correlation measure to detect time series distances whence economy globalization abstract an instantaneous time series distance is defined through the equal time correlation coefficient the idea is applied to the gross domestic product gdp yearly increments of 21 rich countries between 1950 and 2005 in order to test the process of economic globalisation some data discussion is first presented to decide what eks gk or derived gdp series should be studied distances are then calculated from the correlation coefficient values between pairs of series the role of time averaging of the distances over finite size windows is discussed three network structures are next constructed based on the hierarchy of distances it is shown that the mean distance between the most developed countries on several networks actually decreases in time which we consider as a proof of globalization an empirical law is found for the evolution after 1990 similar to that found in flux creep the optimal observation time window size is found 15 years

statistical properties of german dax and chinese indices abstract we investigate statistical properties of the german dax and chinese indices including the volatility distribution autocorrelation function dfa function and return volatility correlation function with both the daily data and minutely data at the minutely time scale the chinese indices may show irregular dynamic behavior at the daily time scale the volatility distribution autocorrelation function and dfa function of the chinese indices are qualitatively similar to those of the german dax while the return volatility correlation function exhibits an anti leverage effect different from the leverage effect of the german dax

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

volatility clustering and scaling for financial time series due to attractor bubbling a microscopic model of financial markets is considered consisting of many interacting agents spins with global coupling and discrete time heat bath dynamics similar to random ising systems the interactions between agents change randomly in time in the thermodynamic limit the obtained time series of price returns show chaotic bursts resulting from the emergence of attractor bubbling or on off intermittency resembling the empirical financial time series with volatility clustering for a proper choice of the model parameters the probability distributions of returns exhibit power law tails with scaling exponents close to the empirical ones

statistical properties of short term price trends in high frequency stock market data we investigated distributions of short term price trends for high frequency stock market data a number of trends as a function of their lengths were measured we found that such a distribution does not fit to the results following from an uncorrelated stochastic process we proposed a simple model with a memory that gives a qualitative agreement with the real data

fixed set systems of equivariant infinite loop spaces we develop machinery enabling us to show that suitable g spaces including the equivariant version of bf are equivariant infinite loop spaces this involves a recognition principle for systems of spaces which behave for mally like the system of fixed sets of a g space that is we give a necessary and sufficient condition for such a system to be equivalent to the fixed set system of an equivariant infinite loop space the advantage of using the language of fixed set systems is that one can frequently replace the system of fixed sets of an ac tual g space by an equivalent formal system which is considerably simpler and which admits the requisite geometry necessary for delooping we also apply this machinery to construct equivariant eilenberg mac lane spaces corresponding to mackey functors

noise dressing of financial correlation matrices we show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate time series the central result of the present study which focuses on the case of financial price fluctuations is the remarkable agreement between the theoretical prediction based on the assumption that the correlation matrix is random and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the s 500 or other major markets in particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management

on the classification of g spheres i equivariant transversality this paper is the first in a series of three stated in geometric terms the papers examine locally linear group actions on spheres for odd order groups g in essentially equivalent homotopy theoretic terms the papers study the homotopy types of the spaces plc v and tope v of equivariant pl homeomorphisms and homeomorphisms of a linear representation v in fact it is the homogeneous spaces f6 v plg v and top6 v pl6 v we study where fc v is the space of proper equivariant homotopy equivalences our results generalize theorems of haefliger kirby siebenmann sullivan and wall and others the link between classification of manifolds and classification of homotopy types is transversality and this is the subject of the present first paper the second paper generalizes wall s classification of fake lens spaces to the classification of g spheres which are equivariantly homotopy equivalent to a given linear action this involves the determination of the equivariant homotopy type of the g space f pl and a complete calculation of the pl equivariant surgery sequence for a linear g sphere as a result we show that the homotopy groups of pl v u plc v vanish in dimensions less than dim v g in the third paper we study g triangulation theory in particular we study the homotopy groups of top6 v u topc v in a range the homotopy groups of the stiefel spaces plc v u plc v and topc v u top6 v are in turn needed for equivariant transversality so the three papers are locked together in an inductive fashion the reader is referred to w 4 below and to the individual parts ii and iii for more information we now give a brief discussion of the content of the present paper let g denote an arbitrary finite group we consider the g transversality question in the locally linear

