurst exponent h has been obtained which may be useful for predicting the price time series in addition with funds being viewed as nodes and the connections among the funds being determined by the cross correlation coefficients using a winner takes all approach we investigate the topological properties of the fund network our analysis reveals that during different time periods the cumulative degree distributions of the fund network all obey the double power law format moreover the small world property is also found for the fund network

modeling interactions of trading volumes in financial dynamics abstract a dynamic herding model with interactions of trading volumes is introduced at time t an agent trades with a probability which depends on the ratio of the total trading volume at time t 1 to its own trading volume at its last trade the price return is determined by the volume imbalance and number of trades the model can reproduce the power law distributions of the trading volume number of trades and price return and the probable relation between them the exponents are tunable by adjusting the values of the parameters but show slight deviation from those revealed in empirical studies moreover the time series generated are long range correlated we demonstrate that the results are rather robust and do not depend on the particular form of the trading probability

comment on tests of scaling and universality of the distributions of trade size and share volume evidence from three distinct markets in a recent publication plerou and stanley phys rev e 76 046109 2007 use the meerschaert scheffler estimator to verify the inverse half cubic law of trade size distributions we show that this procedure systematically underestimates these tail exponents

general wiener hopf factorization of matrix kernels with exponential phase factors the factorization of wiener hopf matrices with exponentially growing elements has long remained an unsolved problem such matrices often occur in the calculation of scattering from complex canonical geometries abrahams and wickham proc roy soc london ser a pp 131 156 and other problems in mathematical physics here a general method is given for resolving the difficulty and obtaining a single scalar integral equation the solution of which generates the required factors it is proven that this solution has a simple infinite series representation the method is illustrated by reference to three particular examples the first is a model matrix arising from a system of simple delay differential equations and the second occurs in the diffraction of sound by two knife edges finally a heat conduction problem is solved for an infinite wedge with asymmetric mixed boundary conditions on its faces

quantifying the cross correlations between online searches and bitcoin market abstract in this paper we quantify the cross correlations between google trends and bitcoin market by employing the multifractal detrended cross correlation analysis mf dcca method we find that the change of google trends cgt and bitcoin market i e returns and changes of volume are overall significantly cross correlated based on the cross correlation test in particular the empirical results show that 1 there exist power law cross correlations between cgt and bitcoin returns as well as cgt and changes of volume 2 the cross correlations between cgt and returns have a higher degree of multifractal in the long term and weak multifractal in the short term while the cross correlations between cgt and change of volume show the opposite trend 3 with the rolling window analysis we further find that there is a decrease trend for the cross correlations between cgt and bitcoin returns over time and the cross correlations scaling exponents are less than 0 5 which indicate that they are both anti persistent cross correlated

position space renormalisation group for aggregation fractals a simple position space renormalisation group scheme is used to find the fractal dimension of sutherland type aggregation clusters grown in low dimensional space clusters which move along paths of fractal dimension dw 0 1 2 are considered and a systematic variation in cluster fractal dimension matching that of recent computer simulation is found

the inefficiency of cryptocurrency and its cross correlation with dow jones industrial average abstract as a form of cryptocurrency the issue of informational efficiency of bitcoin has received much attention recently we add to the literature by investigating nine forms of cryptocurrencies i e bitcoin ripple ethereum nem stellar litecoin dash monero and verge with a battery of efficiency tests and the empirical results indicate that all these cryptocurrencies are inefficient markets what is more we further construct a value weighted cryptocurrency composite index cci and show that cci and dow jones industrial average are persistently cross correlated

