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

on distribution of number of trades in different time windows in the stock market abstract properties of distributions of the number of trades in different intraday time intervals for five stocks traded in micex are studied the dependence of the mean number of trades on the capital turnover is analyzed correlation analysis using factorial and h q moments demonstrates the multifractal nature of these distributions as well as some peculiar changes in the correlation pattern guided by the analogy with the analysis of particle multiplicity distributions in multiparticle production at high energies an evolution equation relating changes in capital turnover and a number of trades is proposed we argue that such equation can describe the observed features of the distribution of the number of trades in the stock market

modelling price dynamics a hybrid truncated levy flight garch approach abstract arch and garch stochastic processes are widely used in finance and are generally accepted as good approximations when modelling the price dynamics with gaussian conditional probability it can be seen that certain aspects of the empirical data for asset price changes seems to more closely fit a truncated levy flight or garch model but each with individual shortfalls in this paper therefore we combine the garch process with a conditional truncated levy distribution in order to build a hybrid model that most notably describes the price change and associated volatility probability density distributions and scaling behaviour over different time horizons

statistical properties of trading volume depending on size abstract by analyzing high frequency data of transactions on the italian stock index futures we show that the statistical properties of average volume depend on the size of transactions defined as the number of contracts transacted in a single operation in particular we find that large transactions are less correlated with market volatility and display a longer memory

analysis of aggregated tick returns evidence for anomalous diffusion in order to investigate the origin of large price fluctuations we analyze stock price changes of ten frequently traded nasdaq stocks in the year 2002 though the influence of the trading frequency on the aggregate return in a certain time interval is important it cannot alone explain the heavy tailed distribution of stock price changes for this reason we analyze intervals with a fixed number of trades in order to eliminate the influence of the trading frequency and investigate the relevance of other factors for the aggregate return we show that in tick time the price follows a discrete diffusion process with a variable step width while the difference between the number of steps in positive and negative direction in an interval is gaussian distributed the step width is given by the return due to a single trade and is long term correlated in tick time hence its mean value can well characterize an interval of many trades and turns out to be an important determinant for large aggregate returns we also present a statistical model reproducing the cumulative distribution of aggregate returns for an accurate agreement with the empirical distribution we also take into account asymmetries of the step widths in different directions together with cross correlations between these asymmetries and the mean step width as well as the signs of the steps

properties of generalized predictive control control design using long range prediction based on a dynamic model of the plant has become an important contender for high performance applications the model can be derived analytically but more typically it is provided by simple experiments or in the adaptive context by recursive estimation many methods have been proposed in the literature depending on the assumed model structure and the choice of cost function here the approach called generalized predictive control or gpc is reviewed of special interest is the derivation of prediction equations using an observer polynomial and a demonstration that the selection of particular horizons the costing horizons and the control horizon leads to well understood basic techniques such as dead beat pole placement and lq simulated examples show that gpc is suitable for controlling a complex plant such as unstable inverse unstable systems and how the observer polynomial independently tailors the response to the disturbances preprogrammed set points as with robot trajectory control and actuator nonlinearities can also be catered for a discussion of adaptive applications of gpc to several industrial process concludes that the method is easy to use and effective

fractional wave equation with a frictional memory kernel of mittag leffler type abstract in this paper we give an analytical treatment of a fractional wave equation with caputo time fractional derivative and frictional memory kernel of mittag leffler type this problem generalizes a recently solved problem 62 of a wave equation for a vibrating string in presence of a fractional friction with power law memory kernel such equations can be used in the context of modeling processes in complex and viscoelastic media

value at risk estimation with wavelet based extreme value theory evidence from emerging markets abstract this paper introduces wavelet based extreme value theory evt for univariate value at risk estimation wavelets and evt are combined for volatility forecasting to estimate a hybrid model in the first stage wavelets are used as a threshold in generalized pareto distribution and in the second stage evt is applied with a wavelet based threshold this new model is applied to two major emerging stock markets the istanbul stock exchange ise and the budapest stock exchange bux the relative performance of wavelet based evt is benchmarked against the riskmetrics ewma arma garch generalized pareto distribution and conditional generalized pareto distribution models the empirical results show that the wavelet based extreme value theory increases predictive performance of financial forecasting according to number of violations and tail loss tests the superior forecasting performance of the wavelet based evt model is also consistent with basel ii requirements and this new model can be used by financial institutions as well

