long term dependence with asymmetric conditional heteroscedasticity in stock returns abstract this paper studies the long term dependence and the possible asymmetric behavior of the financial time series both can be modeled using a fractionally integrated autoregressive moving average time series model with threshold type conditional heteroscedasticity denoted as an arfima tgarch model into which a bayesian approach is introduced to conduct the parameter estimation with these parameters we apply the arfima tgarch model to describe the daily stock returns of six markets from the empirical results we find that the returns of these markets exhibit mildly long memory processes and reveal an asymmetric response to the negative and positive news

time independent models of asset returns revisited abstract in this study we investigate various well known time independent models of asset returns being simple normal distribution student t distribution levy truncated levy general stable distribution mixed diffusion jump and compound normal distribution for this we use standard and poor s 500 index data of the new york stock exchange helsinki stock exchange index data describing a small volatile market and artificial data the results indicate that all models excluding the simple normal distribution are at least quite reasonable descriptions of the data furthermore the use of differences instead of logarithmic returns tends to make the data looking visually more levy type distributed than it is this phenomenon is especially evident in the artificial data that has been generated by an inflated random walk process

rbf methods in a stochastic volatility framework for greeks computation abstract in this paper we aim to apply a new proposed meshless approach for heston pde resolution in mathematical finance most classical models may be reformulated as partial differential equations pde which are commonly solved by finite difference and monte carlo methods alternatively bio inspired methods may be considered to select parameters and to solve said pdes in particular we focus on heston model pde and we solve it via radial basis functions rbf methods moreover some considerations on the computation of model parameters through learning approaches have been discussed we aim to price a vanilla call option focusing on the derivation of the formulae for its greeks profiles eventually we conclude rbfs are an accurate alternative method to price derivatives in a stochastic volatility framework especially since they allow for a fast and precise computation of greeks

modeling maxima with autoregressive conditional frechet model abstract this paper introduces a novel dynamic generalized extreme value gev framework for modeling the time varying behavior of maxima in financial time series specifically an autoregressive conditional frechet acf model is proposed in which the maxima are modeled by a frechet distribution with time varying scale parameter volatility and shape parameter tail index conditioned on past information the acf provides a direct and accurate modeling of the time varying behavior of maxima and furthermore offers a new angle to study the tail risk dynamics in financial markets probabilistic properties of acf are studied and a maximum likelihood estimator is used for model estimation with its statistical properties investigated simulations show the flexibility of acf and confirm the reliability of its estimators two real data examples on cross sectional stock returns and high frequency foreign exchange returns are used to demonstrate the acf modeling approach where significant improvement over the static gev has been observed for market tail risk monitoring and conditional var estimation empirical result of acf is consistent with the findings of the dynamic peak over threshold pot literature that the tail index of financial markets varies through time

diagnostic checking for time series models with conditional heteroscedasticity estimated by the least absolute deviation approach the recent paper by peng yao 2003 gave an interesting extension of least absolute deviation estimation to generalised autoregressive conditional heteroscedasticity garch time series models the asymptotic distributions of absolute residual autocorrelations and squared residual autocorrelations from the garch model estimated by the least absolute deviation method are derived in this paper these results lead to two useful diagnostic tools which can be used to check whether or not a garch model fitted by using the least absolute deviation method is adequate some simulation experiments give further support to the asymptotic theory and a real data example is also reported

symmetry adapted equilibrium matrices a number of authors have previously used group representation theory to block diagonalise the stiffness matrix of a symmetric structure this paper describes how similar techniques can be used to block diagonalise the equilibrium matrix of a symmetric structure this is shown to provide useful insight into the static and kinematic response of such systems in particular it simplifies finding and classifying states of self stress and mechanisms as well as reducing the computational effort required for a force method analysis

can the random walk model be beaten in out of sample density forecasts evidence from intraday foreign exchange rates abstract it has been documented that random walk outperforms most economic structural and time series models in out of sample forecasts of the conditional mean dynamics of exchange rates in this paper we study whether random walk has similar dominance in out of sample forecasts of the conditional probability density of exchange rates given that the probability density forecasts are often needed in many applications in economics and finance we first develop a nonparametric portmanteau test for optimal density forecasts of univariate time series models in an out of sample setting and provide simulation evidence on its finite sample performance then we conduct a comprehensive empirical analysis on the out of sample performances of a wide variety of nonlinear time series models in forecasting the intraday probability densities of two major exchange rates euro dollar and yen dollar it is found that some sophisticated time series models that capture time varying higher order conditional moments such as markov regime switching models have better density forecasts for exchange rates than random walk or modified random walk with garch and student t innovations this finding dramatically differs from that on mean forecasts and suggests that sophisticated time series models could be useful in out of sample applications involving the probability density

