the trading time risks of stock investment in stock price drop abstract this article investigates the trading time risk ttr of stock investment in the case of stock price drop of dow jones industrial average dji and hushen300 data csi300 respectively the escape time of stock price from the maximum to minimum in a data window length dwl is employed to measure the absolute ttr the ratio of the escape time to data window length is defined as the relative ttr empirical probability density functions of the absolute and relative ttrs for the dji and csi300 data evidence that i whenever the dwl increases the absolute ttr increases the relative ttr decreases otherwise ii there is the monotonicity or non monotonicity for the stability of the absolute or relative ttr iii there is a peak distribution for shorter trading days and a two peak distribution for longer trading days for the pdf of ratio iv the trading days play an opposite role on the absolute or relative ttr and its stability between dji and csi300 data

on actor critic algorithms in this article we propose and analyze a class of actor critic algorithms these are two time scale algorithms in which the critic uses temporal difference learning with a linearly parameterized approximation architecture and the actor is updated in an approximate gradient direction based on information provided by the critic we show that the features for the critic should ideally span a subspace prescribed by the choice of parameterization of the actor we study actor critic algorithms for markov decision processes with polish state and action spaces we state and prove two results regarding their convergence

a new approach to inversion based feedforward control design for nonlinear systems the finite time transition between stationary setpoints of nonlinear siso systems is considered as a scenario for the presentation of a new design approach for inversion based feedforward control design techniques which are based on a stable system inversion result in input trajectories with pre and or post actuation intervals the presented approach treats the considered transition task as a two point boundary value problem bvp and yields causal feedforward trajectories which are constant outside the transition interval the main idea of this approach is to provide free parameters in the desired output trajectory to solve the bvp of the internal dynamics thereby a standard matlab function can be used for the numerical solution of the bvp feedforward control design techniques are illustrated by simulation results for a simple 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

stochastic approximation for nonexpansive maps application to q learning algorithms we discuss synchronous and asynchronous iterations of the form xk 1 x k gamma k h x k w k where h is a suitable map and wk is a deterministic or stochastic sequence satisfying suitable conditions in particular in the stochastic case these are stochastic approximation iterations that can be analyzed using the ode approach based either on kushner and clark s lemma for the synchronous case or on borkar s theorem for the asynchronous case however the analysis requires that the iterates xk be bounded a fact which is usually hard to prove we develop a novel framework for proving boundedness in the deterministic framework which is also applicable to the stochastic case when the deterministic hypotheses can be verified in the almost sure sense this is based on scaling ideas and on the properties of lyapunov functions we then combine the boundedness property with borkar s stability analysis of odes involving nonexpansive mappings to prove convergence with probability 1 in the stochastic case we also apply our convergence analysis to q learning algorithms for stochastic shortest path problems and are able to relax some of the assumptions of the currently available results

noncausal inverses for linear systems suppose we are to guide a plant with a square transfer matrix through a series of way points this can be accomplished by output tracking of trajectories which are fitted together in a sufficiently smooth manner each segment of each output is prescribed in terms of a polynomial or sine function or the product thereof our technique is to compute 1 a noncausal particular solution based on the desired trajectory over each segment and the movement from one segment to the next and this particular solution consists of a particular control and a particular state trajectory and 2 a regulator to handle modeling errors disturbances etc we concentrate on the particular solution

stability of stochastic approximation under verifiable conditions in this paper we address the problem of the stability and convergence of the stochastic approximation procedure theta n 1 theta n gamma n 1 h theta n xi n 1 the stability of such sequences theta n is known to heavily rely on the behavior of the mean field h at the boundary of the parameter set and the magnitude of the stepsizes used the conditions typically required to ensure convergence and in particular the boundedness or stability of theta n are either too difficult to check in practice or not satisfied at all this is the case even for very simple models the most popular technique for circumventing the stability problem consists of constraining theta n to a compact subset mathcal k in the parameter space this is obviously not a satisfactory solution as the choice of mathcal k is a delicate one in this paper we first prove a deterministic stability result which relies on simple conditions on the sequences xi n and gamma n we then propose and analyze an algorithm based on projections on adaptive truncation sets which ensures that the aforementioned conditions required for stability are satisfied we focus in particular on the case where xi n is a so called markov state dependent noise we establish both the stability and convergence with probability 1 w p 1 of the algorithm under a set of simple and verifiable assumptions we illustrate our results with an example related to adaptive markov chain monte carlo algorithms