on the invariance of the lagrange multiplier test with respect to certain changes in the alternative hypothesis this paper examines some implications of the observation that the same lagrange multiplier test is sometimes appropriate for quite different alternative hypotheses a characterization of the class of such alternatives is developed which suggests a simple approach to testing for misspecification and the consequences for finite sample power properties are examined by monte carlo experiments

memory effect and multifractality of cross correlations in financial markets abstract we introduce an instantaneous and an average instantaneous cross correlation function to detect the temporal cross correlations between individual stocks based on the daily data of the united states and the chinese stock markets the memory effect of the instantaneous cross correlations is investigated by applying the detrended fluctuation analysis dfa where the dfa exponents can be partly explained by the correlation function from the common sense long range memory is observed for the average instantaneous cross correlations and persists up to a month magnitude of timescale for the united states stock market and half a month magnitude of timescale for the chinese stock market in addition multifractal nature is investigated by a multifractal detrended fluctuation analysis

the role of signal processing methods in the robust design of predictive control abstract this paper blends the ideas of estimation of model plant uncertainty from process data with the robust design of generalized predictive control gpc based on the small gain theorem classical signal processing methods with appropriate smoothing techniques are used for the estimation of model plant uncertainty and its upper bound for siso linear time invariant systems the choice of proper input excitation in the estimation of uncertainty spectrum in the presence of additive noise is also discussed the estimated uncertainty spectrum with the stability bounds are then used to provide simple graphical based tuning guidelines for robust design of gpc a more accurate estimate of the uncertainty bound allows one to trade off robustness with performance the use of important gpc tuning parameters that allow one to shape the stability bound for robust performance is highlighted evaluation of this technique is illustrated via simulation and experimental application

impact of foreign exchange rate on oil companies risk in stock market during the recent years the importance of effective risk management has become extremely crucial value at risk var is a standard downside measure to explain the behavior of financial series as the garch models have been successfully applied in modeling the volatility structure of securities and other financial assets the var of garch models has turned into an important quantity to study in addition to garch family models the markov regime switching garch mrs garch models are a widely used approach to model financial volatility with potential structural breaks in this paper we evaluated the performance of the mrs garch models with the traditional arma garch family models for estimating var of the stock return of operating companies in the oil industry srocoi in irans stock market under the normal student t and ged distributions our findings showed that the mrs garch models outperform the arma garch family models to capture the characteristics of the srocois volatility additionally we evaluated impact of the foreign exchange rate fluctuations on the var of srocois that were calculated from the optimal models under two regimes usingardl model the results further demonstrated that foreign exchange rate fluctuations have significant and different impacts on the var of srocois across regimes we modeled srocois in irans stock market using mrs garch and arma garch family models mrs garch models under student t and ged distributions have better performance to capture srocois we estimated in sample and out of sample var of srocois from optima models we evaluated impact of the foreign exchange rate fluctuations on the var of srocois foreign exchange rate significantly effect on the var of srocois in different regimes

understanding the cubic and half cubic laws of financial fluctuations recent empirical research has uncovered regularities in nancial u ii the half cubic law of volumes volumes follow a power law distribution with exponent 3 iii approximate cubic law of number of trades the number of trades in a given time intervals follows a power law distribution with exponent around 3 we discuss a new theory that explains them as well as some related facts c 2003 published by elsevier science b v

closed loop least mean square time delay estimator an lms closed loop time delay estimator is presented it uses the error between two samples of the incoming signal the difference between the delayed signal and the reference signal passed through a known delay as a performance index for the estimator the lms algorithm adaptively controls the delay so as to minimize the mean square of this error the controlled delay is implemented using surface acoustic wave devices certain design conditions are applied resulting in a unique minimum for the performance surface it is shown that the proposed estimator is unbiased and has a small variance if the input signal occupies most of the system bandwidth in fact the variance depends on the input noise power and the generalized noise to signal power ratio r n 0 r s 0 as well as on the loop gain the analysis performed also gives a bound on the loop gain required for convergence of the estimator and predicts its rate of convergence computer simulation results show good agreement with the theory

price fluctuations and market activity we empirically quantify the relation between trading activity measured by the number of transactions n and the price change g t for a given stock over a time interval t t t we relate the time dependent standard deviation of price changes volatility to two microscopic quantities the number of transactions n t in t and the variance w 2 t of the price changes for all transactions in t we find that the long ranged volatility correlations are largely due to those of n we then argue that the tail exponent of the distribution of n is insufficient to account for the tail exponent of p g x our results suggest that the fat tails of the distribution p g x arises from w which has a power law distribution with an exponent consistent with that of g