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

prediction in dynamic models with time dependent conditional variances abstract this paper considers forecasting the conditional mean and variance from a single equation dynamic model with autocorrelated disturbances following an arma process and innovations with time dependent conditional heteroskedasticity as represented by a linear garch process expressions for the minimum mse predictor and the conditional mse are presented we also derive the formula for all the theoretical moments of the prediction error distribution from a general dynamic model with garch 1 1 innovations these results are then used in the construction of ex ante prediction confidence intervals by means of the cornish fisher asymptotic expansion an empirical example relating to the uncertainty of the expected depreciation of foreign exchange rates illustrates the usefulness of the results

when is a symmetric pin jointed framework isostatic maxwell s rule from 1864 gives a necessary condition for a framework to be isostatic in 2d or in 3d given a framework with point group symmetry group representation theory is exploited to provide further necessary conditions this paper shows how for an isostatic framework these conditions imply very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework in particular it turns out that an isostatic framework in 2d can belong to one of only six point groups some conjectures and initial results are presented that would give sufficient conditions in both 2d and 3d for a framework that is realized generically for a given symmetry group to be an isostatic framework

large deviation estimates for exceedance times of perpetuity sequences and their dual processes in a variety of problems in pure and applied probability it is relevant to study the large exceedance probabilities of the perpetuity sequence yn b1 a1b2 a1 an 1 bnyn b1 a1b2 a1 an 1 bn where ai bi 0 r ai bi 0 r estimates for the stationary tail distribution of yn yn have been developed in the seminal papers of kesten acta math 131 1973 207 248 and goldie ann appl probab 1 1991 126 166 specifically it is well known that if m supnynm supnyn then p m u cmu p m u cmu as u u while much attention has been focused on extending such estimates to more general settings little work has been devoted to understanding the path behavior of these processes in this paper we derive sharp asymptotic estimates for the normalized first passage time tu logu 1inf n yn u tu log u 1inf n yn u we begin by showing that conditional on tu tu tu tu as u u for a certain positive constant we then provide a conditional central limit theorem for tu tu and study p tu g p tu g as u u for sets g 0 g 0 if g 0 g 0 then we show that p tu g ui g c g p tu g ui g c g as u u for a certain large deviation rate function ii and constant c g c g on the other hand if g g then we show that the tail behavior is actually quite complex and different asymptotic regimes are possible we conclude by extending our results to the corresponding forward process understood in the sense of letac in random matrices and their applications brunswick maine 1984 1986 263 273 amer math soc namely to the reflected process m n max anm n 1 bn 0 mn max anmn 1 bn 0 n z n z using siegmund duality we relate the first passage times of yn yn to the finite time exceedance probabilities of m n mn yielding a new result concerning the convergence of m n mn to its stationary distribution

on the extremes of a class of non linear processes with heavy tailed innovations the aim of this paper is to look at the limiting form of certain empirical point processes induced by a particular class of non linear processes generated by heavy tailed innovations such asymptotic results will be highly useful in obtaining the weak limiting behavior of various functionals of the underlying process including the asymptotic distribution of upper and lower order statistics in particular we investigate the maximum limiting distribution and its corresponding extremal index the results are applied to the study of the extremal properties of bilinear processes

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

expectation propagation for likelihood free inference many models of interest in the natural and social sciences have no closed form likelihood function which means that they cannot be treated using the usual techniques of statistical inference in the case where such models can be efficiently simulated bayesian inference is still possible thanks to the approximate bayesian computation abc algorithm although many refinements have been suggested abc inference is still far from routine abc is often excruciatingly slow due to very low acceptance rates in addition abc requires introducing a vector of summary statistics s y the choice of which is relatively arbitrary and often require some trial and error making the whole process laborious for the user we introduce in this work the ep abc algorithm which is an adaptation to the likelihood free context of the variational approximation algorithm known as expectation propagation the main advantage of ep abc is that it is faster by a few orders of magnitude than standard algorithms while producing