scaling in currency exchange we study the scaling behavior in currency exchange rates our results suggest that they satisfy scaling with an exponent close to 0 5 but that it differs qualitatively from that of a simple random walk indeed price variations cannot be considered as independent variables and subtle correlations are present furthermore we introduce a novel statistical analysis for economic data which makes the physical properties of a signal more evident and eliminates the systematic effects of time periodicity

a general framework for approximated model stable inversion abstract in this paper we propose an approximated method for the design of feedforward actions based on model stable inversion in the proposed framework the solution of the model stable inversion is approximated in the least squares sense by a suitable combination of any arbitrary set of basis functions the paper makes use of operator theory to derive a closed form formula to compute such approximation and to provide boundedness properties for the computed solution simulations are provided to show the effectiveness of the proposed method with different families of basis functions

measuring multifractality of stock price fluctuation using multifractal detrended fluctuation analysis abstract analyzing the shanghai stock price index daily returns using mf dfa method it is found that there are two different types of sources for multifractality in time series namely fat tailed probability distributions and non linear temporal correlations based on that a sliding window of 240 frequency data in 5 trading days was used to study stock price index fluctuation it is found that when the stock price index fluctuates sharply a strong variability is clearly characterized by the generalized hurst exponents h q therefore two measures h and based on generalized hurst exponents were proposed to compare financial risks before and after price limits and reform of non tradable shares the empirical results verify the validity of the measures and this has led to a better understanding of complex stock markets

research on the fractal structure in the chinese stock market abstract applying fractal theory this paper probes and discusses self similarity and scale invariance of the chinese stock market it analyses three kinds of scale indexes i e autocorrelation index hurst index and the scale index on the basis of detrended fluctuation analysis dfa algorithm and promotes dfa into a recursive algorithm using the three kinds of scale indexes we conduct empirical research on the chinese shanghai and shenzhen stock markets the results indicate that the rate of returns of the two stock markets does not obey the normal distribution a correlation exists between the stock price indexes over time scales the stock price indexes exhibit fractal time series it indicates that the policy guide hidden at the back influences the characteristic of the chinese stock market

scaling characteristics in the taiwan stock market some statistical tools including histogram spectral analysis and fractal theory were used on the daily taiwan stock price index tspi from 1987 to 2002 to examine the possible scale invariant behavior and the clustering characteristics in taiwan stock market it was found that the tspi data exhibited the characteristic of right skewed frequency distribution the long term memory and the possibility of scale invariance were roughly identified through the analysis of autocorrelation and power spectrum respectively the monofractal analysis was then performed by the box counting method scale invariance was clearly found in the time series and the box dimension was shown to be a decreasing function of the threshold index level implying multifractal characteristics i e the low and high regions scale differently to test this hypothesis the time series were transferred into a useful compact form through the multifractal formalism namely the q q and f plots the analysis confirmed the existence of multifractal characteristics in the investigated time series the origin of multifractal phenomena in taiwan stock market might be interpreted in terms of the multiplicative cascade process of stock market information