a new κ deformed parametric model for the size distribution of wealth abstract it has been pointed out by patriarca et al 2005 that the power law tailed equilibrium distribution in heterogeneous kinetic exchange models with a distributed saving parameter can be resolved as a mixture of gamma distributions corresponding to particular subsets of agents here we propose a new four parameter statistical distribution which is a deformation of the generalized gamma distribution with a power law tail based on the deformed exponential and logarithm functions introduced by kaniadakis 2001 we found that this new distribution is also an extension to the generalized distribution proposed by clementi et al 2010 with an additional shape parameter and properly reproduces the whole range of the distribution of wealth in such heterogeneous kinetic exchange models we also provide various associated statistical measures and inequality measures

multifractality in the stock market price increments versus waiting times abstract by applying the multifractal detrended fluctuation analysis to the high frequency tick by tick data from deutsche borse both in the price and in the time domains we investigate multifractal properties of the time series of logarithmic price increments and inter trade intervals of time we show that both quantities reveal multiscaling and that this result holds across different stocks the origin of the multifractal character of the corresponding dynamics is among others the long range correlations in price increments and in inter trade time intervals as well as the non gaussian distributions of the fluctuations since the transaction to transaction price increments do not strongly depend on or are almost independent of the inter trade waiting times both can be sources of the observed multifractal behaviour of the fixed delay returns and volatility the results presented also allow one to evaluate the applicability of the multifractal model of asset returns in the case of tick by tick data

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

a unified approach to closed loop time delay estimation systems two generalized configurations for a closed loop delay estimation system cldes are discussed the indirect correlation ic configuration is compared to the conventional cldes the direct correlation dc configuration it is shown that the baseband equivalents of the two configurations differ only by the input noise however the noise power in the ic configuration is far less than that of the dc configuration using the known procedure for calculation of the variance of the time delay estimator it is shown that the two configurations result in the same variance however this procedure is known to be incorrect since for the direct correlation configuration which is known to have an intrinsic noise that persists even when the input signals are ideal the variance is nonzero for zero input signal to noise ratio snr thus another procedure is suggested for variance calculation that overcomes this problem it is shown using this expression that the variance of the time delay estimator is smaller for the ic configuration provided the input snr is not less than 0 db

preferential growth solution and application to modeling stock market abstract we consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles a new particle can either form a new cluster with probability q or join an already existing cluster with a probability proportional to the size thereof we calculate exactly the probability p i k t that the size of the i th cluster at time t is k we applied our model as a background for a microscopic economic model

economic fluctuations and statistical physics quantifying extremely rare and less rare events in finance one challenge of economics is that the systems treated by these sciences have no perfect metronome in time and no perfect spatial architecture crystalline or otherwise nonetheless as if by magic out of nothing but randomness one finds remarkably fine tuned processes in time we present an overview of recent research joining practitioners of economic theory and statistical physics to try to better understand puzzles regarding economic fluctuations one of these puzzles is how to describe outliers phenomena that lie outside of patterns of statistical regularity we review evidence consistent with the possibility that such outliers may not exist this possibility is supported by recent analysis of databases containing information about each trade of every stock r 2007 elsevier b v all rights reserved

variational principle for fractional kinetics and the levy ansatz a variational principle is developed for fractional kinetics based on the auxiliary field formalism it is applied to the fokker planck equation with spatiotemporal fractionality and a variational solution is obtained with the help of the levy ansatz it is shown how the whole range from subdiffusion to superdiffusion is realized by the variational solution as a competing effect between the long waiting time and the long jump the motion of the center of the probability distribution is also analyzed in the case of a periodic drift

model for non gaussian intraday stock returns stock prices are known to exhibit non gaussian dynamics and there is much interest in understanding the origin of this behavior here we present a model that explains the shape and scaling of the distribution of intraday stock price fluctuations called intraday returns and verify the model using a large database for several stocks traded on the london stock exchange we provide evidence that the return distribution for these stocks is non gaussian and similar in shape and that the distribution appears stable over intraday time scales we explain these results by assuming the volatility of returns is constant intraday but varies over longer periods such that its inverse square follows a gamma distribution this produces returns that are student distributed for intraday time scales the predicted results show excellent agreement with the data for all stocks in our study and over all regions of the return distribution

