varieties of nilpotent lie algebras of dimension less than six the set of all nilpotent ide algebra multiplications on a fixed vector space of dimension n over a field k forms an affine variety n isomorphism classes of these lie algebras are orbits in i under the change of basis action of gl n k by examining the orbit structure of n for small n we hope to gain a new perspective on the classification of nilpotent lie algebras in this paper we determine completely the orbit structure of the variety n when n 6 5 and k c we also show that the homomorphic image of a nilpotent lie algebra is in the closure of the orbit of that lie algebra taking the direct product with an abelian lie algebra to make the dimension right some of the orbit structure of n for n 6 and other geometric properties of n were described by vergne in vl v2 v3 recently carles has used vergne s results to study the variety of all lie algebras cl our motivation for studying the classification of nilpotent lie algebras is to gain information about the classification of nilpotent groups the correspondence between nilpotent lie algebras and nilpotent groups is described in go

bandt pompe approach to the classical quantum transition abstract by regarding the celebrated classical quantum transition problem as one pertaining to the domain of dynamic systems theory we present a discussion that exhibits the superiority of the bandt pompe approach to the extraction of a probability distribution from time series values

can one make any crash prediction in finance using the local hurst exponent idea abstract we apply the hurst exponent idea for investigation of djia index time series data the behavior of the local hurst exponent prior to drastic changes in financial series signal is analyzed the optimal length of the time window over which this exponent can be calculated in order to make some meaningful predictions is discussed our prediction hypothesis is verified with examples of 1929 and 1987 crashes as well as with more recent phenomena in stock market from the period 1995 to 2003 some interesting agreements are found

sampling period statistical complexity and chaotic attractors abstract we analyze the statistical complexity measure vs entropy plane representation of sampled chaotic attractors as a function of the sampling period and show that if the bandt and pompe procedure is used to assign a probability distribution function pdf to the pertinent time series the statistical complexity measure scm attains a definite maximum for a specific sampling period t m on the contrary the usual histogram approach for assigning pdfs to a time series leads to essentially constant scm values for any sampling period the significance of t m is further investigated by comparing it with typical times found in the literature for the two main reconstruction processes the takens one in a delay time embedding on one hand and the exact nyquist shannon reconstruction on the other one it is shown that t m is compatible with those times recommended as adequate delay ones in takens reconstruction the reported results correspond to three representative chaotic systems having correlation dimension 2 d 2 3 one recent experiment confirms the analysis presented here

multivariate multiscale fractional order weighted permutation entropy of nonlinear time series abstract in this letter multivariate multiscale fractional permutation entropy mmfpe and multivariate weighted multiscale fractional permutation entropy mwmfpe have been proposed to provide insights for the study of time series when measuring the dynamics of complex systems the mmfpe and mwmfpe methods are sensitive to the signal evolution meanwhile they can provide some analysis of complexity over multiple time series as well as multiple channel signals we perform these methods on synthetic tri variate time series to explore some of the interesting properties especially for negative information and information deception it can be seen that more complex system is more likely to be deceptive the amplitude information of time series which is taken into account in the mwmfpe can weaken this deception the methods are also employed to the closing prices and trade volume of financial stock markets from different areas according to the mwmfpe results the indices can be divided into three groups 1 cac40 hsi nasdaq s p500 2 n225 and 3 shencheng implying that it has a capacity to distinguish these financial stock market

the entropy as a tool for analysing statistical dependences in financial time series abstract the entropy is a concept which may serve to define quantities such as the conditional entropy and the mutual information using a novel algorithm for the estimation of the mutual information from data we analyse several financial time series and demonstrate the usefulness of this new approach the issues of long range dependence and non stationarity are discussed

refined composite multiscale weighted permutation entropy of financial time series abstract for quantifying the complexity of nonlinear systems multiscale weighted permutation entropy mwpe has recently been proposed mwpe has incorporated amplitude information and been applied to account for the multiple inherent dynamics of time series however mwpe may be unreliable because its estimated values show large fluctuation for slight variation of the data locations and a significant distinction only for the different length of time series therefore we propose the refined composite multiscale weighted permutation entropy rcmwpe by comparing the rcmwpe results with other methods results on both synthetic data and financial time series rcmwpe method shows not only the advantages inherited from mwpe but also lower sensitivity to the data locations more stable and much less dependent on the length of time series moreover we present and discuss the results of rcmwpe method on the daily price return series from asian and european stock markets there are significant differences between asian markets and european markets and the entropy values of hang seng index hsi are close to but higher than those of european markets the reliability of the proposed rcmwpe method has been supported by simulations on generated and real data it could be applied to a variety of fields to quantify the complexity of the systems over multiple scales more accurately