on the non commutative factorization of wiener hopf kernels of khrapkov type there are a great many problems in mathematical physics and engineering which when modelled mathematically are reduced to wiener hopf functional equations defined in some region of a complex plane in simple models this equation is scalar but in more complicated situations inherent coupling etc can often give rise to coupled systems of equations and so the resulting wiener hopf kernels are of matrix form the crucial step in the solution of any wiener hopf equation is to decompose the kernel which can be a quite general function of the complex transform variable into a product of two factors which are regular in overlapping half planes this can be accomplished explicitly for scalar kernels and may be generalized to a particular class of matrix kernels namely those which permit a commutative decomposition although this class is wide and therefore contains some valuable physical problems it is found that many such kernels yield factorization elements with exponentially large behaviour at infinity in their half planes of analyticity this prevents a later step in the wiener hopf procedure being carried through and therefore introduces a serious limitation to the usefulness of khrapkov s approach previous researchers have offered schemes to eliminate the exponential behaviour of the khrapkov factors but for reasons discussed herein these have problems in their successful implementation this article offers a new procedure for quenching the exponential growth which is based on a method proposed recently by the author for fully coupled kernels which do not have commutative factors the approach is two step first a commutative factorization is obtained which is algebraic at infinity as required but which has spurious branch cuts in the regions of intended analyticity second an approximate procedure is used to eliminate the offending branch points by introduction of pade approximants for a certain scalar function and by inclusion of a regularizing meromorphic matrix for one particular example kernel in which an exact factorization happens to be known the explicit approximate kernel factors thus derived are shown to yield very close agreement to the exact factors the application of this work to problems in the area of fluid structural interaction is discussed

on the solution of wiener hopf problems involving noncommutative matrix kernel decompositions many problems in physics and engineering with semi infinite boundaries or interfaces are exactly solvable by the wiener hopf technique it has been used successfully in a multitude of different disciplines when the wiener hopf functional equation contains a single scalar kernel for complex boundary value problems however the procedure often leads to coupled equations which therefore have a kernel of matrix form the key step in the technique is to decompose the kernel into a product of two functions one analytic in an upper region of a complex transform plane and the other analytic in an overlapping lower half plane this is straightforward for scalar kernels but no method has yet been proposed for general matrices in this article a new procedure is introduced whereby pade approximants are employed to obtain an approximate but explicit noncommutative factorization of a matrix kernel as well as being simple to apply the use of approximants allows the accuracy of the factorization to be increased

a contribution to the quarter plane problem in diffraction theory abstract the three dimensional analog of sommerfeld s famous half plane problem for a screen 1 x1 0 x2 0 x3 0 is treated by an operator theoretic approach this paper shows that the dirichlet problem is well posed for any complex wave number k r if we look for a solution u h1 r3 of the helmholtz equation k2 u 0 in e 7mid 1 g h 1 2 1 with u 1 g h 1 2 1 an explicit representation formula for the solution is established by use of general wiener hopf operator theory sobolev space properties and hilbert space methods the corresponding neumann problem can be solved by analogy

analytical representation of stock and stock indexes returns non gaussian random walks with various jump laws abstract empirical data for stock and stock indexes returns that is available for international markets as well as for the russian stock market is introduced and discussed random walk process with a specific law of an elementary independent increment jump in some random walk space is proposed for a proper basic description an analytical representation of a random walk distribution law is derived from a general conception of stochastic elementary jumps this representation covers classic s chandrasekhar s results for gauss random walks with limited jumps and jumps having distributions with all moments as well as p levy flights with jump distributions without moments starting from the second one finally it describes truncated levy random walks for jumps having distributions with at least the second moment the natural generalization of truncated levy walks is done the random walk process is compared with known empirical data for the above discussed return fluctuations of international assets and stock indexes there is a very good agreement of the elaborated theory with empirical data

statistical properties of derivatives a journey in term structures abstract this article presents an empirical study of 13 derivative markets for commodities and financial assets the study goes beyond statistical analysis by including the maturity as a variable for the daily returns of futures contracts from 1998 to 2010 and for delivery dates up to 120 months we observe that the mean and variance of the commodities follow a scaling behavior in the maturity dimension with an exponent characteristic of the samuelson effect the comparison between the tails of the probability distribution according to the expiration dates shows that there is a segmentation in the fat tails exponent term structure above the levy stable region finally we compute the average tail exponent for each maturity and we observe two regimes of extreme events for derivative markets reminiscent of a phase diagram with a sharp transition at the 18th delivery month