hard frequency domain model error bounds from least squares like identification techniques the problem of deriving so called hard error bounds for estimated transfer functions is addressed a hard bound is one that is sure to be satisfied i e the true system nyquist plot will be confined with certainty to a given region provided that the underlying assumptions are satisfied by blending a priori knowledge and information obtained from measured data it is shown how the uncertainty of transfer function estimates can be quantified the emphasis is on errors due to model mismatch the effects of unmodeled dynamics can be considered as bounded disturbances hence techniques from set membership identification can be applied to this problem the approach taken corresponds to weighted least squares estimation and provides hard frequency domain transfer function error bounds the main assumptions used in the current contribution are that the measurement errors are bounded that the true system is indeed linear with a certain degree of stability and that there is some knowledge about the shape of the true frequency response

scale invariance and universality of economic fluctuations in recent years physicists have begun to apply concepts and methods of statistical physics to study economic problems and the neologism econophysics is increasingly used to refer to this work much recent work is focused on understanding the statistical properties of time series one reason for this interest is that economic systems are examples of complex interacting systems for which a huge amount of data exist and it is possible that economic time series viewed from a dierent perspective might yield new results this manuscript is a brief summary of a talk that was designed to address the question of whether two of the pillars of the eld of phase transitions and critical phenomena scale invariance and universality can be useful in guiding research on economics we shall see that while scale invariance has been tested for many years universality is relatively less frequently discussed this article reviews the results of two recent 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 in size by as much as eight orders of magnitude ii quantifying business rm uctuations we analyze the computstat database comprising all publicly traded united states manufacturing companies within the years 1974 1993 we nd that the distributions of growth rates is dierent for dierent bins of rm size with a width that varies inversely with a power of rm size similar variation is found for other complex organizations including country size university research budget size and size of species of bird populations c 2000 elsevier science b v all rights reserved

volatility distribution in the s p500 stock index abstract we study the volatility of the s p500 stock index from 1984 to 1996 and find that the volatility distribution can be very well described by a log normal function further using detrended fluctuation analysis we show that the volatility is power law correlated with hurst exponent 0 9

stochastic volatility of financial markets as the fluctuating rate of trading an empirical study we present an empirical study of the subordination hypothesis for a stochastic time series of a stock price the fluctuating rate of trading is identified with the stochastic variance of the stock price as in the continuous time random walk ctrw framework the probability distribution of the stock price changes log returns for a given number of trades n is found to be approximately gaussian the probability distribution of n for a given time interval dt is nonpoissonian and has an exponential tail for large n and a sharp cutoff for small n combining these two distributions produces a non trivial distribution of log returns for a given time interval dt which has exponential tails and a gaussian central part in agreement with empirical observations r 2007 elsevier b v all rights reserved

intraday lebaron effects we study the relation at intraday level between serial correlation and volatility of the standard and poor s p 500 stock index futures returns at daily and weekly levels serial correlation and volatility forecasts have been found to be negatively correlated lebaron effect after finding a significant attenuation of the original effect over time we show that a similar but more pronounced effect holds by using intraday measures by such as realized volatility and variance ratio we also test the impact of unexpected volatility defined as the part of volatility which cannot be forecasted on the presence of intraday serial correlation in the time series by employing a model for realized volatility based on the heterogeneous market hypothesis we find that intraday serial correlation is negatively correlated to volatility forecasts whereas it is positively correlated to unexpected volatility

set membership identification of systems with parametric and nonparametric uncertainty a method for parameter set estimation in which the system model is assumed to contain both parametric and nonparametric uncertainty is presented in the disturbance free case the parameter set estimate is guaranteed to contain the parameter set of the true plant in the presence of stochastic disturbances the parameter set estimate obtained from finite data records is shown to have the property that it contains the true plant parameter set with probability one as the data length tends to infinity

dynamics of implied volatility surfaces from random matrix theory abstract we analyze the dynamics of the implied volatility surface of kospi 200 futures options from random matrix theory to extract the informative data we use random matrix criteria implied volatility data have a colossal eigenvalue and the order of eigenvalues in a noisy regime is distinguishably smaller than a random matrix theory prediction we discern the marketwide knowledge of the implied volatility surface movement such as the level skew and smile effect these dynamics has the ergodic property and long range autocorrelation we also study the relationship between the three implied volatility surface dynamics and the underlying asset dynamics and confirm the existence of leverage effect even in the short time interval