analysis of crude oil markets with improved multiscale weighted permutation entropy abstract entropy measures are recently extensively used to study the complexity property in nonlinear systems weighted permutation entropy wpe can overcome the ignorance of the amplitude information of time series compared with pe and shows a distinctive ability to extract complexity information from data having abrupt changes in magnitude improved or sometimes called composite multi scale ms method possesses the advantage of reducing errors and improving the accuracy when applied to evaluate multiscale entropy values of not enough long time series in this paper we combine the merits of wpe and improved ms to propose the improved multiscale weighted permutation entropy imwpe method for complexity investigation of a time series then it is validated effective through artificial data white noise and 1 f noise and real market data of brent and daqing crude oil meanwhile the complexity properties of crude oil markets are explored respectively of return series volatility series with multiple exponents and eemd produced intrinsic mode functions imfs which represent different frequency components of return series moreover the instantaneous amplitude and frequency of brent and daqing crude oil are analyzed by the hilbert transform utilized to each imf

characterization of time dynamical evolution of electroencephalographic epileptic records abstract since traditional electrical brain signal analysis is mostly qualitative the development of new quantitative methods is crucial for restricting the subjectivity in the study of brain signals these methods are particularly fruitful when they are strongly correlated with intuitive physical concepts that allow a better understanding of the brain dynamics the processing of information by the brain is reflected in dynamical changes of the electrical activity in time frequency and space therefore the concomitant studies require methods capable of describing the qualitative variation of the signal in both time and frequency the entropy defined from the wavelet functions is a measure of the order disorder degree present in a time series in consequence this entropy evaluates over eeg time series gives information about the underlying dynamical process in the brain more specifically of the synchrony of the group cells involved in the different neural responses the total wavelet entropy results independent of the signal energy and becomes a good tool for detecting dynamical changes in the system behavior in addition the total wavelet entropy has advantages over the lyapunov exponents because it is parameter free and independent of the stationarity of the time series in this work we compared the results of the time evolution of the chaoticity lyapunov exponent as a function of time with the corresponding time evolution of the total wavelet entropy in two different eeg records one provide by depth electrodes and other by scalp ones

complex and composite entropy fluctuation behaviors of statistical physics interacting financial model abstract in an attempt to investigate and reproduce the fluctuation dynamics of price changes in financial markets a novel complex random interacting financial price model is developed by combining voter interacting system with compound poisson process in this model the dissemination of investors investment attitudes can simulate normal and frequent small price fluctuations of financial markets while the random drastic jumps can capture undue and rare large price fluctuations as results of sudden economic events and political events in the markets in order to verify the rationality of the model some statistical characteristics of the model returns including fat tail power law scaling complexity and multifractal are compared with real returns by probability density functions composite distance fuzzy entropy c fuzzyen matching energy and multifractal detrended fluctuation analysis the c fuzzyen is a new entropy based approach based on fuzzy entropy and complexity invariant to measure the complexity behaviors of return series the effectiveness analysis of c fuzzyen indicates that it has a higher estimation accuracy and stronger robustness than fuzzy entropy the empirical results show that the price model is able to reproduce some important statistical properties of financial markets to a certain extent and the complexity of returns for the proposed model increases when infection intensity or jump intensity increases

ordinal analysis of time series abstract in order to develop fast and robust methods for extracting qualitative information from non linear time series bandt and pompe have proposed to consider time series from the pure ordinal viewpoint on the basis of counting ordinal patterns which describe the up and down in a time series they have introduced the concept of permutation entropy for quantifying the complexity of a system behind a time series the permutation entropy only provides one detail of the ordinal structure of a time series here we present a method for extracting the whole ordinal information