multifractal behavior of the korean stock market index kospi abstract we investigate multifractality in the korean stock market index kospi the generalized qth order height height correlation function shows multiscaling properties there are two scaling regimes with a crossover time around t c 40 min we consider the original data sets and the modified data sets obtained by removing the daily jumps which occur due to the difference between the closing index and the opening index to clarify the origin of the multifractality we also smooth the data through convolution with a gaussian function after convolution we observe that the multifractality disappears in the short time scaling regime t t c but remains in the long time scaling regime t t c regardless of whether or not the daily jumps are removed we suggest that multifractality in the short time scaling regime is caused by the local fluctuations of the stock index but the multifractality in the long time scaling regime appears to be due to the intrinsic trading properties such as herding behavior information outside the market the long memory of the volatility and the nonlinear dynamics of the stock market

dynamic scaling approach to study time series fluctuations we propose an approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface growth problem in this framework the fluctuation sampling time interval plays the role of time variable whereas the physical time is treated as the analog of spatial variable in this way we found that the fluctuations of many real world time series satisfy the analog of the family viscek dynamic scaling ansatz this finding permits us to use the powerful tools of kinetic roughening theory to classify model and forecast the fluctuations of real world time series

real ade equivariant co homotopy and super m branes a key open problem in m theory is the identification of the degrees of freedom that are expected to be hidden at ade singularities in spacetime comparison with the classification of d branes by k theory suggests that the answer must come from the right choice of generalized cohomology theory for m branes here we show that real equivariant cohomotopy on superspaces is a consistent such choice at least rationally after explaining this new approach we demonstrate how to use elmendorf s theorem in equivariant homotopy theory to reveal ade singularities as part of the data of equivariant s 4 valued super cocycles on 11d super spacetime we classify these super cocycles and find a detailed black brane scan that enhances the entries of the old brane scan to cascades of fundamental brane super cocycles on strata of intersecting black m brane species we find that on each singular stratum the black brane s instanton contribution namely its super nambu goto green schwarz action appears as the homotopy datum associated to the morphisms in the orbit category

rational equivariant homotopy theory we give an algebraicization of rational s 1 equivariant homotopy theory there is an algebraic category of t systems which is equival nt to the a homotopy category of rational s 1 simply connected s 1 spaces there is is also a theory of minimal models for t systems analogous to sullivan mini nal algebras each s 1 space has an associated minimal t system whic ence des 2 all of its rational homotopy information including its rational equivariant cohomology and postnikov decomposition

completion of g spectra and stable maps between classifying spaces abstract we prove structural theorems for computing the completion of a g spectrum at the augmentation ideal of the burnside ring of a finite group g first we show that a g spectrum can be replaced by a spectrum obtained by allowing only isotropy groups of prime power order without changing the homotopy type of the completion we then show that this completion can be computed as a homotopy colimit of completions of spectra obtained by further restricting isotropy to one prime at a time and that these completions can be computed in terms of completion at a prime as an application we show that the spectrum of stable maps from bg to the classifying space of a compact lie group k splits non equivariantly as a wedge sum of p completed suspension spectra of classifying spaces of certain subquotients of g k in particular this describes the dual of bg

dynamic numerical models of stock market price from microscopic determinism to macroscopic randomness abstract a variant of threshold dynamics is introduced to model the behaviors of a large assembly of dealers in a stock market although the microscopic evolution dynamics is deterministic the collective behaviors such as market prices show seemingly stochastic fluctuations the statistical properties of market price change can be well approximated by a simple discrete langevin type equation with random amplification the macroscopic stochastic equation is solved both numerically and analytically showing that the market price change generally follow power law distributions in the steady state the reason for the appearance of rapid decay in the distribution tails are discussed

a multi interacting agent model for financial markets abstract microscopic models which resemble random magnetic systems have been used recently in the literature for the description of financial markets in the present work a model with many interacting agents similar to an ising random magnet with infinite range interactions is investigated the introduction of a local field term depending on the absolute value of a magnetization like parameter which measures the volatility of a financial market leads to a significant improvement with respect to previously studied models in the literature by investigating the return time series we show that several features characteristic of real financial markets are better reproduced by the present model in particular within this approach one is able to provide a proper behavior for the following properties i the power law tails and the nonzero skewness of the probability distribution of returns ii the exponential decay of the two time autocorrelation function of returns typical of high frequency financial data iii the so called leverage effect which corresponds to a negative correlation between past returns and future volatility

