detrended fluctuation analysis of intertrade durations abstract the intraday pattern long memory and multifractal nature of the intertrade durations which are defined as the waiting times between two consecutive transactions are investigated based upon the limit order book data and order flows of 23 liquid chinese stocks listed on the shenzhen stock exchange in 2003 an inverse u shaped intraday pattern in the intertrade durations with an abrupt drop in the first minute of the afternoon trading is observed based on a detrended fluctuation analysis we find a crossover of power law scaling behaviors for small box sizes trade numbers in boxes and large box sizes and strong evidence in favor of long memory in both regimes in addition the multifractal nature of intertrade durations in both regimes is confirmed by a multifractal detrended fluctuation analysis for individual stocks with a few exceptions in the small duration regime the intraday pattern has little influence on the long memory and multifractality

multifractal detrended cross correlation analysis on benchmark cryptocurrencies and crude oil prices abstract in this paper we investigate the cross correlations between three benchmark cryptocurrencies including bitcoin ethereum and ripple and some of the well known crude oils west texas intermediate and brent the data of the study spans from 7 august 2015 to 10 june 2019 we utilized the multifractal detrending moving average cross correlation analysis mf x dma method to examine the multifractal features among data we find that the cross correlations between each pair of time series are significant by using the cross correlation test statistic q c c m analysis and detrended moving average cross correlation analysis dmca coefficient also the cross correlation coefficients d m c a show that the data are positively correlated but the degree of correlation has been elevated by increasing the window intervals v the observed results obtained through the mf x dma method infer the existence of multifractal cross correlations on ten bivariate time series in the study and that the strength of multifractality between ethereum and ripple is the highest followed by the strength of multifractality between wti crude oil and ethereum

recursive utility for stochastic trees stochastic trees are semi markov processes represented using tree diagrams such trees have been found useful for prescriptive modeling of temporal medical treatment choice we consider utility functions over stochastic trees which permit recursive evaluation in a graphically intuitive manner analogous to decision tree rollback such rollback is computationally intractable unless a low dimensional preference summary exists we present the most general classes of utility functions having specific tractable preference summaries we examine three preference summaries memoryless markovian and semi markovian which promise both computational feasibility and convenience in assessment their use is illustrated by application to a previous medical decision analysis of whether to perform carotid endarterectomy

a class of variance constrained problems a lagrange multiplier solution procedure is developed for a class of variance constrained problems the method based on the separation of the variance and an algorithm for determining the optimal value of the mean relies on the availability of a method of solving a modified problem in which the variance operation is replaced by the generalized variance operator it is indicated that the procedure can be used in conjunction with dynamic programming to solve a variety of variance constrained problems which allow the consideration of adaptive strategies the procedure is demonstrated by a simple numerical example

multifractal analysis of ssec in chinese stock market a different empirical result from heng seng index abstract in this paper high frequency per 5 min data of shanghai stock exchange composite index ssec from january 1999 to july 2001 is analyzed by multifractal we find that the correlation of the parameters of the multifractal spectra with the variation of daily return z in ssec is noticeably different from that in previous studies of heng seng index in hong kong stock market sun et al phys a 291 2001 553 562 sun et al phys a 301 2001 473 482 so we suppose that there may not be a universal rule for the dependence of the parameters of the multifractal spectra with daily return of a stock index then we construct a new measurement of market risk based on multifractal spectra and test its ability of predicting index fluctuations with a more thorough method than that in sun et al phys a 301 2001 473 482

multifractal analysis of chinese stock volatilities based on the partition function approach abstract we have performed a detailed multifractal analysis on the 1 min volatility of two indexes and 1139 stocks in the chinese stock markets based on the partition function approach the partition function q s scales as a power law with respect to the box size s the scaling exponents q form a nonlinear function of q statistical tests based on bootstrapping show that the extracted multifractal nature is significant at the 1 significance level the individual securities can be well modeled by the p model in turbulence with p 0 40 0 02 based on the idea of ensemble averaging including quenched and annealed average we treat each stock exchange as a whole and confirm the existence of multifractal nature in the chinese stock markets

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

multifractal detrended cross correlation analysis of carbon and crude oil markets abstract the complex dynamics between carbon and crude oil markets have been an increasingly interesting area of research in this paper we try to take a fresh look at the cross correlations between carbon and crude oil markets as well as their dynamic behavior employing multifractal detrended cross correlation analysis first we find that the return series of carbon and crude oil markets are significantly cross correlated second we confirm the existence of multifractality for the return series of carbon and crude oil markets by the multifractal detrended fluctuation analysis third based on the multifractal detrended cross correlation analysis we find the existence of power law cross correlations between carbon and crude oil markets the cross correlated behavior of small fluctuations is found to be more persistent than that of large fluctuations at last some relevant discussions and implications of the empirical results are presented