fractional fokker planck equation with space and time dependent drift and diffusion in this paper we aim to answer the question proposed by magdziarz stoch proc appl 119 3238 3252 2009 i e we investigate the solution of an anomalous diffusion equation with time and space dependent force and diffusion coefficient first we try to find the stochastic representation of this equation which means the pdf of this stochastic process is rightly the solution of the equation we aim to solve then we also simulate the sample paths of the stochastic process at last taking advantage of the stochastic representation method we employed monte carlo method to approximate the solution of the mentioned equation

fractal analysis on human dynamics of library loans abstract in this paper the fractal characteristic of human behaviors is investigated from the perspective of time series constructed with the amount of library loans the values of the hurst exponent and length of non periodic cycle calculated through rescaled range analysis indicate that the time series of human behaviors and their sub series are fractal with self similarity and long range dependence then the time series are converted into complex networks by the visibility algorithm the topological properties of the networks such as scale free property and small world effect imply that there is a close relationship among the numbers of repetitious behaviors performed by people during certain periods of time our work implies that there is intrinsic regularity in the human collective repetitious behaviors the conclusions may be helpful to develop some new approaches to investigate the fractal feature and mechanism of human dynamics and provide some references for the management and forecast of human collective behaviors

effects of a fractional friction with power law memory kernel on string vibrations in this paper we give an analytical treatment of a wave equation for a vibrating string in the presence of a fractional friction with power law memory kernel the exact solution is obtained in terms of the mittag leffler type functions and a generalized integral operator containing a four parameter mittag leffler function in the kernel the method of separation of the variables laplace transform method and sturm liouville problem are used to solve the equation analytically the asymptotic behaviors of the solution of a special case fractional differential equation are obtained directly from the analytical solution of the equation and by using the tauberian theorems the proposed model may be used for describing processes where the memory effects of complex media could not be neglected

modeling long range memory trading activity by stochastic differential equations we propose a model of fractal point process driven by the nonlinear stochastic differential equation the model is adjusted to the empirical data of trading activity in financial markets this reproduces the probability distribution function and power spectral density of trading activity observed in the stock markets we present a simple stochastic relation between the trading activity and return which enables us to reproduce long range memory statistical properties of volatility by numerical calculations based on the proposed fractal point process r 2007 elsevier b v all rights reserved

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

time evolution of stochastic processes with correlations in the variance stability in power law tails of distributions abstract we model the time series of the s p500 index by a combined process the ar garch process where ar denotes the autoregressive process which we use to account for the short range correlations in the index changes and garch denotes the generalized autoregressive conditional heteroskedastic process which takes into account the long range correlations in the variance we study the ar garch process with an initial distribution of truncated levy form we find that this process generates a new probability distribution with a crossover from a levy stable power law to a power law with an exponent outside the levy range beyond the truncation cutoff we analyze the sum of n variables of the ar garch process and find that due to the correlations the ar garch process generates a probability distribution which exhibits stable behavior in the tails for a broad range of values n a feature which is observed in the probability distribution of the s p500 index we find that this power law stability depends on the characteristic scale in the correlations we also find that inclusion of short range correlations through the ar process is needed to obtain convergence to a limiting gaussian distribution for large n as observed in the data

quantifying the error in estimated transfer functions with application to model order selection previous results on estimating errors or error bounds on identified transfer functions have relied on prior assumptions about the noise and the unmodeled dynamics this prior information took the form of parameterized bounding functions or parameterized probability density functions in the time or frequency domain with known parameters it is shown that the parameters that quantify this prior information can themselves be estimated from the data using a maximum likelihood technique this significantly reduces the prior information required to estimate transfer function error bounds the authors illustrate the usefulness of the method with a number of simulation examples how the obtained error bounds can be used for intelligent model order selection that takes into account both measurement noise and under modeling is shown another simulation study compares the method to akaike s well known fpe and aic criteria