non extensive random walks stochastic variables whose addition leads to q gaussian distributions gq x 1 q 1 bx 2 1 1 q with b40 1pqo3 and where f x maxff x 0g as limit law for a large number of terms are investigated random walk sequences related to this problem possess a simple additive multiplicative structure commonly found in several contexts thus justifying the ubiquity of those distributions a characterization of the statistical properties of the random walk step lengths is performed moreover a connection with non linear stochastic processes is exhibited q gaussian distributions have special relevance within the framework of non extensive statistical mechanics a generalization of the standard boltzmann gibbs formalism introduced by tsallis over one decade ago therefore the present findings may give insights on the domain of applicability of such generalization r 2005 elsevier b v all rights reserved

finite size effects in monte carlo simulations of two stock market models abstract the microscopic market models of kim markowitz and of lux marchesi are simulated for varying number of investors if this number goes to infinity in some quantities nearly periodic oscillations occur

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

universal and nonuniversal properties of cross correlations in financial time series we use methods of random matrix theory to analyze the cross correlation matrix c of stock price changes of the largest 1000 u s companies for the 2 year period 1994 1995 we find that the statistics of most of the eigenvalues in the spectrum of c agree with the predictions of random matrix theory but there are deviations for a few of the largest eigenvalues we find that c has the universal properties of the gaussian orthogonal ensemble of random matrices furthermore we analyze the eigenvectors of c through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum a situation reminiscent of localization theory results

a filtration of spectra arising from families of subgroups of symmetric groups let ffn be a family of subgroups of enx which is closed under taking subgroups and conjugates such a family has a classifying space byfn and we showed in an earlier paper that a cormpatible choice of tfn for each n gives a simplicial monoid jjn btf which group completes to an infinite loop space in this paper we define a filtration of the associated spectrum whose filtration quotients given an extra condition on the families can be identified in terms of the classifying spaces of the families of subgroups that were chosen this gives a way to go from group theoretic data about the families to homotopy theoretic information about the associated spectrum we calculate two examples the first is related to elementary abelian p groups and the second gives a new expression for the desuspension of sp so spm i so as a suspension spectrum

modele minimal equivariant et formalite we study the rational equivariant homotopy type of a topological space x equipped with an action of the group of integers modulo n for n pk p prime k a positive integer we build an algebraic model which gives the rational equivariant homotopy type of x the homotopical fixed point set appears in the construction of a model of the fixed points set in general this model is different from g triantafillou s model ti for n p p prime we then give a notion of equivariant formality we prove that this notion is equivalent to the formalizability of the inclusion of fixed points set i xzp x examples and counterexamples of zp formal spaces are given

frequency analysis of tick quotes on foreign currency markets and the double threshold agent model abstract power spectrum densities for the number of tick quotes per minute market activity on three currency markets usd jpy eur usd and jpy eur are analyzed for periods from january 2000 to december 2000 we find some peaks on the power spectrum densities at a few minutes we develop the double threshold agent model and confirm that the corresponding periodicity can be observed for the activity of this model even though market participants perceive common weaker periodic information than threshold for decision making of them this model is numerically performed and theoretically investigated by utilizing the mean field approximation we propose a hypothesis that the periodicities found on the power spectrum densities can be observed due to nonlinearity and diversity of market participants

dynamical behaviors of inter out of equilibrium state intervals in korean futures exchange markets a recently discovered feature of financial markets the two phase phenomenon is utilized to categorize a financial time series into two phases namely equilibrium and out of equilibrium states for out of equilibrium states we analyze the time intervals at which the state is revisited the power law distribution of inter out of equilibrium state intervals is shown and we present an analogy with discrete time heat bath dynamics similar to random ising systems in the mean field approximation this model reduces to a one dimensional multiplicative process by varying global and local model parameters the relevance between volatilities in financial markets and the interaction strengths between agents in the ising model are investigated and discussed

stochastic cellular automata model for stock market dynamics in the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market a direct percolation method is used to create a hierarchy of clusters of active traders on a two dimensional grid active traders are characterized by the decision to buy ensuremath sigma i t 1 or sell ensuremath sigma i t ensuremath 1 a stock at a certain discrete time step the remaining cells are inactive ensuremath sigma i t 0 the trading dynamics is then determined by the stochastic interaction between traders belonging to the same cluster extreme intermittent events such as crashes or bubbles are triggered by a phase transition in the state of the bigger clusters present on the grid where almost all the active traders come to share the same spin orientation most of the stylized aspects of the financial market time series including multifractal proprieties are reproduced by the model a direct comparison is made with the daily closures of the s index