multiplier phenomenology in random multiplicative cascade processes we demonstrate that the correlations observed in conditioned multiplier distributions of the energy dissipation in fully developed turbulence can be understood as an unavoidable artifact of the observation procedure taking the latter into account all reported properties of both unconditioned and conditioned multiplier distributions can be reproduced by cascade models with uncorrelated random weights if their bivariate splitting function is nonenergy conserving for the ensuremath alpha model we show that the simulated multiplier distributions converge to a limiting form which is very close to the experimentally observed one if random translations of the observation window are accounted for also the subtle effects found in conditioned multiplier distributions are precisely reproduced

detrending moving average algorithm for multifractals the detrending moving average dma algorithm is a widely used technique to quantify the long term correlations of nonstationary time series and the long range correlations of fractal surfaces which contains a parameter ensuremath theta determining the position of the detrending window we develop multifractal detrending moving average mfdma algorithms for the analysis of one dimensional multifractal measures and higher dimensional multifractals which is a generalization of the dma method the performance of the one dimensional and two dimensional mfdma methods is investigated using synthetic multifractal measures with analytical solutions for backward ensuremath theta 0 centered ensuremath theta 0 5 and forward ensuremath theta 1 detrending windows we find that the estimated multifractal scaling exponent ensuremath tau q and the singularity spectrum f ensuremath alpha are in good agreement with the theoretical values in addition the backward mfdma method has the best performance which provides the most accurate estimates of the scaling exponents with lowest error bars while the centered mfdma method has the worse performance it is found that the backward mfdma algorithm also outperforms the multifractal detrended fluctuation analysis the one dimensional backward mfdma method is applied to analyzing the time series of shanghai stock exchange composite index and its multifractal nature is confirmed

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

isometries on unit sphere of lβn in this paper we characterize isometries between unit spheres of f space furthermore we study the isometric extension problem on such kind of metric linear spaces

research on the relationship between the multifractality and long memory of realized volatility in the sseci abstract we examine the multifractal properties of the realized volatility rv and realized bipower variation rbv series in the shanghai stock exchange composite index sseci by using the multifractal detrended fluctuation analysis mf dfa method we find that there exist distinct multifractal characteristics in the volatility series the contributions of two different types of source of multifractality namely fat tailed probability distributions and nonlinear temporal correlations are studied by using the unit root test we also find the strength of the multifractality of the volatility time series is insensitive to the sampling frequency but that the long memory of these series is sensitive

crossing of two mobile averages a method for measuring the roughness exponent self affine signals characterized by a defined hurst roughness exponent h can be investigated through mobile averages the density ensuremath rho of crossing points between any two moving averages is a measure of long range power law correlations in the signal the method is compared to the detrended fluctuation analysis we take advantage of our findings in order to propose a practically powerful and accurate technique for determining h and apply it right away to cases with persistent or antipersistent correlations

some comments on preference order dynamic programming models abstract a simple deterministic dynamic programming model is used as a general framework for the analysis of stochastic versions of three classical optimization problems knapsack traveling salesperson and assembly line balancing problems it is shown that this model can provide an alternative to the preference order models proposed for these problems counterexample to the optimality of the preference order models are presented

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

fractionally integrated process with power law correlations in variables and magnitudes we propose a new stochastic process de ned by only two parameters 1 and 2 which generates power law correlations or anticorrelations in the variable increments and power law correlations in their magnitudes to account for empirical observations in a range of physical systems to demonstrate the utility of our process we consider the case with power law anticorrelations in the variable increments and power law correlations in their magnitudes to model scaling properties in heartbeat data the parameters 1 and 2 control separately the correlations in the increments and their magnitudes and we nd linear relations between each parameter and the corresponding correlation exponent

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

nonlinear complexity of random visibility graph and lempel ziv on multitype range intensity interacting financial dynamics abstract in an attempt to investigate the nonlinear complex evolution of financial dynamics a new financial price model the multitype range intensity contact mric financial model is developed based on the multitype range intensity interacting contact system in which the interaction and transmission of different types of investment attitudes in a stock market are simulated by viruses spreading two new random visibility graph vg based analyses and lempel ziv complexity lzc are applied to study the complex behaviors of return time series and the corresponding random sorted series the vg method is the complex network theory and the lzc is a non parametric measure of complexity reflecting the rate of new pattern generation of a series in this work the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model further the numerical empirical study shows the similar complexity behaviors between the model and the real markets the research confirms that the financial model is reasonable to some extent

some fixed point theorems for s convex subsets in p normed spaces abstract the existence of fixed points of operators on s convex sets in p normed spaces is studied where 0 p 1 0 s p by means of homeomorphisms the fixed point theorems of the types of brouwer schauder kakutani rothe petryshyn altman and krasnosel skii are proved for s convex sets as an application the existence result of solutions for the game concerning s convex concave operators is given in product p normed spaces

multifractal fourier detrended cross correlation analysis of traffic signals abstract multifractal detrended cross correlation analysis mf dxa has been developed to detect the long range power law cross correlation of considered signals in the presence of non stationarity however crossovers arising from extrinsic periodic trends make the scaling behavior difficult to analyze we introduce a fourier filtering method to eliminate the trend effects and systematically investigate the multifractal cross correlation of simulated and real traffic signals the crossover locations are found approximately corresponding to the periods of underlying trend traffic velocity on one road and flows on adjacent roads show strong cross correlation they also present weak multifractality after periodic trends are removed the traffic velocity and flow are cross correlated in opposite directions which is accordant to their actual evolution