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

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

stabilization of stochastic approximation by step size adaptation a scheme for stabilizing stochastic approximation iterates by adaptively scaling the step sizes is proposed and analyzed this scheme leads to the same limiting differential equation as the original scheme and therefore has the same limiting behavior while avoiding the difficulties associated with projection schemes the proof technique requires only that the limiting o d e descend a certain lyapunov function outside an arbitrarily large bounded set c 2012 elsevier b v all rights reserved

the o d e method for convergence of stochastic approximation and reinforcement learning it is shown here that stability of the stochastic approximation algorithm is implied by the asymptotic stability of the origin for an associated ode this in turn implies convergence of the algorithm several specific classes of algorithms are considered as applications it is found that the results provide i a simpler derivation of known results for reinforcement learning algorithms ii a proof for the first time that a class of asynchronous stochastic approximation algorithms are convergent without using any a priori assumption of stability iii a proof for the first time that asynchronous adaptive critic and q learning algorithms are convergent for the average cost optimal control problem

nonlinear inversion based output tracking an inversion procedure is introduced for nonlinear systems which constructs a bounded input trajectory in the preimage of a desired output trajectory in the case of minimum phase systems the trajectory produced agrees with that generated by hirschorn s inverse dynamic system however the preimage trajectory is noncausal rather than unstable in the nonminimum phase case in addition the analysis leads to a simple geometric connection between the unstable manifold of the system zero dynamics and noncausality in the nonminimum phase case with the addition of stabilizing feedback to the preimage trajectory asymptotically exact output tracking is achieved tracking is demonstrated with a numerical example and compared to the well known byrnes isidori regulator rather than solving a partial differential equation to construct a regulator the inverse is calculated using a picard like interaction when preactuation is not possible noncausal inverse trajectories can be truncated resulting in the tracking error transients found in other control schemes

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

on the stock market recurrence abstract we analyze the return of the s p 500 index and characterize its evolution as being typical of a low dimensional recurrent deterministic system the first poincare return time of the chaotic logistic mapping trajectories is used to model the return evolution the efficiency of the model is demonstrated by daily predictions over an interval of time since january 1950 of this index and long term prediction for a period of 150 days

a stochastic approximation algorithm with varying bounds many optimization problems that are intractable with conventional approaches will yield to stochastic approximation algorithms this is because these algorithms can be used to optimize functions that cannot be evaluated analytically but have to be estimated for instance through simulation or measured thus stochastic approximation algorithms can be used for optimization in simulation unfortunately the classical stochastic approximation algorithm sometimes diverges because of unboundedness problems we study the convergence of a variant of stochastic approximation defined over a growing sequence of compact sets we show that this variant converges under more general conditions on the objective function than the classical algorithm while maintaining the same asymptotic convergence rate we also present empirical evidence that shows that this algorithm sometimes converges much faster than the classical algorithm

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

optimal inversion based control for the set point regulation of nonminimum phase uncertain scalar systems we propose an optimal inversion based control for the set point constrained regulation of nonminimum phase uncertain scalar systems this approach is based on a new control architecture where the main purpose of the feedback is to reduce the sensitivity to parametric plant uncertainties permitting in such a way the effective use of a feedforward action determined via a stable dynamic inversion essential constituents of the architecture are a parameterized family of transition polynomials to shape ideal output transfers and a parameterized controller ensuring the internal model principle the methodology is then centered on the optimal combined design of the feedback controller and of the inversion based command signal in order to minimize the worst case settling time subject to an amplitude constraint on the control variable and to arbitrarily assigned overshoot and undershoot bounds finally an approximate or suboptimal solution to the resulting nonlinear optimization problem can be obtained by genetic algorithms a worked example highlights the effectiveness of the overall methodology

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

enlightenment from various conditional probabilities about hang seng index in hong kong stock market abstract the daily hang seng index in the hong kong stock market has been analyzed in this paper two kinds of sign sequences as given conditions have been used to predict the future price movements one is the parameter of multifractal spectrum f based on the indexes recorded in every minute and the other is the variation of the close index i results show that correlation between large fluctuations of the close price and the condition in these two methods is strong and some sign sequences of the parameter f can be used to predict the probability of the near future price movements