minority games with score dependent and agent dependent payoffs score dependent and agent dependent payoffs of the strategies are introduced into the standard minority game the intrinsic periodicity is consequently removed and the stylized facts arise such as long range volatility correlations and fat tails in the distribution of the returns the agent dependence of the payoffs is essential in producing the long range volatility correlations the new payoffs lead to a better performance in the dynamic behavior nonlocal in time and can coexist with the inactive strategy we also observe that the standard deviation ensuremath sigma 2 n is significantly reduced thus the efficiency of the system is distinctly improved based on this observation we give a qualitative explanation for the long range volatility correlations

a self adjusted monte carlo simulation as a model for financial markets with central regulation abstract properties of the self adjusted monte carlo algorithm applied to 2d ising ferromagnet are studied numerically the endogenous feedback form expressed in terms of the instant running averages is suggested in order to generate a biased random walk of the temperature that converges to criticality without an external tuning the robustness of a stationary regime with respect to partial accessibility of the information is demonstrated several statistical and scaling aspects have been identified which allow to establish an alternative spin lattice model of the financial market it turns out that our model alike model suggested by bornholdt int j mod phys c 12 2001 667 may be described by levy type stationary distribution of feedback variations with unique exponent 1 3 3 however the differences reflected by hurst exponents suggest that resemblances between the studied models seem to be non trivial

transmission of information and herd behavior an application to financial markets we propose a model for stochastic formation of opinion clusters modeled by an evolving network and herd behavior to account for the observed fat tail distribution in returns of financial price data the only parameter of the model is h the rate of information dispersion per trade which is a measure of herding behavior for h below a critical h the system displays a power law distribution of the returns with exponential cutoff however for hg h an increase in the probability of large returns is found and may be associated with the occurrence of large crashes

enforcing social behavior in an ising model with complex neighborhoods abstract we consider the problem of enforcing desired behavior in a population of individuals modeled by an ising model although there is a large literature dealing with social interaction models the problem of controlling behavior in a system modeled by the ising model seems to be an unexplored field first we provide and analytically characterize an optimal policy that may be used to achieve this objective second we show that complex neighborhoods highly influence the decision making process third we use lagrange multipliers associated to some constraints of a related problem to identify the role of individuals in the system

non monotonic spontaneous magnetization in a sznajd like consensus model abstract ising or potts models of ferromagnetism have been widely used to describe locally interacting social or economic systems we consider a related model introduced by sznajd to describe the evolution of consensus in a society in this model the opinion or state of any spins can only be changed through the influence of neighbouring pairs of similarly aligned spins such pairs can polarize their neighbours we show that assuming the global dynamics evolved in a synchronous manner the two state sznajd model exhibits a non monotonically decreasing overall orientation that has a maximum value when the system is subject to a finite value of noise reinterpreting the model in terms of opinions within a society we predict that consensus can be increased by the addition of an appropriate amount of random noise these features are explained by the presence of islands of complete orientation that are stable in the absence of noise but removed via the presence of added noise

persistence probabilities of the german dax and shanghai index abstract we present a relatively detailed analysis of the persistence probability distributions in financial dynamics compared with the auto correlation function the persistence probability distributions describe dynamic correlations nonlocal in time universal and non universal behaviors of the german dax and shanghai index are analyzed and numerical simulations of some microscopic models are also performed around the fixed point z 0 0 the interacting herding model produces the scaling behavior of the real markets

asymptotic power law of moments in a random multiplicative process with weak additive noise it is well known that a random multiplicative process with weak additive noise generates a power law probability distribution it has recently been recognized that this process exhibits another type of power law the moment of the stochastic variable scales as a function of the additive noise strength we clarify the mechanism for this power law behavior of moments by treating a simple langevin type model both approximately and exactly and argue this mechanism is universal we also discuss the relevance of our findings to noisy on off intermittency and to singular spatio temporal chaos recently observed in systems of non locally coupled elements

scaling of the distribution of fluctuations of financial market indices up to more than one month we find that the distributions for dt 4d 1560 min are consistent with a power law asymptotic behavior characterized by an exponent a 3 well outside the stable levy regime 0 a 2 to test the robustness of the s p result we perform a parallel analysis on two other financial market indices database iv contains 3560 daily records of the nikkei index for the 14 year period 1984 1997 and database v contains 4649 daily records of the hang seng index for the 18 year period 1980 1997 we find estimates ofa consistent with those describing the distribution of s p 500 daily returns one possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility for time scales longer than dt 3 4 d our results are consistent with a slow convergence to gaussian behavior s1063 651x 99 11211 x pacs number s 05 40 fb 05 45 tp 89 90 1n