randomizing nonlinear maps via symbolic dynamics abstract pseudo random number generators prng have attracted intense attention due to their obvious importance for many branches of science and technology a randomizing technique is a procedure designed to improve the prng randomness degree according the specific requirements it is obviously important to quantify its effectiveness in order to classify randomizing techniques based on a symbolic dynamics approach we advance a novel physically motivated representation based on the statistical properties of chaotic systems recourse is made to a plane that has as coordinates i the shannon entropy and ii a form of the statistical complexity measure each statistical quantifier incorporates a different probability distribution function generating thus a representation that i sheds insight into just how each randomizing technique operates and also ii quantifies its effectiveness using the logistic map and the three way bernoulli map as typical examples of chaotic dynamics it is shown that our methodology allows for choosing the more convenient randomizing technique in each instance comparison with measures of complexity based on diagonal lines on the recurrence plots n marwan m c romano m thiel j kurths phys rep 438 2007 237 support the main conclusions of this paper

forbidden patterns permutation entropy and stock market inefficiency abstract in this paper we introduce two new quantifiers for the stock market inefficiency the number of forbidden patterns and the normalized permutation entropy they are model independent measures thus they have more general applicability we find robust evidence that degree of market inefficiency is positively correlated with the number of forbidden patterns and negatively correlated with the permutation entropy our empirical results suggest that these two physical tools are useful to discriminate the stage of stock market development and can be easily implemented

forecasting the crude oil prices based on econophysics and bayesian approach abstract in view of the importance and complexity of crude oil price we investigate the dynamic forecasting of crude oil prices via bayesian and econophysics approaches we propose information entropy to measure the predictability of crude oil prices and employ the rolling window approach to forecast the dynamic price of crude oil in this article bayesian approach is applied to estimate the parameters at the same time the classic estimate approach is also adopted finally we compare the forecasting results of the two methods the results of this paper indicates that 1 both estimate approaches can effectively estimate the parameters of heston model 2 under a specific loss function bayesian approach has advantage over classical estimation approach when estimated sample size is small while the estimate sample size increases classical method slightly outperforms bayesian method 3 the predicted entropy of the estimated interval of 200 days under the bayesian method are closest to the actual information entropy while the estimated interval of 600 days under the maximum likelihood method is closest to the information entropy 4 except for the estimation interval of 200 days the predicted entropy under the maximum likelihood estimation is more representative of the predictability of the crude oil price we also consider the more general case we test this two methods of different steps ahead and compare the stability of the two methods

revisiting the decay of missing ordinal patterns in long term correlated time series abstract we revisit the decay of missing ordinal patterns in long term correlated time series more precisely a stretched exponential model is proposed to describe more appropriately how the number of missing ordinal patterns decreases as a function of the time series length in the case of correlated stochastic data numerical analysis and experimental applications confirm that this generalized model allows a more accurate characterization of the underlying dynamics and a reliable quantification of the long range temporal correlations

weighted permutation entropy based on different symbolic approaches for financial time series abstract in this paper we introduce weighted permutation entropy wpe and three different symbolic approaches to investigate the complexities of stock time series containing amplitude coded information and explore the influence of using different symbolic approaches on obtained wpe results we employ wpe based on symbolic approaches to the us and chinese stock markets and make a comparison between the results of us and chinese stock markets three symbolic approaches are able to help the complexity containing in the stock time series by wpe method drop whatever the embedding dimension is the similarity between these stock markets can be detected by the wpe based on binary coding method while the difference between them can be revealed by the wpe based on method max min method the combinations of the symbolic approaches method and max min method and wpe method are capable of reflecting the multiscale structure of complexity by different time delay and analyze the differences between complexities of stock time series in more detail and more accurately furthermore the correlations between stock markets in the same region and the similarities hidden in the s p500 and dji shangzheng and shencheng are uncovered by the comparison of the wpe based on binary coding method of six stock markets

modeling the predictive power of the singular value decomposition based entropy empirical evidence from the dow jones global titans 50 index abstract in this paper we are analyzing the predictive power of the singular value decomposition entropy for the dow jones global titans 50 djgt index of the new york stock exchange nyse market for the correlation matrix of the djgt index components we then calculate the entropy of the singular value decomposition granger causality test was used to prove that entropy has a predictive power for stock market dynamics of the djgt index the results of our paper are revealing the importance of considering structural breaks when analyzing financial stock markets our analysis is conducting to the conclusion that the singular value decomposition entropy has predictive power for the nyse djgt index