statistical properties of the yuan exchange rate index abstract we choice the yuan exchange rate index based on a basket of currencies as the effective exchange rate of the yuan and investigate the statistical properties of the yuan exchange rate index after china s exchange rate system reform on the 21st july 2005 after dividing the time series into two parts according to the change in the yuan exchange rate regime in july 2008 we compare the statistical properties of the yuan exchange rate index during these two periods we find that the distribution of the two return series has the exponential form we also perform the detrending moving average analysis dma and the multifractal detrending moving average analysis mfdma the two periods possess different degrees of long range correlations and the multifractal nature is also unveiled in these two time series significant difference is found in the scaling exponents q and singularity spectra f of the two periods obtained from the mfdma analysis besides in order to detect the sources of multifractality shuffling and phase randomization procedures are applied to destroy the long range temporal correlation and fat tailed distribution of the yuan exchange rate index respectively we find that the fat tailedness plays a critical role in the sources of multifractality in the first period while the long memory is the major cause in the second period the results suggest that the change in china s exchange rate regime in july 2008 gives rise to the different multifractal properties of the yuan exchange rate index in these two periods and thus has an effect on the effective exchange rate of the yuan after the exchange rate reform on the 21st july 2005

financial multifractality and its subtleties an example of dax abstract detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency deutsche aktienindex data the tail index the renyi exponents based on the box counting algorithm for the graph d q and the generalized hurst exponents h q are computed in parallel for short and daily return times the results indicate a more complicated nature of the stock market dynamics than just consistent multifractal

multifractal geometry in stock market time series it has been recently noticed that time series of returns in stock markets are of multifractal multiscaling character in that context multifractality has been always evidenced by its statistical signature i e the scaling exponents associated to a related variable however a direct geometrical framework much more revealing about the underlying dynamics is possible in this paper we present the techniques allowing the multifractal decomposition we will show that there exists a particular fractal component the most singular manifold msm which contains the relevant information about the dynamics of the series it is possible to reconstruct the series at a given precision from the msm we analyze the dynamics of the msm which shows revealing features about the evolution of this type of series

scale invariant distribution and multifractality of volatility multipliers in stock markets abstract the statistical properties of the multipliers of the absolute returns are investigated using 1 min high frequency data of financial time series the multiplier distribution is found to be independent of the box size s when s is larger than some crossover scale providing direct evidence of the existence of scale invariance in financial data the multipliers with base a 2 are well approximated by a normal distribution and the most probable multiplier scales as a power law with respect to the base a we unravel that the volatility multipliers possess multifractal nature which is independent of construction of the multipliers that is the values of s and a

improved shell model of turbulence we introduce a shell model of turbulence that exhibits improved properties in comparison to the standard and very popular gledzer ohkitani and yamada goy model the nonlinear coupling is chosen to minimize correlations between different shells in particular the second order correlation function is diagonal in the shell index and the third order correlation exists only between three consecutive shells spurious oscillations in the scaling regime which are an annoying feature of the goy model are eliminated by our choice of nonlinear coupling we demonstrate that the model exhibits multiscaling similar to the goy model the scaling exponents are shown to be independent of the viscous mechanism as is expected for navier stokes turbulence and other shell models these properties of the model make it optimal for further attempts to achieve understanding of multiscaling in nonlinear dynamics

modified detrended fluctuation analysis based on empirical mode decomposition for the characterization of anti persistent processes abstract detrended fluctuation analysis dfa is a simple but very efficient method for investigating the power law long term correlations of non stationary time series in which a detrending step is necessary to obtain the local fluctuations at different timescales we propose to determine the local trends through empirical mode decomposition emd and perform the detrending operation by removing the emd based local trends which gives an emd based dfa method similarly we also propose a modified multifractal dfa algorithm called an emd based mfdfa the performance of the emd based dfa and mfdfa methods is assessed with extensive numerical experiments based on fractional brownian motion and multiplicative cascading process we find that the emd based dfa method performs better than the classic dfa method in the determination of the hurst index when the time series is strongly anticorrelated and the emd based mfdfa method outperforms the traditional mfdfa method when the moment order q of the detrended fluctuations is positive we apply the emd based mfdfa to the 1 min data of shanghai stock exchange composite index and the presence of multifractality is confirmed we also analyze the daily austrian electricity prices and confirm its anti persistence

a new approach to quantify power law cross correlation and its application to commodity markets abstract we proposed a new method detrended moving average cross correlation analysis dmca to detect the power law cross correlation between two correlated non stationary time series by combining detrended cross correlation analysis dcca and detrended moving average dma in order to compare the performance of dmca and dcca in the detection of cross correlation and to estimate the influence of periodic trend we generate two cross correlated time series x i and y i by a periodic two component fractionally autoregressive integrated moving average arfima process then we apply both methods to quantify the cross correlations of the generated series whose theoretical values are already known to us by comparing the results we obtained we find that the performance of this new approach is comparable to dcca with less calculating amounts our method can also reduce the impact of trends furthermore dmca for background and forward moving average case outperforms dcca in more accurate estimation when the analyzed times series are short in length to provide an example we also apply this new method to the time series of the real world data from brent and wti crude oil spot markets to investigate the complex cross market correlation between these commodity markets in all our method is another practical choice to detect the cross correlation between two short period non stationary time series and has potential application to real world problems