wiener hopf splitting of a 2 x 2 matrix explicit expressions for the wiener hopf factors of a 2 x 2 matrix are determined in terms of a single scalar examples of the application to various matrices are given

on the scattering of sound by two semi infinite parallel staggered plates i explicit matrix wiener hopf factorization this paper discusses the two dimensional scattering of sound waves by two semi infinite rigid parallel plates the plates are staggered so that a line in the plane of the motion passing through both edges is not in general perpendicular to the plane of either plate the problem is formulated as a matrix wiener hopf functional equation which exhibits the difficulty of a kernel containing exponentially growing elements we show how this difficulty may be overcome by constructing an explicit product decomposition of the matrix kernel with both factors having algebraic behaviour at infinity this factorization is written in terms of a single entire auxiliary function that has a simple infinite series representation the wiener hopf equation is solved for arbitrary incident wave fields and we derive an asymptotic expression for the field scattered to infinity the latter includes the possibility of propagating modes in the region between the plates in part ii of this work we will evaluate our solution numerically and obtain some analytical estimates in a number of physically interesting limits

numerical solution of scattering problems using a riemann hilbert formulation a fast and accurate numerical method for the solution of scalar and matrix wiener hopf wh problems is presented the wh problems are formulated as riemann hilbert problems on the real line and a numerical approach developed for these problems is used it is shown that the known far field behaviour of the solutions can be exploited to construct numerical schemes providing spectrally accurate results a number of scalar and matrix wh problems that generalize the classical sommerfeld problem of diffraction of plane waves by a semi infinite plane are solved using the approach

price fluctuations from the order book perspective empirical facts and a simple model abstract statistical properties of an order book and the effect they have on price dynamics were studied using the high frequency nasdaq level ii data it was observed that the size distribution of marketable orders transaction sizes has power law tails with an exponent 1 market 2 4 0 1 the distribution of limit order or quote sizes was found to be consistent with a power law with an exponent close to 2 a somewhat better fit to this distribution was obtained by using a log normal distribution which has an effective power law exponent equal to 2 in the middle of the observed range the depth of the order book measured as a price impact of a hypothetical large market order was observed to be a non linear function of its size a large imbalance in the number of limit orders placed at bid and ask sides of the book was shown to lead to a predictable short term price change which is in accord with the law of supply and demand

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

a cluster cluster aggregation model with tunable fractal dimension a hierarchical cluster cluster aggregation computer model is introduced which allows one to build random fractal aggregates on a d dimensional lattice with a fractal dimension fixed a priori the algorithm works iteratively by sticking aggregates of the same number of particles at the correct centre to centre distance in order to recover the desired scaling with the more efficient versions of the model any fractal dimension ranging from 1 up to a d dependent upper limit dm d can be obtained one estimates dm 2 approximately 1 80 or 0 03 and dm 3 approximately 2 55 or 0 04 calculations up to d 8 show that the ratio dm d d decreases as d increases

mode conversion corner singularities and matrix wiener hopf factorization in diffraction theory the diffraction of acoustic electromagnetic and elastic waves by an edge is a subject of continuing mathematical and physical importance the physical motivation for research is the vast number of technological and geophysical applications of the fundamental models of linear wave propagation in continuous media while the mathematical drive is to understand and devise new analytical and numerical techniques for their quantification this paper is concerned with certain physical aspects of diffraction which have proven to give the most troublesome of mathematical difficulties these are mode conversion that is when the incident wave is scattered among different modes supported by the propagating medium and edge or corner singularities when the diffracting obstacle creates a stress singularity it is shown by way of a particular example that the exact solution of diffraction problems involving these phenomena will in general give rise to a vector wiener hopf equation with a matrix kernel whose factorization is non commutative the main result of this paper is a new procedure motivated by a precise treatment of both the corner singularity and mode conversion for determining the factors in this case

ballistic chain chain aggregation in d 1 3 the on lattice ballistic chain chain aggregation model is studied by monte carlo simulations in one two and three dimensions the chains move along the lattice directions with a velocity proportional to kgamma for a k mer the fractal dimension of the large polymers and the mass distribution are computed for different values of the mobility exponent gamma in two and three dimensions a long preasymptotic behaviour is observed and in all dimensions the asymptotic behaviour is in agreement with the smoluchowski theory