statistical properties of one dimensional binary sequences with power law power spectrum abstract by the fourier filtering method we generate one dimensional binary sequences from coarse grained continuous sequences with preset exponents 0 using the spectrum analysis we find that the corresponding binary sequences have pure 1 f power spectrum and spectrum exponents 0 0 2 0 where f is the frequency we evaluate numerically the relation between and 0 using the autocorrelation function analysis the detrended fluctuation analysis the duration time analysis and the entropy analysis we investigate extensively the statistical properties of such binary sequences we find that the statistical properties are basically different for 1 and 1 and binary sequences become more and more ordered as increases

uniform coverage bounds for confidence intervals and berry esseen theorems for edgeworth expansion we derive upper bounds for the coverage error of confidence intervals for a population mean uniformly over large classes of populations and different types of confidence intervals it is shown that the order of these bounds is achieved by the normal approximation method for constructing confidence intervals uniformly over distributions with finite third moment and by an empirical edgeworth correction of this approach uniformly over smooth distributions with finite fourth moments these results have straightforward extensions to higher orders of edgeworth correction and higher orders of moments our upper bounds to coverage accuracy are based on berry esseen theorems for edgeworth expansions of the distribution of the studentized mean

characterization of autoregressive processes using entropic quantifiers abstract the aim of the contribution is to introduce a novel information plane the causal amplitude informational plane as previous works seems to indicate bandt and pompe methodology for estimating entropy does not allow to distinguish between probability distributions which could be fundamental for simulation or for probability analysis purposes once a time series is identified as stochastic by the causal complexity entropy informational plane the novel causal amplitude gives a deeper understanding of the time series quantifying both the autocorrelation strength and the probability distribution of the data extracted from the generating processes two examples are presented one from climate change model and the other from financial markets

missing ordinal patterns in correlated noises abstract recent research aiming at the distinction between deterministic or stochastic behavior in observational time series has looked into the properties of the ordinal patterns c bandt b pompe phys rev lett 88 2002 174102 in particular new insight has been obtained considering the emergence of the so called forbidden ordinal patterns j m amigo s zambrano m a f sanjuan europhys lett 79 2007 50001 it was shown that deterministic one dimensional maps always have forbidden ordinal patterns in contrast with time series generated by an unconstrained stochastic process in which all the patterns appear with probability one techniques based on the comparison of this property in an observational time series and in white gaussian noise were implemented however the comparison with correlated stochastic processes was not considered in this paper we used the concept of missing ordinal patterns to study their decay rate as a function of the time series length in three stochastic processes with different degrees of correlation fractional brownian motion fractional gaussian noise and noises with f k power spectrum we show that the decay rate of missing ordinal patterns in these processes depend on their correlation structures we finally discuss the implications of the present results for the use of these properties as a tool for distinguishing deterministic from stochastic processes

gas liquid two phase flow structure in the multi scale weighted complexity entropy causality plane abstract the multi scale weighted complexity entropy causality plane ms wcecp is proposed for characterizing the physical structure of complex system firstly we use the method to investigate typical nonlinear time series compared with the multi scale complexity entropy causality plane ms cecp the ms wcecp can not only uncover the dynamic information loss of complex system with the increase of scale but also can characterize the complexity of nonlinear dynamic system in particular the algorithm of ms wcecp performs strong anti noise ability then we calculate the ms wcecp for the conductance fluctuating signals measured from vertical upward gas liquid two phase flow experiments in a small diameter pipe the results demonstrate that the ms wcecp is a useful approach for exploring the stability and complexity in gas liquid two phase flows

intensive statistical complexity measure of pseudorandom number generators abstract a statistical complexity measure has been recently proposed to quantify the performance of chaotic pseudorandom number generators prng physica a 354 2005 281 here we revisit this quantifier and introduce two important improvements i consideration of an intensive statistical complexity physica a 334 2004 119 and ii following the prescription of brand and pompe phys rev lett 88 2002 174102 1 in evaluating the probability distribution associated with the prng the ensuing new measure is applied to a very well tested prng advanced by marsaglia