negative fractal dimensions and multifractals abstract a new notion of fractal dimension is defined when it is positive it effectively falls back on known definitions but its motivating virtue is that it can take negative values which measure usefully the degree of emptiness of empty sets the main use concerns random multifractals for which f

scaling self similarity and multifractality in fx markets abstract this paper presents an empirical investigation of scaling and multifractal properties of us dollar deutschemark usd dem returns the data set is ten years of 5 min returns the cumulative return distributions of positive and negative tails at different time intervals are linear in the double logarithmic space this presents strong evidence that the usd dem returns exhibit power law scaling in the tails to test the multifractal properties of usd dem returns the mean moment of the absolute returns as a function of time intervals is plotted for different powers of absolute returns these moments show different slopes for these powers of absolute returns the nonlinearity of the scaling exponent indicates that the returns are multifractal

are crude oil markets multifractal evidence from mf dfa and mf ssa perspectives abstract in this article we investigated the multifractality and its underlying formation mechanisms in international crude oil markets namely brent and wti which are the most important oil pricing benchmarks globally we attempt to find the answers to the following questions 1 are those different markets multifractal 2 what are the dynamical causes for multifractality in those markets if any to answer these questions we applied both multifractal detrended fluctuation analysis mf dfa and multifractal singular spectrum analysis mf ssa based on the partition function two widely used multifractality detecting methods we found that both markets exhibit multifractal properties by means of these methods furthermore in order to identify the underlying formation mechanisms of multifractal features we destroyed the underlying nonlinear temporal correlation by shuffling the original time series thus we identified that the causes of the multifractality are influenced mainly by a nonlinear temporal correlation mechanism instead of a non gaussian distribution at last by tracking the evolution of left and right half multifractal spectra we found that the dynamics of the large price fluctuations is significantly different from that of the small ones our main contribution is that we not only provided empirical evidence of the existence of multifractality in the markets but also the sources of multifractality and plausible explanations to current literature furthermore we investigated the different dynamical price behaviors influenced by large and small price fluctuations

s orlicz convex functions in linear spaces and jensen s discrete inequality in this paper we consider the class ofs orlicz convex functions defined on as orlicz convex subset of a real linear space some inequalities of jensen s type for this class of mappings are pointed out

application of multifractal measures to tehran price index we report an empirical study of tehran price index tepix to analyze our data we use various methods like as rescaled range analysis r s modified rescaled range analysis lo s method detrended fluctuation analysis dfa and generalized hurst exponents analysis based on numerical results the scaling range of tepix returns is specified long memory effect or long range correlation property in this market is investigated characteristic exponent for probability distribution function of tepix returns is derived and finally the stage of development in tehran stock exchange is determined

on the properties of random multiplicative measures with the multipliers exponentially distributed under the formalism of annealed averaging of the partition function a type of random multifractal measures with the multipliers exponentially distributed is investigated in detail branching emerges in the curve of generalized dimensions and negative values of generalized dimensions arise three equivalent methods of classification of the random multifractal measures are proposed which is based on i the properties of the curves of generalized dimensions ii the solution properties of equation q 0 and iii the relative position of the curve f and the diagonal f in the first quadrant these classes of measures correspond to 0 1 0 1 1 and 0 1 0 respectively phase diagram is introduced to illustrate the diverse performance of the random measures that is multiplicatively generated

the effects of common risk factors on stock returns a detrended cross correlation analysis abstract in this paper we investigate the cross correlations between fama and french three factors and the return of american industries on the basis of cross correlation statistic test and multifractal detrended cross correlation analysis mf dcca qualitatively we find that the return series of fama and french three factors and american industries were overall significantly cross correlated based on the analysis of a statistic quantitatively we find that the cross correlations between three factors and the return of american industries were strongly multifractal and applying mf dcca we also investigate the cross correlation of industry returns and residuals we find that there exists multifractality of industry returns and residuals the result of correlation coefficients we can verify that there exist other factors which influence the industry returns except fama three factors

inhomogeneous scaling behaviors in malaysian foreign currency exchange rates in this paper we investigate the fractal scaling behaviors of foreign currency exchange rates with respect to malaysian currency ringgit malaysia these time series are examined piecewise before and after the currency control imposed in 1st september 1998 using the monofractal model based on fractional brownian motion the global hurst exponents are determined using the r s analysis the detrended fluctuation analysis and the method of second moment using the correlation coefficients the limitation of these monofractal analyses is discussed the usual multifractal analysis reveals that there exists a wide range of hurst exponents in each of the time series a new method of modelling the multifractal time series based on multifractional brownian motion with time varying hurst exponents is studied