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

financial time series modeling using the hurst exponent abstract this study aims to enhance the understanding of logarithmic asset returns in particular more emphasis is given to the long memory property of financial returns a well documented stylized fact however in the presence of structural breaks other studies suggest that statistical tools such as the autocorrelation function acf can wrongly indicate long memory we propose an insensitive to structural breaks method to test for dependence between distant observations furthermore a model which combines memory in returns and memory in absolute returns is developed in two stages first return series are segmented with respect to changes in the volatility and then the two parameters of the model are estimated to assess the capabilities of the model historical prices of the standard and poor 500 index s p500 financial time stocks exchange 100 index ftse100 deutsche boerse ag german stock index dax and crude oil are used 1 given the estimated parameters and the volatility within each regime 10000 vectors are generated and compared to the original data in terms of the kolmogorov smirnov k s statistical test the obtained results suggest that long memory is present and provide evidence that the additional memory information captured by the model improves financial returns modeling

consistency and asymptotic normality of the quasi maximum likelihood estimator in igarch 1 1 and covariance stationary garch 1 1 models this paper provides a proof of the consistency and asymptotic normality of the quasi maximum likelihood estimator in garch 1 1 and igarch 1 1 models in contrast to the case of a unit root in the conditional mean the presence of a unit root in the conditional variance does not affect the limiting distribution of the estimators in both models estimators are normally distributed in addition a consistent estimator of the covariance matrix is available enabling the use of standard test statistics for inference

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

bayes inference in regression models with arma p q errors we develop practical and exact methods of analyzing arma p 4 regression error models in a bayesian framework by using the gibbs sampling and metropolis hastings algorithms and we prove that the kernel of the proposed markov chain sampler converges to the true density the procedures can be applied to pure arma time series models and to determine features of the likelihood function by choosing appropriate diffuse priors our results are unconditional on the initial observations we also show how the algorithm can be further simplified for the important special cases of stationary ar p and invertible ma q models recursive transformations developed in this paper to diagonalize the covariance matrix of the errors should prove useful in frequentist estimation examples with simulated and actual economic data are presented kpj ourls gibbs sampling metropolis hastings algorithm data augmentation time series arma processes markov chain bayesian statistics

likelihood based estimation of latent generalized arch structures garch models are commonly used as latent processes in econometrics financial economics and macroeconomics yet no exact likelihood analysis of these models has been provided so far in this paper we outline the issues and suggest a markov chain monte carlo algorithm which allows the calculation of a classical estimator via the simulated em algorithm or a bayesian solution in o t computational operations where t denotes the sample size we assess the performance of our proposed algorithm in the context of both artificial examples and an empirical application to 26 uk sectorial stock returns and compare it to existing approximate solutions

testing for garch effects a one sided approach arch models often lie at the boundary of the parameter space under conditional homoskedasticity which invalidates the usual s2 distribution of lr and wald tests although lm tests are not a ected the one sided nature of the alternative hypothesis should result in more powerful tests we propose a simple one sided version of the lm test which is closely related to the kuhn tucker multiplier test we also present critical values for lr wald and one sided lm tests the results of a monte carlo comparison suggest that one sided tests are indeed more powerful than their two sided counterparts 1998 elsevier science s a all rights reserved jel classification c22

a symmetry extension of maxwell s rule for rigidity of frames a symmetry extension of maxwell s rule for rigidity of frames is found this rule subsumes and strengthens maxwell s 1864 rule by requiring that the internal and external degrees of freedom of a pin jointed structure are not only numerically equal but are also equisymmetric a number of special cases of maxwell s original rule are studied to show the improved insight that the symmetry adapted version can give

small sample tests for stock return predictability with possibly non stationary regressors and garch type effects we develop a simulation based procedure to test for stock return predictability with multiple regressors the process governing the regressors is left completely free and the test procedure remains valid in small samples even in the presence of non normalities and garch type effects in the stock returns

symmetry and states of self stress in triangulated toroidal frames abstract a symmetry extension of maxwell s rule for rigidity of frames shows that every fully triangulated torus has at least six states of self stress with a well defined set of symmetries related to rotational and translational representations in the point group in contrast in trivalent polyhedral toroidal frames i e the duals of the deltahedra the rigid body motions plus the mechanisms are at least equal in number to the bars and their symmetry representation contains that of a set of vector slides along the bars

a top bottom price approach to understanding financial fluctuations abstract the presence of sequences of top and bottom tb events in financial series is investigated for the purpose of characterizing such switching points they clearly mark a change in the trend of rising or falling prices of assets to the opposite tendency are of crucial importance for the players decision and also for the market stability previous attempts to characterize switching points have been based on the behavior of the volatility and on the definition of microtrends the approach used herein is based on the smoothing of the original data with a gaussian kernel the events are identified by the magnitude of the difference of the extreme prices by the time lag between the corresponding events waiting time and by the time interval between events with a minimal magnitude return time results from the analysis of the inter day dow jones industrial average index djia from 1928 to 2011 are discussed q gaussian functions with power law tails are found to provide a very accurate description of a class of measures obtained from the series statistics