evidence of increment of efficiency of the mexican stock market through the analysis of its variations abstract it is well known that there exist statistical and structural differences between the stock markets of developed and emerging countries in this work and in order to find out if the efficiency of the mexican stock market has been changing over time we have performed and compared several analyses of the variations of the mexican stock market index ipc and dow jones industrial average index djia for different periods of their historical daily data we have analyzed the returns autocorrelation function acf and used detrended fluctuation analysis dfa to study returns variations we also analyze the volatility mean value and standard deviation of both markets and compare their evolution we conclude from the overall result of these studies that they show compelling evidence of the increment of efficiency of the mexican stock market over time the data samples analyzed here correspond to daily values of the ipc and djia for the period 10 30 1978 02 28 2006

on commutative polarizations let l be a finite dimensional lie algebra over a field k of characteristic zero and let u l be its enveloping algebra with quotient division ring d l let p be a commutative lie subalgebra of l in o2 the necessary and sufficient condition on p was given in order for d p to be a maximal commutative subfield of d l in particular this condition is satisfied if p is a commutative polarization cp with respect to any regular f l and the converse holds if l is ad algebraic the purpose of this paper is to study lie algebras admitting these cp s and to demonstrate their widespread occurrence first we have the following characterisation if l is completely solvable p is a cp of l if and only if there exists a descending chain of lie subalgebras

edgeworth expansion for student s t statistic under minimal moment conditions recent advances in the theory of edgeworth expansion allow rigorous estimation of remainder terms under explicit regularity conditions however even in the important case of student s t statistic the moment conditions required are unrealistically stringent in this note we relax those conditions to the minimum needed to define terms in the edgeworth expansion

the experimental signals analysis for bubbly oil in water flow using multi scale weighted permutation entropy abstract we firstly combine multi scale method ms and weighted permutation entropy wpe to analyze chaotic noisy and fractal time series and find that mswpe can distinguish different nonlinear time series and exhibit a better robustness in the presence of higher levels of noise a task that multi scale permutation entropy mspe fails to work we then apply mswpe to analyze the signals from vertical upward oil in water two phase flow experiments our results suggest that the change rate of mswpe enables to characterize the transition of flow patterns and multi scale weighted permutation entropy allows indicating the discrepancy of complexity of oil in water two phase flow

econophysics financial time series from a statistical physics point of view in recent years physicists have started applying concepts and methods of statistical physics to study economic problems the word econophysics is sometimes used to refer to this work much recent work is focused on understanding the statistical properties of nancial time series one reason for this interest is that nancial markets are examples of complex interacting systems for which a huge amount of data exist and it is possible that nancial time series viewed from a dierent perspective might yield new results this article reviews the results of three recent phenomenological studies i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to drastic events such as market crashes 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 eight orders of magnitude in addition this distribution preserves its functional form for uctuations on time scales that dier by three orders of magnitude from 1 min up to approximately 10 d 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 and persist for several months iii correlations among dierent companies the third result bears on the application of random matrix theory to understand the correlations among price uctuations of any two dierent stocks from a study of the eigenvalue statistics of the cross correlation matrix constructed from price uctuations of the leading 1000 stocks we nd that the largest 1 of the eigenvalues and the corresponding eigenvectors show systematic deviations from the predictions for a random matrix whereas the rest of the eigenvalues conform to random matrix behavior suggesting that these 1 of the eigenvalues contain system specic information about correlated time evolution of dierent companies c 2000 published by elsevier science b v all rights reserved

markov processes hurst exponents and nonlinear diffusion equations with application to finance abstract we show by explicit closed form calculations that a hurst exponent h 1 2 does not necessarily imply long time correlations like those found in fractional brownian motion fbm we construct a large set of scaling solutions of fokker planck partial differential equations pdes where h 1 2 thus markov processes which by construction have no long time correlations can have h 1 2 if a markov process scales with hurst exponent h 1 2 then it simply means that the process has nonstationary increments for the scaling solutions we show how to reduce the calculation of the probability density to a single integration once the diffusion coefficient d x t is specified as an example we generate a class of student t like densities from the class of quadratic diffusion coefficients notably the tsallis density is one member of that large class the tsallis density is usually thought to result from a nonlinear diffusion equation but instead we explicitly show that it follows from a markov process generated by a linear fokker planck equation and therefore from a corresponding langevin equation having a tsallis density with h 1 2 therefore does not imply dynamics with correlated signals e g like those of fbm a short review of the requirements for fbm is given for clarity and we explain why the usual simple argument that h 1 2 implies correlations fails for markov processes with scaling solutions finally we discuss the question of scaling of the full green function g x t x t of the fokker planck pdes