modeling non stationarities in high frequency financial time series abstract we study tick by tick financial returns for the ftse mib index of the italian stock exchange borsa italiana we confirm previously detected non stationarities scaling properties reported before for other high frequency financial data are only approximately valid as a consequence of our empirical analyses we propose a simple model for non stationary returns based on a non homogeneous normal compound poisson process it turns out that our model can approximately reproduce several stylized facts of high frequency financial time series moreover using monte carlo simulations we analyze order selection for this class of models using three information criteria akaike s information criterion aic the bayesian information criterion bic and the hannan quinn information criterion hq for comparison we perform a similar monte carlo experiment for the acd autoregressive conditional duration model our results show that the information criteria work best for small parameter numbers for the compound poisson type models whereas for the acd model the model selection procedure does not work well in certain cases

similarities and differences between physics and economics in this opening talk we discuss some of the similarities between work being done by economists and by physicists seeking to contribute to economics we also mention some of the dierences in the approaches taken and justify these dierent approaches by developing the argument that by approaching the same problem from dierent points of view new results might emerge in particular we review some recent results for example the 1nding that there are two new universal scaling models in economics i the 3uctuation of price changes of any stock market is characterized by a pdf which is a simple power law with exponent 4 that extends over 10 2 standard deviations a factor of 10 8 on the y axis ii for a wide range of economic organizations the histogram that shows how size of organization is inversely correlated to 3uc tuations in size with an exponent 1 6 neither of these two new laws has a 1rm theoretical foundation we also discuss results that are reminiscent of phase transitions in spin systems where the divergent behavior of the response function at the critical point zero magnetic 1eld leads to large 3uctuations c 2001 published by elsevier science b v

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

joint estimation of pn code delay and multipath using the extended kalman filter the problem of delay estimation in the presence of multipath is considered it is shown that the extended kalman filter ekf can be used to obtain joint estimates of time of arrival and multipath coefficients for deterministic signals when the channel can be modeled as a tapped delay line simulation results are presented for the ekf joint estimator used for synchronization in a direct sequence spread spectrum system operating over a frequency selective fading channel a simplified model of the ekf joint estimator is considered for analysis purposes the evolution in time of the tracking error probability density function and the nonlinear tracking error variance are examined through numerical solution of the chapman kolmogorov equation the nonlinear tracking error variance is compared to both the linear error variance estimate directly provided by the ekf and the cramer rao lower bound

estimation of transfer functions asymptotic theory and a bound of model uncertainty abstract the problem of transfer function estimation is considered we will discuss the problem in two related aspects firstly how to obtain a good black box transfer function model secondly how to derive a suitable description of the model uncertainty modelling errors we will emphasize the second point we shall discuss the asymptotic theory on the properties of transfer function estimates developed recently by ljung and yuan this new theory shows that the transfer function estimate is consistent the error of the estimate is asymptotically normal with a very simple expression for its variance their results will be extended here to cases where spectral analysis is used based on this theory we will propose the method for obtaining a low order nominal model of linear processes and define and estimate an upper bound of the model uncertainty an upper bound of the model uncertainty is a suitable description of the modelling errors for the robust controller design

the power law distribution of cumulative coal production abstract the coal industry is dominated by the largest mines with 1 of coal mines in the u s being responsible for 65 of the coal cumulatively produced we show that this heavy tail can be well approximated by a power law where mine level cumulative production is inversely proportionate to distributional rank maximum likelihood and regression based procedures estimate the counter cumulative power law parameter to be less than one indicating there is no well defined mean or variance for cumulative production goodness of fit tests indicate the power law is a better fit to the data than other competing distributions including the lognormal

out of sample forecasts of quadratic variation we compare the forecasts of quadratic variation given by the realized volatility rv and the two scales realized volatility tsrv computed from high frequency data in the presence of market microstructure noise under several different dynamics for the volatility process and assumptions on the noise we show that tsrv largely outperforms rv whether looking at bias variance rmse or out of sample forecasting ability an empirical application to all djia stocks confirms the simulation results

existence and uniqueness results for a time fractional nonlinear diffusion equation abstract in this work we consider a nonlinear ordinary integro differential equation which arises in the studies of time fractional porous medium equation the nonlocality of the resulting free boundary problem is governed by the erdelyi kober operator which requires using other than classical proof techniques to prove the existence and uniqueness of a compactly supported solution we reduce the free boundary case to the initial value problem next we use the sub and supersolution technique to show that there exists a globally defined unique solution as a side product some estimates on the exact solution are found