nonlinear structure of some classical quasi banach spaces and f spaces we investigate the lipschitz structure of lp and lp for 0 p 1 as quasi banach spaces and as metric spaces with the metric induced by the p norm and show that they are not lipschitz isomorphic we prove that the f space l0 is not uniformly homeomorphic to any other lp space that the lp spaces for 0 p 1 embed isometrically into one another and reduce the problem of the uniform equivalence amongst lp spaces to their lipschitz equivalence as metric spaces

predictability of multifractal analysis of hang seng stock index in hong kong in this paper the daily hang seng index in hong kong stock market is studied by multifractal analysis the main parameter of multifractal spectra used is f which can be used to characterize the ratio of number of highest index moments to that of lowest ones the dependence of today s gain probability g and the day s index increase probability n with f of the previous 3 days are studied it is found that g and n can reach 70 80 at the large positive f region and can be very close to 20 at the big negative f region the predictability decreases with the increasing number of the previous days

on the wavelet transformation of fractal objects the wavelet transformation is briefly presented it is shown how the analysis of the local scaling behavior of fractals can be transformed into the investigation of the scaling behavior of analytic functions over the half plane near the boundary of its domain of analyticity as an example a weierstrass like fractal function is considered for which the wavelet transform is related to a jacobi theta function some of the scalings of this theta function are analyzed and give some information about the scaling behavior of this fractal

fix point multiplier distributions in discrete turbulent cascade models abstract one point time series measurements limit the observation of three dimensional fully developed turbulence to one dimension for one dimensional models like multiplicative branching processes this implies that the energy flux from large to small scales is not conserved locally this then renders the random weights used in the cascade curdling to be different from the multipliers obtained from a backward averaging procedure the resulting multiplier distributions become solutions of a fix point problem with a further restoration of homogeneity all observed correlations between multipliers in the energy dissipation field can be understood in terms of simple scale invariant multiplicative branching processes

nonlinear structure analysis of carbon and energy markets with mfdcca based on maximum overlap wavelet transform abstract this paper investigates the nonlinear structure between carbon and energy markets by employing the maximum overlap wavelet transform modwt as well as the multifractal detrended cross correlation analysis based on maximum overlap wavelet transform mfdcca modwt based on the modwt multiresolution analysis and the statistic q c c m significance relatively significant cross correlations are obtained between carbon and energy future markets either on different time scales or on the whole the result of the granger causality test indicates bidirectional granger causality between carbon and electricity future markets although the granger causality relationship between the carbon and oil price is not evident the existence of multifractality for the returns between carbon and energy markets is proven with the mfdcca modwt algorithm in addition results of investigating the origin of multifractality demonstrate that both long range correlations and fat tailed distributions play important roles in the contributions of multifractality

multifractal analysis of hang seng index in hong kong stock market abstract in this paper the daily hang seng index in hong kong stock market is analyzed by multifractal the correlation of the parameters of the multifractal spectra with the variation of close return z is studied statistically it is found that the amount of the variation of return is correlated with the amount of of that day the increase or decrease of the return is related to the positive or negative value of f the gain probability and the increasing day s probability can be higher than 70 at the larger f region and be lower than 20 at the more negative region

the informativeness of options trading activities non linear analysis based on mf dcca and granger test abstract using both put call ratio p c and option to stock volume ratio o s as measures of options trading activities this paper investigates the information content of sse 50 etf options we begin by using detrended fluctuation analysis mf dfa method to examine the multifractal properties of p c ratio change series o s ratio change series and etf returns and find that these time series exhibit strong multifractality moreover employing multifractal detrended cross correlation analysis mf dcca we show that there exists strong anti persistent cross correlation between p c ratios and 50 etf returns but no significant cross correlation between o s ratios and 50 etf returns suggesting that p c ratio is more pronounced detecting the information content of options furthermore we use nonlinear granger causality test and show that the granger causality relationships between p c ratio and 50 etf return series is more significant and stronger than that between o s ratio and 50 etf return series our findings imply that p c ratio can better capture the informativeness of options

comparative analysis of grey detrended fluctuation analysis methods based on empirical research on china s interest rate market abstract this study empirically compares the development of china s interest rate market in the past decade the yield of shibor market from 2006 to 2016 showed anti persistence and the later five year trend was stronger than that in the previous half period indicating a significantly growing trend of china s interest rate market we perform a comparative analysis of detrended fluctuation analysis dfa detrending moving average dma algorithm and the maximum overlap wavelet transform dfa modwt using grey and original sequences the autoregressive integrated moving average model is adopted to generate set point h sequences results illustrated that 1 for original sequences both the dfa modwt and dma 0 5 shows outstanding performances when the set hurst exponents are 0 6 and 0 7 and 0 8 and 0 9 respectively 2 for grey sequences g dfa performs best among the three methods followed by g dma and g dfa modwt 3 the long range correlation of the original sequences is slightly lower than the set values on the contrary the long range correlation of grey sequences is much higher than the set values thus the grey sequence exerts a strong aggregation effect as it can accumulate the trend of the sequence our results show that the grey sequence can determine the regular pattern from the messy sequence however grey sequences tend to be overly analyzed and misleading when large volumes of data are involved empirical studies confirm that china s interest rate market remains an inefficient market