does the singular value decomposition entropy have predictive power for stock market evidence from the shenzhen stock market abstract this paper analyzes the predictive ability of the singular value decomposition entropy for the shenzhen component index based on different scales it is found that the predictive ability of the entropy for the index is affected by the width of moving time windows and the structural break in stock market by moving time windows with one year the predictive power of singular value decomposition entropy of shenzhen stock market for its component index is found after the reform of non tradable shares

info quantifiers map characterization revisited abstract we highlight the potentiality of a special information theory it approach in order to unravel the intricacies of nonlinear dynamics the methodology being illustrated with reference to the logistic map a rather surprising dynamic feature plane topography map becomes available

topological permutation entropy permutation entropy quantifies the diversity of possible ordering of the successively observed values a random or deterministic system can take just as shannon entropy quantifies the diversity of the values themselves when the observable or state variable has a natural order relation making permutation entropy possible to compute then the asymptotic rate of growth in permutation entropy with word length forms an alternative means of describing the intrinsic entropy rate of a source herein extending a previous result on metric entropy rate we show that the topological permutation entropy rate for expansive maps equals the conventional topological entropy rate familiar from symbolic dynamics this result is not limited to one dimensional maps

on simple novikov algebras and their irreducible modules abstract we give a complete classification of finite dimensional simple novikov algebras and their irreducible modules over an algebraically closed field with prime characteristic moreover we introduce novikov poisson algebras and their tensor theory our tensor theory enables us to understand better certain finite dimensional simple novikov algebras and their irreducible modules

some p v equivalences and a classification of 2 simple prehomogeneous vector spaces of type a classification of 2 simple prehomogeneous vector spaces is completed by using some p v equivalences together with 3 some part is very different from the previous classification of the irreducible or simple cases 1 2 and some new method is necessary this result shows the difficult point of a classification problem of reductive prehomogeneous vector spaces introduction in m sato and t kimura 1 all irreducible prehomogeneous vector spaces abbreviated irreducible p v s are classified up to castling equivalence and it is proved that any irreducible p v is castling equivalent to a 2 simple p v or to sl m x sl m x gl 2 a1 x a1 x a1 with m 2 3 therefore as a step to a classification of the general case it is natural to classify all nonirreducible 2 simple p v s in this paper we shall classify all 2 simple p v s of type ii and give the complete list of them up to strong equivalence in the sense of definition 4 p 36 in 1 however we need various p v equivalences cf propositions 1 7 1 12 1 34 1 36 1 37 theorem 1 16 and its corollary corollary 1 26 definition 1 31 remark 1 32 to carry out the classification and hence first we shall prove them we also investigate the regularity in some cases since all 2 simple p v s of type i are already classified in 3 this completes the classification of all 2 simple p v s here we say that g p v or simply g p is a 2 simple p v if it is a prehomogeneous vector space of the following form g gl 1 k s t xg x g2 where g1 and g2 are simple algebraic groups p the composition of the scalar multiplications gl l k s on each irreducible component and the representation p p1 p 1 pk p k a1 s 1 1 t1 t ofthegroupg1 x g2 where pi aj resp p tj are nontrivial irreducible representations of g1 resp g2 we write g p v instead of g p v for simplicity to avoid confusion we write instead of clearly each gl 1 x g1 x g2 pi p i 1 k is an irreducible 2 simple p v if at least one of them is a nontrivial p v see definition 1 1 we call it a 2 simple p v of type i on the other hand if all of them are trivial p v s we call it a 2 simple p v of type ii in this case we have g2 sl n received by the editors march 3 1986 and in revised form july 30 1986 1980 mathematics subject classification 1985 revision primary 11r20 11r29 secondary 11n25 11r18 01988 american mathematical society 0002 9947 88 1 00 25 per page

on certain maximal subfields in the quotient division ring of an enveloping algebra univ limburg dept math b 3590 diepenbeek belgium ooms ai univ limburg dept math b 3590 diepenbeek belgium