scaling and memory of intraday volatility return intervals in stock markets we study the return interval tau between price volatilities that are above a certain threshold q for 31 intraday data sets including the standard and poor s 500 index and the 30 stocks that form the dow jones industrial index for different threshold q the probability density function pq tau scales with the mean interval tau as formula see text similar to that found in daily volatilities since the intraday records have significantly more data points compared to the daily records we could probe for much higher thresholds and still obtain good statistics we find that the scaling function f x is consistent for all 31 intraday data sets in various time resolutions and the function is well approximated by the stretched exponential f x similar to e ax gamma with gamma 0 38 0 05 and a 3 9 0 5 which indicates the existence of correlations we analyze the conditional probability distribution pq tau tau0 for tau following a certain interval tau0 and find pq tau tau0 depends on tau0 which demonstrates memory in intraday return intervals also we find that the mean conditional interval tau tau0 increases with tau0 consistent with the memory found for pq tau tau0 moreover we find that return interval records in addition to having short term correlations as demonstrated by pq tau tau0 have long term correlations with correlation exponents similar to that of volatility records

quantifying economic fluctuations abstract this manuscript is a brief summary of a talk designed to address the question of whether two of the pillars of the field of phase transitions and critical phenomena scale invariance and universality can be useful in guiding research on interpreting empirical data on economic fluctuations using this conceptual framework as a guide we empirically quantify the relation between trading activity measured by the number of transactions n and the price change g t for a given stock over a time interval t t t we relate the time dependent standard deviation of price changes volatility to two microscopic quantities the number of transactions n t in t and the variance w2 t of the price changes for all transactions in t we find that the long ranged volatility correlations are largely due to those of n we then argue that the tail exponent of the distribution of n is insufficient to account for the tail exponent of p g x since n and w display only weak inter dependency our results show that the fat tails of the distribution p g x arises from w finally we review recent work on quantifying collective behavior among stocks by applying the conceptual framework of random matrix theory rmt rmt makes predictions for universal properties that do not depend on the interactions between the elements comprising the system and deviations from rmt provide clues regarding system specific properties we compare the statistics of the cross correlation matrix c whose elements cij are the correlation coefficients of price fluctuations of stock i and j against a random matrix having the same symmetry properties it is found that rmt methods can distinguish random and non random parts of c the non random part of c which deviates from rmt results provides information regarding genuine collective behavior among stocks we also discuss results that are reminiscent of phase transitions in spin systems where the divergent behavior of the response function at the critical point zero magnetic field leads to large fluctuations and we discuss a curious symmetry breaking a feature qualitatively identical to the behavior of the probability density of the magnetization for fixed values of the inverse temperature

volatility driven market in a generalized lotka voltera formalism abstract the generalized lotka voltera glv formalism has been introduced in order to explain the power law distributions in the individual wealth w i t pareto law and financial markets returns fluctuations r as a result of the auto catalytic multiplicative random character of the individual capital dynamics as long as the multiplicative random factor is extracted from the same probability distribution for all the individuals the exponent of the power laws turns out to be independent on the time variations of the average this explains also the stability over the past century of experimentally measured pareto exponent in contrast to the scaling properties of the single time unconditional probability distributions the auto correlations between observables measured at different times are not correctly reproduced by the original glv if the variance 2 of is time independent in the glv formalism the volatility r 2 auto correlations decay exponentially while the measurements in real markets indicate a power law with a very small exponent we show in the present paper that by making the variance of the individual wealth changes 2 a function of the market volatility r 2 one correctly reproduces the market volatility long range correlations moreover we show that this non trivial feedback loop between the market price volatility and the variance of the investors wealth leads to non trivial patterns in the overall market trends if the feedback is too strong it may even endanger the market stability

the structure and performance of estimators for real time estimation of randomly varying time delay structures for time delay estimation are described which are deduced using the maximum likelihood technique the performance of estimators designed for time invariant delays is discussed for the case of signals with a time variable delay a two step algorithm for the estimation of a randomly varying time delay between two stochastic signals is developed in the first step the maximum likelihood estimate is computed over an observation interval small enough to consider the delay to be approximately constant due to the short averaging interval the probability of ambiguous peaks in the estimation function and the variance of the estimate are greatly increased therefore in the second step a decision directed adaptive postfiltering algorithm is presented that effectively suppresses outliers and reduces the variance

joint time delay estimation and adaptive recursive least squares filtering a general estimation model is defined in which two observations are available a noisy and a noise filtered and delayed version of the transmitted signal the delay and the filter must be estimated the joint estimator is composed of an adaptive delay element operating in conjunction with an adaptive transversal filter the delay is updated using a form of derivative with respect to the delay of the sum of squared errors the adaptive delay is limited to integer values and is defined as the lag the lag value is computed and updated so that the optimum least squares solution is attained the joint algorithm is obtained by combining the lag update relations with a version of the fast transversal filter rls algorithm simulations show that both stationary and time varying delays are effectively tracked and that the adaptive filter properly estimates the reference filter impulse response