scaling in the norwegian stock market the main objective of this paper is to investigate the validity of the much used assumptions that stock market returns follow a random walk and are normally distributed for this purpose the concepts of chaos theory and fractals are applied two independent models are used to examine price variations in the norwegian and us stock markets the first model used is the range over standard deviation or r s statistic which tests for persistence or antipersistence in the time series both the norwegian and us stock markets show significant persistence caused by long run memory components in the series in addition an average non periodic cycle of four years is found for the us stock market these results are not consistent with the random walk assumption the second model investigates the distributional scaling behaviour of the high frequency price variations in the norwegian stock market the results show a remarkable constant scaling behaviour between different time intervals this means that there is no intrinsic time scale for the dynamics of stock price variations the relationship can be expressed through a scaling exponent describing the development of the distributions as the time scale changes this description may be important when constructing or improving pricing models such that they coincide more closely with the observed market behaviour the empirical distributions of high frequency price variations for the norwegian stock market is then compared to the levy stable distribution with the relevant scaling exponent found by using the r s and distributional scaling analysis good agreement is found between the levy profile and the empirical distribution for price variations less than 6 standard deviations covering almost three orders of magnitude in the data for probabilities larger than 6 standard deviations there seem to be an exponential fall off from the levy profile in the tails which indicates that the second moment may be finite

a scaled stochastic approximation algorithm consider a stochastic system of such complexity that its performance can only be evaluated by using simulation or direct experimentation to optimize the expected performance of such systems as a function of several continuous input parameters decision variables we present a scaled stochastic approximation algorithm for finding the zero root of the gradient of the response function in each iteration of the scaled algorithm two independent gradient estimates are sampled at the current estimate of the optimal input parameter vector to compute a scale free estimate of the next search direction we establish sufficient conditions to ensure strong consistency and asymptotic normality of the resulting estimator of the optimal input parameter vector strong consistency is also established for a variant of the scaled algorithm with kesten s acceleration an experimental performance comparison of the scaled algorithm and the classical robbins monro algorithm in two simple queueing systems reveals some of the practical advantages of the scaled algorithm

multifractal description of stock price index fluctuation using a quadratic function fitting abstract in order to obtain a quantitative multifractal characterization of the stock price index the multifractal spectrum of shanghai stock price index time series in 2005 was investigated and the multifractal spectrum was fitted using a quadratic function a sliding window of 240 frequency data in 5 trading days was used to investigate the stock price index fluctuation the multifractal parameters and coefficients in each window were obtained by fitting the local multifractal spectrum using a quadratic function it is found that when the stock price index fluctuates sharply a strong variability is clearly characterized by the multifractal parameters and the quadratic function coefficients this has led to a better understanding of complex stock markets

convergence of markovian stochastic approximation with discontinuous dynamics this paper is devoted to the convergence analysis of stochastic approximation algorithms of the form theta n 1 theta n gamma n 1 h theta n x n 1 where left theta n n in mathbb n right is an mathbb r d valued sequence left gamma n n in mathbb n right is a deterministic stepsize sequence and left x n n in mathbb n right is a controlled markov chain we study the convergence under weak assumptions on smoothness in theta of the function theta mapsto h theta x it is usually assumed that this function is continuous for any x in this work we relax this condition our results are illustrated by considering stochastic approximation algorithms for adaptive quantile estimation and a penalized version of the vector quantization

hilbert huang transform based multifractal analysis of china stock market national natural science foundation of china nsfc 11202122 11301433 11332006 pu jiang project of shanghai 12pj1403500 social science foundation of fujian 2013c056

largest lyapunov exponent estimation and selective prediction by means of simplex forecast algorithms limited predictability is one of the remarkable features of deterministic chaos and this feature may be quantized in terms of lyapunov exponents accordingly lyapunov exponent estimates may be expected to follow in a natural way from forecast algorithms exploring this idea we propose a method estimating the largest lyapunov exponent from a time series which uses the behavior of so called simplex forecasts the method considers the estimation of properties of the distribution of local simplex expansion coefficients these are also used for the definition of error bars for the lyapunov exponent estimates and allows for selective forecasts with improved prediction accuracy we demonstrate these concepts on standard test examples and three realistic applications to time series concerning largest lyapunov exponent estimation of an experimentally obtained hyperchaotic nmr signal brain state differentiation and stock market prediction