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

stochastic modeling of security returns evidence from the helsinki stock exchange abstract this paper documents the presence of linear and nonlinear dependencies in finnish stock returns and models these dependencies using autoregressive conditional heteroscedastic methods three conditional distributions normal student t and the power exponential are explored the statistical estimates and the corresponding diagnostic tests indicate that a garch 1 1 model with a power exponential conditional distribution which is characterized by an autoregressive mean represents the data better than any of the other models examined

dynamic behaviors and measurements of financial market crash rate abstract this paper proposes the conditional crash rate ccr to study the degree of financial market crisis and evaluate the risk of financial market crash based on maximum drawdown and escape rate it is found that the ccr of stock price in financial market is equivalent to the escape rate of the drawdown time series corresponding to price series based on the mean escape rate the analytical solution of ccr of financial market of stock price described by black scholes model is obtained for the ccr empirical researches show that the theoretical results of the heston model are in good agreement with the results of the real financial data of the sp ii we can find critical phenomena resonance and inverse resonance behaviors in the function of ccr vs mean reversion of volatility ii the parameter variation induces the appearance of noise enhancement stability in the function of ccr vs amplitude of volatility fluctuation

robust score and portmanteau tests of volatility spillover abstract this paper presents a variety of tests of volatility spillover that are robust to heavy tails generated by large errors or garch type feedback the tests are couched in a general conditional heteroskedasticity framework with idiosyncratic shocks that are only required to have a finite variance if they are independent we negligibly trim test equations or components of the equations and construct heavy tail robust score and portmanteau statistics trimming is either simple based on an indicator function or smoothed in particular we develop the tail trimmed sample correlation coefficient for robust inference and prove that its gaussian limit under the null hypothesis of no spillover has the same standardization irrespective of tail thickness further if spillover occurs within a specified horizon our test statistics obtain power of one asymptotically we discuss the choice of trimming portion including a smoothed p value over a window of extreme observations a monte carlo study shows our tests provide significant improvements over extant garch based tests of spillover and we apply the tests to financial returns data finally based on ideas in patton 2011 we construct a heavy tail robust forecast improvement statistic which allows us to demonstrate that our spillover test can be used as a model specification pre test to improve volatility forecasting

detection of finite mechanisms in symmetric structures abstract using group representation theory it is possible to block diagonalise the equilibrium matrix of a symmetric structure this analysis can identify the symmetry properties of any states of self stress or mechanisms present in the structure this paper will show that in some cases this linear analysis combined with symmetry arguments can show that particular mechanisms of a symmetric structure must be finite

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

mobility of n loops bodies cyclically connected by intersecting revolute hinges the mobilities of many objects from toys and molecular models to large scale deployable structures can be understood in terms of n loops sets of n bodies cyclically connected by pairs of intersecting revolute hinges a symmetry extended version of the grubler criterion for counting kinematic degrees of freedom is used to explain and rationalize the observed mobilities of n loops with small n compared with simple counting the symmetry based approach gives improved detection and visualization of mechanisms and states of self stress it can also give a better account of the differing mobilities of conformers occupying different regions of the phase space such as the rigid chair and flexible boat forms of cyclohexane

the limit distribution of the maximum increment of a random walk with dependent regularly varying jump sizes we investigate the maximum increment of a random walk with heavy tailed jump size distribution here heavy tailedness is understood as regular variation of the finite dimensional distributions the jump sizes constitute a strictly stationary sequence using a continuous mapping argument acting on the point processes of the normalized jump sizes we prove that the maximum increment of the random walk converges in distribution to a frechet distributed random variable