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

microscopic spin model for the dynamics of the return distribution of the korean stock market index abstract in this paper we studied the dynamics of the log return distribution of the korean composition stock price index kospi from 1992 to 2004 based on the microscopic spin model we found that while the index during the late 1990s showed a power law distribution the distribution in the early 2000s was exponential this change in distribution shape was caused by the duration and velocity among other parameters of the information that flowed into the market

comparison of regularization methods for solving the cauchy problem associated with the helmholtz equation in this paper several boundary element regularization methods such as iterative conjugate gradient tikhonov regularization and singular value decomposition methods for solving the cauchy problem associated to the helmholtz equation are developed and compared regularizing stopping criteria are developed and the convergence as well as the stability of the numerical methods proposed are analysed the cauchy problem for the helmholtz equation can be regularized by various methods such as the general regularization methods presented in this paper but more accurate results are obtained by classical methods such as the singular value decomposition and the tikhonov regularization methods copyright 2004 john wiley sons ltd

a generalized dynamic herding model with feed back interactions abstract a dynamic feed back interaction is introduced to the eguiluz zimmermann model phys rev lett 85 2000 5659 in application to financial dynamics transmission of information at time t is supposed to depend on the variation of the financial index at t 1 the generated time series is strongly correlated in time at criticality both static and dynamic behavior are investigated

influence of noise near blowout bifurcation we consider effects of zero mean additive noise on systems that are undergoing supercritical blowout bifurcation i e where a chaotic attractor in an invariant subspace loses transverse stability to a nearby on off intermittent attractor we concentrate on the low noise limit and two statistical properties of the trajectories the variance of the normal component and the mean first crossing time of the invariant subspace before blowout we find that the asymptotic variance scales algebraically with the noise level and exponentially with the lyapunov exponent after blowout it is limited to the nonzero variance of the associated on off intermittent state surprisingly for a large enough lyapunov exponent the effect of added noise can be to decrease rather than increase the variance the mean crossing time becomes infinite at and after the blowout in the limit of small noise after the blowout there is exponential dependence on the lyapunov exponent and algebraic dependence on the noise level the results are obtained using a drift diffusion model of venkataramani et al the results are confirmed in numerical experiments on a smooth mapping we observe that although there are qualitative similarities between bubbling noise driven and on off intermittency dynamics driven these can be differentiated using the statistical properties of the variance of the normal dynamics and the mean crossing time of the invariant subspace in the limit of low noise

a novel approach to detect volatility clusters in financial time series abstract the self similarity index has been consolidated as a widely applied measure to quantify long memory in stock markets in this article though we shall provide a novel methodology allowing the detection of clusters of volatility in series of asset returns with this aim the concept of a volatility series is introduced we found that the existence of clusters of high low volatility in the series leads to an increasing hurst exponent of the volatility series some empirical applications were carried out in fact we artificially generated processes with clusters of volatility the mean self similarity exponents of their volatility series were compared with those from a brownian motion and the s p500 index as a result the greater the number of periods used in the calculation of the self similarity exponent the smoother the graph of the volatility series and hence the higher its exponent accordingly the more likely the clusters of volatility appear a dynamic study on the evolution of the self similarity index of the volatility series of the s p500 was also performed it was observed that the greater its self similarity exponent the more frequent the volatility changes which usually corresponds to falls in the index and hence the more likely the volatility clusters appear

systems of fixed point sets let g be a compact lie group a canonical method is given for constructing a c space from homotopy theoretic information about its fixed point sets the construction is a special case of the categorical bar construction applications include easy constructions of certain classifying spaces as well as c eilenbergmac lane spaces and postnikov towers 0 introduction let g be a compact lie group and x a g space the equivariant homotopy theory of x is reflected to a remarkable extent in its system of fixed point sets defined as a functor from a certain category 0g to top the category of topological spaces our spaces will be compactly generated weak hausdorff they may or may not be equipped with a basepoint depending on the context these functors or systems have considerable technical advantages over g spaces it is easy to apply most homotopy theoretic constructions to them whereas in many cases it is unclear how to proceed for g spaces it is the purpose of this paper to present a canonical way of recovering from any system a g space which preserves all the homotopy theoretic structure of the system this allows us to give easy equivariant versions of some standard topological constructions such as eilenberg mac lane spaces and postnikov towers and to simplify other equivariant constructions 1 1 statements of the main theorems throughout g is a fixed compact lie group definitions the category of canonical orbits written 0g is a topological category with discrete object space 0g g 77 77 a closed subgroup of g and morphisms the g maps topologized by requiring the natural bijection hoxn0cig h g k g k h to be a homeomorphism by an oc space we shall mean a continuous contravariant functor from 0g to top these functors form the objects of a topological category in the usual manner we will also consider gg rings oc groups etc defined similarly definition let a1 be a g space the fixed point set system of x written x is an gg space defined as follows g 77 x received by the editors october 30 1981 and in revised form april 26 1982 1980 mathematics subject classification primary 57s10 55n25