mixed boundary value problems of the type of sommerfeld s half plane problem on etudie des modifications du probleme de demi plan de sommerfeld gouverne par deux equations elliptiques propres dans des demi espaces complementaires de r 3 et on pose des conditions aux limites et de transmission sur les deux demi plans qui ensemble forment la frontiere commune de

transparency effects in cluster cluster aggregation with linear trajectories two hierarchical models of cluster cluster aggregation whose aggregates follow random linear trajectories with model i or without model ii random impact parameter are investigated numerically the difference of the fractal dimension d of the clusters as a function of space dimension d is attributed to transparency effects which are less important in model ii a simple argument is given which suggests that in contrast with model i model ii should not have an upper critical dimension

the pareto law of incomes an explanation and an extension abstract a stochastic model for the generation of observed income distributions is used to provide an explanation for the pareto law of incomes analysis of the model also yields a prediction of paretian power law behaviour in the lower tail of the distribution and this is shown to occur in a number of empirical distributions a tractable four parameter distribution is derived and shown to fit extremely well to a number of different empirical income distributions

hierarchical model for irreversible kinetic cluster formation a model is proposed to describe the growth of clusters by a mechanism of irreversible clustering of clusters the fractal exponent is extracted by means of numerical simulations on small systems both directly and in the form of a renormalisation group analysis the results are in excellent agreement with previous monte carlo simulations the numerical precision is better due to the simpler hierarchical formulation of the model in the present form the model looks like the diffusion limited aggregation model which for the sake of comparison is treated by the same renormalisation group method

scaling properties of extreme price fluctuations in bitcoin markets abstract detection of power law behavior and studies of scaling exponents uncover the characteristics of complexity in many real world phenomena the complexity of financial markets has always presented challenging issues and provided interesting findings such as the inverse cubic law in the tails of stock price fluctuation distributions motivated by the rise of novel digital assets based on blockchain technology we study the distributions of cryptocurrency price fluctuations we consider bitcoin returns over various time intervals and from multiple digital exchanges in order to investigate the existence of universal scaling behavior in the tails and ascertain whether the scaling exponent supports the presence of a finite second moment we provide empirical evidence on slowly decaying tails in the distributions of returns over multiple time intervals and different exchanges corresponding to a power law we estimate the scaling exponent and find an asymptotic power law behavior with 2 2 5 suggesting that bitcoin returns in addition to being more volatile also exhibit heavier tails than stocks which are known to be around 3 our results also imply the existence of a finite second moment thus providing a fundamental basis for the usage of standard financial theories and covariance based techniques in risk management and portfolio optimization scenarios

exponentially decayed double power law distribution of bitcoin trade sizes abstract bitcoin is the most important cryptocurrency that leads the cryptocurrency market the 776 629 356 bitcoin trades from 3 january 2009 to 31 december 2017 are retrieved it is found that the medium and large trade sizes comply with the exponentially decayed double power law distribution the tail exponent 1 of the medium trade sizes fluctuates in 2009 increases during the period from 2011 to 2014 and then converges to a stable level at 1 0 266 0 127 the tail exponent 2 of the large trade sizes fluctuates more and we have 2 1 752 1 688

statistical properties of share volume traded in financial markets we quantitatively investigate the ideas behind the often expressed adage it takes volume to move stock prices and study the statistical properties of the number of shares traded q deltat for a given stock in a fixed time interval deltat we analyze transaction data for the largest 1000 stocks for the two year period 1994 95 using a database that records every transaction for all securities in three major us stock markets we find that the distribution p q deltat displays a power law decay and that the time correlations in q deltat display long range persistence further we investigate the relation between q deltat and the number of transactions n deltat in a time interval deltat and find that the long range correlations in q deltat are largely due to those of n deltat our results are consistent with the interpretation that the large equal time correlation previously found between q deltat and the absolute value of price change g deltat related to volatility are largely due to n deltat