measuring daily value at risk of ssec index a new approach based on multifractal analysis and extreme value theory abstract recent studies in the econophysics literature reveal that price variability has fractal and multifractal characteristics not only in developed financial markets but also in emerging markets taking high frequency intraday quotes of the shanghai stock exchange component ssec index as example this paper proposes a new method to measure daily value at risk var by combining the newly introduced multifractal volatility mfv model and the extreme value theory evt method two var backtesting techniques are then employed to compare the performance of the model with that of a group of linear and nonlinear generalized autoregressive conditional heteroskedasticity garch models the empirical results show the multifractal nature of price volatility in chinese stock market var measures based on the multifractal volatility model and evt method outperform many garch type models at high risk levels

multifractal detrending moving average cross correlation analysis there are a number of situations in which several signals are simultaneously recorded in complex systems which exhibit long term power law cross correlations the multifractal detrended cross correlation analysis mfdcca approaches can be used to quantify such cross correlations such as the mfdcca based on the detrended fluctuation analysis mfxdfa method we develop in this work a class of mfdcca algorithms based on the detrending moving average analysis called mfxdma the performances of the proposed mfxdma algorithms are compared with the mfxdfa method by extensive numerical experiments on pairs of time series generated from bivariate fractional brownian motions two component autoregressive fractionally integrated moving average processes and binomial measures which have theoretical expressions of the multifractal nature in all cases the scaling exponents h xy extracted from the mfxdma and mfxdfa algorithms are very close to the theoretical values for bivariate fractional brownian motions the scaling exponent of the cross correlation is independent of the cross correlation coefficient between two time series and the mfxdfa and centered mfxdma algorithms have comparative performances which outperform the forward and backward mfxdma algorithms for two component autoregressive fractionally integrated moving average processes we also find that the mfxdfa and centered mfxdma algorithms have comparative performances while the forward and backward mfxdma algorithms perform slightly worse for binomial measures the forward mfxdma algorithm exhibits the best performance the centered mfxdma algorithms performs worst and the backward mfxdma algorithm outperforms the mfxdfa algorithm when the moment order q 0 we apply these algorithms to the return time series of two stock market indexes and to their volatilities for the returns the centered mfxdma algorithm gives the best estimates of h xy q since its h xy 2 is closest to 0 5 as expected and the mfxdfa algorithm has the second best performance for the volatilities the forward and backward mfxdma algorithms give similar results while the centered mfxdma and the mfxdfa algorithms fail to extract rational multifractal nature

equimodular and linearity in modular spaces abstract in this paper the concept of equimodular is introduced it contains several generalizations of mazur ulam s isometric theorem in modular spaces let x and y be two real modular spaces and x with 1 midpoint shrinking whose modular x satisfies the 2 condition assume that an operator t maps x onto y in an 2 ti equimodular manner for all i 0 n where ti is a null sequence of nonnegative reals with the property that t0 1 t1 1 2 and ti ti 1 2ti for i 2 then t is affine

multifractality in stock indexes fact or fiction abstract multifractal analysis and extensive statistical tests are performed upon intraday minutely data within individual trading days for four stock market indexes including hsi szsc s p 500 and nasdaq to check whether the indexes instead of the returns possess multifractality we find that the mass exponent q is linear and the singularity q is close to 1 for all trading days and all indexes furthermore we find strong evidence showing that the scaling behaviors of the original data sets cannot be distinguished from those of shuffled time series hence the so called multifractality in the intraday stock market indexes is merely an illusion

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

price volume multifractal analysis and its application in chinese stock markets abstract an empirical research on chinese stock markets is conducted using statistical tools first the multifractality of stock price return series r i r i ln p t 1 ln p t and trading volume variation series v i v i ln v t 1 ln v t is confirmed using multifractal detrended fluctuation analysis furthermore a multifractal detrended cross correlation analysis between stock price return and trading volume variation in chinese stock markets is also conducted it is shown that the cross relationship between them is also found to be multifractal second the cross correlation between stock price p i and trading volume v i is empirically studied using cross correlation function and detrended cross correlation analysis it is found that both shanghai stock market and shenzhen stock market show pronounced long range cross correlations between stock price and trading volume third a composite index r based on price and trading volume is introduced compared with stock price return series r i and trading volume variation series v i r variation series not only remain the characteristics of original series but also demonstrate the relative correlation between stock price and trading volume finally we analyze the multifractal characteristics of r variation series before and after three financial events in china namely price limits reform of non tradable shares and financial crisis in 2008 in the whole period of sample to study the changes of stock market fluctuation and financial risk it is found that the empirical results verified the validity of r