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

correlations in economic time series a financial index of the new york stock exchange the sp here f is called the crossover frequency iii we confirm these results using the dfa detrended fluctuation analysis method see fig 2b which allows accurate estimates of exponents independent of local trends

a multifractal detrended fluctuation analysis of trading behavior of individual and institutional traders in tehran stock market abstract employing the multifractal detrended fluctuation analysis mf dfa the multifractal properties of trading behavior of individual and institutional traders in the tehran stock exchange tse are numerically investigated using daily trading volume time series of these two categories of traders the scaling exponents generalized hurst exponents generalized fractal dimensions and singularity spectrum are derived furthermore two main sources of multifractality i e temporal correlations and fat tailed probability distributions are also examined we also compare our results with data of s p 500 results of this paper suggest that for both classes of investors in tse multifractality is mainly due to long range correlation while for s p 500 the fat tailed probability distribution is the main source of multifractality

economic fluctuations and anomalous diffusion we quantify the relation between trading activity measured by the number of transactions n deltat and the price change g deltat for a given stock over a time interval t t deltat to this end we analyze a database documenting every transaction for 1000 u s stocks for the two year period 1994 1995 we find that price movements are equivalent to a complex variant of classic diffusion where the diffusion constant fluctuates drastically in time we relate the analog for stock price fluctuations of the diffusion constant known in economics as the volatility to two microscopic quantities i the number of transactions n deltat in deltat which is the analog of the number of collisions and ii the variance w 2 deltat of the price changes for all transactions in deltat which is the analog of the local mean square displacement between collisions our results are consistent with the interpretation that the power law tails of p g deltat are due to p w deltat and the long range correlations in g deltat are due to n deltat

the properties and mechanism of long term memory in nonparametric volatility abstract recent empirical literature documents the presence of long term memory in return volatility but the mechanism of the existence of long term memory is still unclear in this paper we investigate the origin and properties of long term memory with nonparametric volatility using high frequency time series data of the chinese shanghai composite stock price index we perform detrended fluctuation analysis dfa on three different nonparametric volatility estimators with different sampling frequencies for the same volatility series the hurst exponents reduce as the sampling time interval increases but they are still larger than 1 2 which means that no matter how the interval changes it still cannot change the existence of long memory rrv presents a relatively stable property on long term memory and is less influenced by sampling frequency rv and rbv have some evolutionary trends depending on time intervals which indicating that the jump component has no significant impact on the long term memory property this suggests that the presence of long term memory in nonparametric volatility can be contributed to the integrated variance component considering the impact of microstructure noise rbv and rrv still present long term memory under various time intervals we can infer that the presence of long term memory in realized volatility is not affected by market microstructure noise our findings imply that the long term memory phenomenon is an inherent characteristic of the data generating process not a result of microstructure noise or volatility clustering

statistical properties of trading volume of chinese stocks abstract the cumulative distribution of trading volume is investigated for chinese stocks different from the power law scaling of mature markets the distribution is well fitted by a stretched exponential function f x e x with the autocorrelation function and the detrended fluctuation analysis the long range autocorrelation of trading volume is revealed the conditional dependence of volume on volatility and the volume volatility cross correlation are studied and a positive long range correlation between volume and volatility is observed

testing forecast optimality under unknown loss empirical tests of forecast optimality have traditionally been conducted under the assumption of mean squared error loss or some other known loss function in this article we establish new testable properties that hold when the forecaster s loss function is unknown but testable restrictions can be imposed on the data generating process trading off conditions on the data generating process against conditions on the loss function we propose flexible estimation of the forecaster s loss function in situations where the loss depends not only on the forecast error but also on other state variables such as the level of the target variable we apply our results to the problem of evaluating the federal reserve s forecasts of output growth forecast optimality is rejected if the fed s loss depends only on the forecast error however the empirical findings are consistent with forecast optimality provided that overpredictions of output growth are costlier to the fed than underpredictions particularly during per