using renyi parameter to improve the predictive power of singular value decomposition entropy on stock market abstract this paper generalizes the method of traditional singular value decomposition entropy by incorporating orders q of renyi entropy we analyze the predictive power of the entropy based on trajectory matrix using shanghai composite index and dow jones index data in both static test and dynamic test in the static test on sci results of global granger causality tests all turn out to be significant regardless of orders selected but this entropy fails to show much predictability in american stock market in the dynamic test we find that the predictive power can be significantly improved in sci by our generalized method but not in dji this suggests that noises and errors affect sci more frequently than dji in the end results obtained using different length of sliding window also corroborate this finding

causality and the entropy complexity plane robustness and missing ordinal patterns abstract we deal here with the issue of determinism versus randomness in time series one wishes to identify their relative weights in a given time series two different tools have been advanced in the literature to such effect namely i the causal entropy complexity plane o a rosso h a larrondo m t martin a plastino m a fuentes distinguishing noise from chaos phys rev lett 99 2007 154102 and ii the estimation of the decay rate of missing ordinal patterns j m amigo s zambrano m a f sanjuan true and false forbidden patterns in deterministic and random dynamics europhys lett 79 2007 50001 l c carpi p m saco o a rosso missing ordinal patterns in correlated noises physica a 389 2010 2020 2029 in this work we extend the use of these techniques to address the analysis of deterministic finite time series contaminated with additive noises of different degree of correlation the chaotic series studied here was via the logistic map r 4 to which we added correlated noise colored noise with f k power spectrum 0 k 2 of varying amplitudes in such a fashion important insights pertaining to the deterministic component of the original time series can be gained we find that in the entropy complexity plane this goal can be achieved without additional computations

composition law of cardinal ordering permutations abstract in this paper the theorems that determine composition laws both cardinal ordering permutations and their inverses are proven so the relative position of points in an h s periodic orbit is completely known as well as which order those points are visited no matter how the h s periodic orbit emerges be it through a period doubling cascade s 2 n of as the h periodic orbit or a primary window like saddle node bifurcation cascade with h 2 n or a secondary window the birth of an s periodic window inside the h periodic one certainly period doubling cascade orbits are particular cases with h 2 and s 2 n both composition laws are also shown in algorithmic way for easy use

relationship between efficiency and predictability in stock price change abstract in this study we evaluate the relationship between efficiency and predictability in the stock market the efficiency which is the issue addressed by the weak form efficient market hypothesis is calculated using the hurst exponent and the approximate entropy apen the predictability corresponds to the hit rate this is the rate of consistency between the direction of the actual price change and that of the predicted price change as calculated via the nearest neighbor prediction method we determine that the hurst exponent and the apen value are negatively correlated however predictability is positively correlated with the hurst exponent

fractional brownian motion fractional gaussian noise and tsallis permutation entropy abstract in this work we analyze two important stochastic processes the fractional brownian motion and fractional gaussian noise within the framework of the tsallis permutation entropy this entropic measure evaluated after using the bandt pompe method to extract the associated probability distribution is shown to be a powerful tool to characterize fractal stochastic processes it allows for a better discrimination of the processes than the shannon counterpart for appropriate ranges of values of the entropic index moreover we find the optimum value of this entropic index for the stochastic processes under study

extracting features of gaussian self similar stochastic processes via the bandt pompe approach by recourse to appropriate information theory quantifiers normalized shannon entropy and martin plastino rosso intensive statistical complexity measure we revisit the characterization of gaussian self similar stochastic processes from a bandt pompe viewpoint we show that the ensuing approach exhibits considerable advantages with respect to other treatments in particular clear quantifiers gaps are found in the transition between the continuous processes and their associated noises

unraveling the decay of the number of unobserved ordinal patterns in noisy chaotic dynamics in this paper we introduce a model to describe the decay of the number of unobserved ordinal patterns as a function of the time series length in noisy chaotic dynamics more precisely we show that a stretched exponential model fits the decay of the number of unobserved ordinal patterns for both discrete and continuous chaotic systems contaminated with observational noise independently of the noise level and the sampling time numerical simulations obtained from the logistic map and the x coordinate of the lorenz system both operating in a totally chaotic dynamics were used as test beds in addition we contrast our results with those obtained from pure stochastic dynamics the fitting parameters namely the stretching exponent and the characteristic decay rate are used to distinguish whether the dynamical nature of the data sequence is stochastic or chaotic finally the analysis of experimental records associated with the hyperchaotic pulsations of an optoelectronic oscillator allows us to illustrate the applicability of the proposed approach in a practical context