multifractality attributed to dual central limit like convergence effects abstract multifractals can be defined as fractal systems that express a range of fractal dimensions the origins of multifractality in time series data have conventionally been attributed to fat tailed probability distributions and to long range correlations multifractal sequences can be generated from the eigenvalue deviations of the gaussian unitary and orthogonal ensembles of random matrix theory these deviations can be resolved into component monofractal sequences governed by the tweedie compound poisson distribution a statistical model that expresses a variance to mean power law related to long range correlations fully multifractal descriptions of these deviations can be constructed provided that the parameter of the compound poisson model related to fractal dimension varies in accordance with an asymmetric laplace distribution both the tweedie compound poisson distribution and the asymmetric laplace distribution serve as foci of convergence in limit theorems on independent and identically distributed random variables the hypothesis that multifractal sequences can be attributed to mathematical convergence effects that have as their focus these two statistical models is proposed

inverse statistics and multifractality of exit distances in 3d fully developed turbulence abstract the inverse structure functions of exit distances have been introduced as a novel diagnostic of turbulence which emphasizes the more laminar regions 1 2 3 4 using taylor s frozen field hypothesis we investigate the statistical properties of the exit distances of empirical 3d fully developed turbulence we find that the probability density functions of exit distances at different velocity thresholds v can be approximated by stretched exponentials with exponents varying with the velocity thresholds below a critical threshold we show that the inverse structure functions exhibit clear extended self similarity ess the ess exponents p 2 for small p p 3 5 are well described by p 2 p 2 which derives from the observed approximate universality of the distributions of the exit distances for different velocity thresholds v the data is not sufficient to reject the hypothesis that monofractal ess is sufficient to explain the data in contrast a measure taking into account the dependence between successive exit distances at a given velocity threshold exhibits clear multifractality with negative dimensions suggesting the existence of a non trivial dependence in the time series of exit times

auto correlated behavior of wti crude oil volatilities a multiscale perspective abstract in this paper we investigate the long range auto correlated behavior of wti crude oil volatility series employing multifractal detrended fluctuation analysis our findings show that the for small time scales the auto correlations of volatilities were multifractal while for large time scales the auto correlations were nearly monofractal based on multiscale analysis we also investigate the dynamics of auto correlations for different intervals of time scales and find that several shocks could make significant effects on the auto correlated behaviors for small time scales analyzing the dynamics of multifractality degrees of auto correlations for small time scales we find that the stronger auto correlations were always related to the lower degrees of multifractality at last we have discussions on the determination factors of price behavior the predictive implications of scaling behavior in volatilities for oil markets and the reasons why long range auto correlations of volatility were always strong for both small time scales and large time scales our results are very important theoretically and practically

efficiency and multifractality analysis of csi 300 based on multifractal detrending moving average algorithm abstract we apply the multifractal detrending moving average mfdma to investigate and compare the efficiency and multifractality of 5 min high frequency china securities index 300 csi 300 the results show that the csi 300 market becomes closer to weak form efficiency after the introduction of csi 300 future we find that the csi 300 is featured by multifractality and there are less complexity and risk after the csi 300 index future was introduced with the shuffling surrogating and removing extreme values procedures we unveil that extreme events and fat distribution are the main origin of multifractality besides we discuss the knotting phenomena in multifractality and find that the scaling range and the irregular fluctuations for large scales in the f q s vs s plot can cause a knot

scaling behavior in ranking mobility of chinese stock market abstract as an aggregate measure of the variations in individuals the analysis of mobility provides a substantial and comprehensive perspective into the complexity of socio economic systems in this paper we introduced the ranking mobility index to measure the ranking variations of the stocks in chinese stock market over time using the daily data of 837 constituent stocks of the shanghai a stock composite index from january 1 2002 to december 31 2012 we examined respectively the dependence of ranking mobility with respect to the absolute return trading volume and turnover ratio on the sampling time interval the scaling property is observed in all three relations the fact of long relaxation times gives evidence of long memory property in the stock ranking orders

multifractal formalism for fractal signals the structure function approach versus the wavelet transform modulus maxima method several attempts have been made recently to generalize the multifractal formalism originally introduced for singular measures to fractal signals we report on a systematic comparison between the structure function approach pioneered by parisi and frisch in 2 proceedings of the international school on turbulence and predictability in geophysical fluid dynamics and climate dynamics edited by m ghil r benzi and g parisi north holland amsterdam 1985 p 84 to account for the multifractal nature of fully developed turbulent signals and an alternative method we have developed within the framework of the wavelet transform analysis we comment on the intrinsic limitations of the structure function approach this technique has fundamental drawbacks and does not provide a full characterization of the singularities of a signal in many cases we demonstrate that our method based on the wavelet transform modulus maxima representation works in most situations and is likely to be the ground of a unified multifractal description of self affine distributions our theoretical considerations are both illustrated on pedagogical examples and supported by numerical simulations