stability and lack of memory of the returns of the hang seng index abstract in this paper we show that the logarithmic returns of the hang seng index from january 2 1987 to november 14 2005 statistically resemble a sequence of independent identically distributed levy stable random variables this is in stark contrast to xiu and jin 2007 39 where long memory farima processes with gaussian noise were suggested as well fitted to the data the lack of memory is checked by using lo s modified r s statistic and a new method of estimation of the memory parameter d which applies the notion of empirical mean squared displacement in order to test stability of the data we employ several statistical tests based on the empirical distribution function finally we also show that the returns possess no conditional heteroscedasticity property thus excluding the arch garch family of processes as possible underlying models

adaptive estimation in time series models in a framework particularly suited for many time series models we obtain a lan result under quite natural and economical conditions this enables us to construct adaptive estimators for part of the euclidean parameter in these semiparametric models special attention is directed to group models in time series with the important subclass of models with time varying location and scale our set up is confronted with the existing literature and as examples we reconsider linear regression and arma tar and arch models

anomalous biased diffusion in networks we study diffusion with a bias toward a target node in networks this problem is relevant to efficient routing strategies in emerging communication networks like optical networks bias is represented by a probability p of the packet or particle to travel at every hop toward a site that is along the shortest path to the target node we investigate the scaling of the mean first passage time mfpt with the size of the network we find by using theoretical analysis and computer simulations that for random regular rr and erd ifmmode mbox h o else h o fi s r enyi networks there exists a threshold probability p mathrm th such that for pl p mathrm th the mfpt scales anomalously as n ensuremath alpha where n is the number of nodes and ensuremath alpha depends on p for pg p mathrm th the mfpt scales logarithmically with n the threshold value p mathrm th of the bias parameter for which the regime transition occurs is found to depend only on the mean degree of the nodes an exact solution for every value of p is given for the scaling of the mfpt in rr networks the regime transition is also observed for the second moment of the probability distribution function the standard deviation for the case of scale free sf networks we present analytical bounds and simulations results showing that the mfpt scales at most as mathrm ln n to a positive power for any finite bias which means that in sf networks even a very small bias is considerably more efficient in comparison to unbiased walk

residual based rank specification tests for ar garch type models this paper derives the asymptotic distribution for a number of rank based and classical residual specification tests in ar garch type models we consider tests for the null hypotheses of no linear and quadratic serial residual autocorrelation residual symmetry and no structural breaks we also apply our method to backtesting value at risk for these tests we show that generally no size correction is needed in the asymptotic test distribution when applied to ar garch residuals obtained through gaussian quasi maximum likelihood estimation to be precise we give exact expressions for the limiting null distribution of the test statistics applied to standardized residuals and find that standard critical values often though not always lead to conservative tests for this result we give simple necessary and sufficient conditions simulations show that our asymptotic approximations work well for a large number of ar garch models and parameter values we also show that the rank based tests often though not always have superior power properties over the classical tests even if they are conservative an empirical application illustrates the relevance of these tests to the ar garch models for weekly stock market return indices of some major and emerging countries

a test for volatility spillover with application to exchange rates abstract this paper proposes a class of asymptotic n 0 1 tests for volatility spillover between two time series that exhibit conditional heteroskedasticity and may have infinite unconditional variances the tests are based on a weighted sum of squared sample cross correlations between two squared standardized residuals we allow to use all the sample cross correlations and introduce a flexible weighting scheme for the sample cross correlation at each lag cheung and ng 1996 test and granger 1969 type regression based test can be viewed as uniform weighting because they give equal weighting to each lag non uniform weighting often gives better power than uniform weighting as is illustrated in a simulation study we apply the new tests to study granger causalities between two weekly nominal u s dollar exchange rates deutschemark and japanese yen it is found that for causality in mean there exists only simultaneous interaction between the two exchange rates for causality in variance there also exists strong simultaneous interaction between them moreover a change in past deutschemark volatility granger causes a change in current japanese yen volatility but a change in past japanese yen volatility does not granger cause a change in current deutschemark volatility

intermittency in an interacting generalization of the geometric brownian motion model we propose a minimal interacting generalization of the geometric brownian motion model which turns out to be formally equivalent to a model describing the dynamics of networks of analogue neurons for sufficiently strong interactions such systems may have many meta stable states transitions between meta stable states are associated with macroscopic reorganizations of the system which can be triggered by random external forcing such a system will exhibit intermittent dynamics within a large part of its parameter space we propose market dynamics as a possible application of this model in which case random external forcing would correspond to the arrival of important information the emergence of a model of interacting prices of the type considered here can be argued to follow naturally from a general argument based on integrating out all non price degrees of freedom from the dynamics of a hypothetical complete description of economic dependences