best linear forecast of volatility in financial time series the autocorrelation function of volatility in financial time series is fitted well by a superposition of several exponents this case admits an explicit analytical solution of the problem of constructing the best linear forecast of a stationary stochastic process we describe and apply the proposed analytical method for forecasting volatility the leverage effect and volatility clustering are taken into account parameters of the predictor function are determined numerically for the dow jones 30 industrial average connection of the proposed method to the popular autoregressive conditional heteroskedasticity models is discussed

orbispaces orthogonal spaces and the universal compact lie group this paper identifies the homotopy theories of topological stacks and orbispaces with unstable global homotopy theory at the same time we provide a new perspective by interpreting it as the homotopy theory of spaces with an action of the universal compact lie group the upshot is a novel way to construct and study genuine cohomology theories on stacks orbifolds and orbispaces defined from stable global homotopy types represented by orthogonal spectra the universal compact lie group which is neither compact nor a lie group is a well known object namely the topological monoid mathcal l of linear isometric self embeddings of mathbb r infty the underlying space of mathcal l is contractible and the homotopy theory of mathcal l spaces with respect to underlying weak equivalences is just another model for the homotopy theory of spaces however the monoid mathcal l contains copies of all compact lie groups in a specific way and we define global equivalences of mathcal l spaces by testing on corresponding fixed points we establish a global model structure on the category of mathcal l spaces and prove it to be quillen equivalent to the global model category of orthogonal spaces and to the category of orbispaces i e presheaves of spaces on the global orbit category

algebraic models for equivariant homotopy theory over abelian compact lie groups we describe some algebraic models for equivariant rational and p adic homotopy theory over abelian compact lie groups

on off intermittency power spectrum and fractal properties of time series abstract some dynamical systems possess invariant submanifolds such that the dynamics restricted to the invariant submanifold is chaotic this situation arises in systems with a spatial symmetry or in the synchronization of chaotic oscillators the invariant submanifold could become unstable to perturbations in the transverse directions when a parameter of the system is changed through a critical blow out value this could result in an extreme form of temporally intermittent bursting called on off intermittency we propose a model that incorporates the universal features of systems that display on off intermittency we study this model both with and without additive noise and we derive scaling results for the power spectral density of the on off intermittent process and for the box counting dimension for the set of time intervals when the process takes on values above a given threshold we then present numerical simulations realizing these results

universal features in the growth dynamics of complex organizations we analyze the fluctuations in the gross domestic product gdp of 152 countries for the period 1950 1992 we find that i the distribution of annual growth rates for countries of a given gdp decays with fatter tails than for a gaussian and ii the width of the distribution scales as a power law of gdp with a scaling exponent b 0 15 both findings are in surprising agreement with results on firm growth these results are consistent with the hypothesis that the evolution of organizations with complex structure is governed by similar growth mechanisms s0031 9007 98 07339 6 pacs numbers 02 50 ey 01 75 m 05 40 j 05 45 b in the study of physical systems the analysis of the scaling properties of the fluctuations has been shown to give important information regarding the underlying processes responsible for the observed macroscopic behavior in contrast most studies on the time evolution of economic time series have concentrated on average growth rates 1 18 here we investigate the possibility that the study of fluctuations in economics may also lead to a better understanding of the mechanisms responsible for the observed dynamics 19 23 we therefore analyze the fluctuations in the growth rate of the gross domestic product gdp of 152 countries during the period 1950 1992 24 we will show that i the distribution of annual growth rates for countries of a given gdp is consistent for a certain range with an exponential decay and ii the width of the distribution scales as a power law of gdp with a scaling exponent b 0 15 both findings are in surprising agreement with