detrended fluctuation analysis on spot and futures markets of west texas intermediate crude oil abstract in this paper we study the auto correlations and cross correlations of west texas intermediate wti crude oil spot and futures return series employing detrended fluctuation analysis dfa and detrended cross correlation analysis dcca scaling analysis shows that for time scales smaller than a month the auto correlations and cross correlations are persistent for time scales larger than a month but smaller than a year the correlations are anti persistent while for time scales larger than a year the series are neither auto correlated nor cross correlated indicating the efficient operation of the crude oil markets moreover for small time scales the degree of short term cross correlations is higher than that of auto correlations using the multifractal extension of dfa and dcca we find that for small time scales the correlations are strongly multifractal while for large time scales the correlations are nearly monofractal analyzing the multifractality of shuffled and surrogated series we find that both long range correlations and fat tail distributions make important contributions to the multifractality our results have important implications for market efficiency and asset pricing models

theory and applications of generalized dynamic programming an overview abstract extensions of dynamic programming dp into generalized preference structures such as exist in multicriteria optimization have invariably assumed sufficient structure to ensure the validity of bellman s principle of optimality or the presence of monotonicity hence ensuring the validity of the functional equations of dp often however the only reasonable formulation of problem in terms of the size of the resulting state space is one for which neither monotonicity nor the strong principle of optimality is satisfied generalized dp based on a weaker principle of optimality is a generalization of dp that produces optimal solutions even in the absence of monotonicity it is shown both to subsume conventional dp and to provide an alternative means of implementing mitten s preference order dp this paper provides an overview of generalized dp and its applications to date summarizing our computational experiences in the process

generic multifractality in exponentials of long memory processes we find that multifractal scaling is a robust property of a large class of continuous stochastic processes constructed as exponentials of long memory processes the long memory is characterized by a power law kernel with tail exponent ensuremath varphi 1 2 where ensuremath varphi g0 this generalizes previous studies performed only with ensuremath varphi 0 with a truncation at an integral scale by showing that multifractality holds over a remarkably large range of dimensionless scales for ensuremath varphi g0 the intermittency multifractal coefficient can be tuned continuously as a function of the deviation ensuremath varphi from 1 2 and of another parameter ensuremath sigma 2 embodying information on the short range amplitude of the memory kernel the ultraviolet cutoff viscous scale and the variance of the white noise innovations in these processes both a viscous scale and an integral scale naturally appear bracketing the inertial scaling regime we exhibit a surprisingly good collapse of the multifractal spectra ensuremath zeta q on a universal scaling function which enables us to derive high order multifractal exponents from the small order values and also obtain a given multifractal spectrum ensuremath zeta q by different combinations of ensuremath varphi and ensuremath sigma 2

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

a non standard explicit integration scheme for initial value problems in this paper we present the construction of a non standard explicit algorithm for initial value problems the method results to be of second order and a stable this new algorithm has been proven to be suitable for solving different kind of initial value problems specifically non singular problems singular problems stiff problems and singularly perturbed problems some numerical experiments are considered in order to check the behaviour of the method when applied to a variety of initial value problems

the dynamic and stochastic knapsack problem the dynamic and stochastic knapsack problem dskp is defined as follows items arrive according to a poisson process in time each item has a demand size for a limited resource the knapsack and an associated reward the resource requirements and rewards are jointly distributed according to a known probability distribution and become known at the time of the item s arrival items can be either accepted or rejected if an item is accepted the item s reward is received and if an item is rejected a penalty is paid the problem can be stopped at any time at which time a terminal value is received which may depend on the amount of resource remaining given the waiting cost and the time horizon of the problem the objective is to determine the optim al policy that maximizes the expected value rewards minus costs accumulated assuming that all items have equal sizes but random rewards optimal solutions are derived for a variety of cost structures and time horizons and recursive algorithms for computing them are developed optimal closed form solutions are obtained for special cases the dskp has applications in freight transportation in scheduling of batch processors in selling of assets and in selection of investment projects

the dynamic and stochastic knapsack problem with deadlines in this paper a dynamic and stochastic model of the well known knapsack problem is developed and analyzed the problem is motivated by a wide variety of real world applications objects of random weight and reward arrive according to a stochastic process in time the weights and rewards associated with the objects are distributed according to a known probability distribution each object can either be accepted to be loaded into the knapsack of known weight capacity or be rejected the objective is to determine the optimal policy for loading the knapsack within a fixed time horizon so as to maximize the expected accumulated reward the optimal decision rules are derived and are shown to exhibit surprising behavior in some cases it is also shown that if the distribution of the weights is concave then the decision rules behave according to intuition

inverse structure functions while the ordinary structure function in turbulence is concerned with the statistical moments of the velocity increment ensuremath delta u measured over a distance r the inverse structure function is related to the distance r where the turbulent velocity exits the interval ensuremath delta u we study inverse structure functions of wind tunnel turbulence which covers a range of reynolds numbers mathrm re ensuremath lambda 400 1100 we test a recently proposed relation between the scaling exponents of the ordinary structure functions and those of the inverse structure functions s roux and m h jensen phys rev e 69 16309 2004 the relatively large range of reynolds numbers in our experiment also enables us to address the scaling with reynolds number that is expected to highlight the intermediate dissipative range while we firmly establish the relative scaling of inverse structure functions our experimental results fail both predictions therefore the question of the significance of inverse structure functions remains open