exact predictive densities for linear models with arch disturbances abstract it is shown how exact predictive densities may be formed in the arch linear model by means of monte carlo integration with importance sampling several improvements in computational efficiency over earlier implementations of this procedure are developed including use of the exact likelihood function rather than an asymptotic approximation to construct the importance sampling distribution and antithetic acceleration of convergence a numerical approach to the formulation of posterior odds ratios and the combination of non nested models is also introduced these methods are applied to daily quotations of closing stock prices forecasts are formulated using linear models arch linear models and an integrated model constructed from the posterior probabilities of the respective models the use of the exact predictive density in a decision theoretic context is illustrated by deriving the optimal day to day portfolio adjustments of a trader with constant relative risk aversion

application of the beck model to stock markets value at risk and portfolio risk assessment abstract we apply the beck model developed for turbulent systems that exhibit scaling properties to stock markets our study reveals that the beck model elucidates the properties of stock market returns and is applicable to practical use such as the value at risk estimation and the portfolio analysis we perform empirical analysis with daily intraday data of the s p500 index return and find that the volatility fluctuation of real markets is well consistent with the assumptions of the beck model the volatility fluctuates at a much larger time scale than the return itself and the inverse of variance or inverse temperature obeys distribution as predicted by the beck model the distribution of returns is well fitted by q gaussian distribution of tsallis statistics the evaluation method of value at risk var one of the most significant indicators in risk management is studied for q gaussian distribution our proposed method enables the var evaluation in consideration of tail risk which is underestimated by the variance covariance method a framework of portfolio risk assessment under the existence of tail risk is considered we propose a multi asset model with a single volatility fluctuation shared by all assets named the single model and empirically examine the agreement between the model and an imaginary portfolio with dow jones indices it turns out that the single model gives good approximation to portfolios composed of the assets with non gaussian and correlated returns

volatility behavior of visibility graph emd financial time series from ising interacting system abstract a financial market dynamics model is developed and investigated by stochastic ising system where the ising model is the most popular ferromagnetic model in statistical physics systems applying two graph based analysis and multiscale entropy method we investigate and compare the statistical volatility behavior of return time series and the corresponding imf series derived from the empirical mode decomposition emd method and the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model further we find that the degree distribution of visibility graph for the simulation series has the power law tails and the assortative network exhibits the mixing pattern property all these features are in agreement with the real market data the research confirms that the financial model established by the ising system is reasonable

bayesian analysis of arma garch models a markov chain sampling approach abstract we develop a markov chain monte carlo method for a linear regression model with an arma p q garch r s error to generate a monte carlo sample from the joint posterior distribution we employ a markov chain sampling with the metropolis hastings algorithm as illustration we estimate an arma garch model of simulated time series data

monte carlo inference in econometric models with symmetric stable disturbances the paper develops markov chain monte carlo methods to perform exact posterior analysis in models with symmetric stable paretian disturbances it is shown how posterior moments and marginal densities of functions of parameters can be computed methodically by combining a gibbs sampler with metropolis independence chains the new method is shown to perform satisfactorily in constructed examples the method is also applied to a set of monthly real exchange rates and the question of difference versus trend stationarity is taken up jointly with the problem of inference about the parameter of the stable distribution

factor garch ito models for high frequency data with application to large volatility matrix prediction abstract several novel large volatility matrix estimation methods have been developed based on the high frequency financial data they often employ the approximate factor model that leads to a low rank plus sparse structure for the integrated volatility matrix and facilitates estimation of large volatility matrices however for predicting future volatility matrices these nonparametric estimators do not have a dynamic structure to implement in this paper we introduce a novel ito diffusion process based on the approximate factor models and call it a factor garch ito model we then investigate its properties and propose a quasi maximum likelihood estimation method for the parameter of the factor garch ito model we also apply it to estimating conditional expected large volatility matrices and establish their asymptotic properties simulation studies are conducted to validate the finite sample performance of the proposed estimation methods the proposed method is also illustrated by using data from the constituents of the s p 500 index and an application to constructing the minimum variance portfolio with gross exposure constraints

interval estimation of value at risk based on garch models with heavy tailed innovations arch and garch models are widely used to model financial market volatilities in risk management applications considering a garch model with heavy tailed innovations we characterize the limiting distribution of an estimator of the conditional value at risk var which corresponds to the extremal quantile of the conditional distribution of the garch process we propose two methods the normal approximation method and the data tilting method for constructing confidence intervals for the conditional var estimator and assess their accuracies by simulation studies finally we apply the proposed approach to an energy market data set

optimal predictions of powers of conditionally heteroscedastic processes in conditionally heteroskedastic models the optimal prediction of powers or logarithms of the absolute process has a simple expression in terms of the volatility process and an expectation involving the independent process a standard procedure for estimating this prediction is to estimate the volatility by gaussian quasi maximum likelihood qml in a first step and to use empirical means based on rescaled innovations to estimate the expectation in a second step this paper proposes an alternative one step procedure based on an appropriate non gaussian qml estimation of the model and establishes the asymptotic properties of the two approaches their performances are compared for finite order garch models and for the infinite arch for the standard garch p q and the asymmetric power garch p q it is shown that the are of the estimators only depends on the prediction problem and some moments of the independent process an application to indexes of major stock exchanges is proposed

forecasting volatility in shanghai and shenzhen markets based on multifractal analysis abstract this paper analyzes the multifractality in shanghai and shenzhen stock markets using multifractal spectrum analysis and multifractal detrended fluctuation analysis we find that the main source of multifractality is long range correlations of large and small fluctuations then we introduce a multifractal volatility measure mv and find that by taking mv as daily conditional volatility the simulated series displayed similar stylized facts to the original daily return series by capturing the dynamics of mv using the arfima model we find that the out of sample forecasting performance of the arfima mv model is better than some garch class models and the arfima rv model under some criteria of loss function

neglecting parameter changes in garch models if a garch model is estimated on a time series that contains parameter changes in the conditional volatility process and these parameter changes are not accounted for a distinct error in the estimation occurs the sum of the estimated autoregressive parameters of the conditional variance converges to one in finite samples the sum of the estimated autoregressive parameters is heavily biased towards one this paper shows that this convergence holds for all common estimators of garch simulations of the garch model show that the effect occurs for realistic parameter changes and sample sizes for financial volatility data

forecasting volatility of fuel oil futures in china garch type sv or realized volatility models abstract in most previous works on forecasting oil market volatility squared daily returns were taken as the proxy of unobserved actual volatility however as demonstrated by andersen and bollerslev 1998 22 this proxy with too high measurement noise could be perfectly outperformed by a so called realized volatility rv measure calculated by the cumulative sum of squared intraday returns with this motivation we further extend earlier works by employing intraday high frequency data to compare the performance of three typical volatility models in the daily out of sample volatility forecasting of fuel oil futures on the shanghai futures exchange shfe the garch type stochastic volatility sv and realized volatility models by taking rv as the proxy of actual daily volatility and then computing forecasting errors we find that the realized volatility model based on intraday high frequency data produces significantly more accurate volatility forecasts than the garch type and sv models based on daily returns furthermore the sv model outperforms many linear and nonlinear garch type models that capture long memory volatility and or the asymmetric leverage effect in volatility these results also prove that abundant volatility information is available in intraday high frequency data and can be used to construct more accurate oil volatility forecasting models

the roles of mean residence time on herd behavior in a financial market abstract we investigate the herd behavior of stock prices in a finance system with the heston model based on parameter estimation of the heston model obtained by minimizing the mean square deviation between the theoretical and empirical return distributions we simulate mean residence time of positive return mrtpr plots of mrtpr against the amplitude or mean reversion of volatility demonstrate a phenomenon of herd behavior for a positive cross correlation between noise sources of the heston model also for a negative cross correlation a phenomenon of herd behavior is observed in plots of mrtpr against the long run variance by increasing amplitude or mean reversion of volatility

managing distribution changes in time series prediction when a problem is modeled statistically a single distribution model is usually postulated that is assumed to be valid for the entire space nonetheless this practice may be somewhat unrealistic in certain application areas in which the conditions of the process that generates the data may change as far as we are aware however no techniques have been developed to tackle this problem this article proposes a technique for modeling and predicting this change in time series with a view to improving estimates and predictions the technique is applied among other models to the hypernormal distribution recently proposed when tested on real data from a range of stock market indices the technique produces better results that when a single distribution model is assumed to be valid for the entire period of time studied moreover when a global model is postulated it is highly recommended to select the hypernormal distribution parameter in the same likelihood maximization process

maximum entropy autoregressive conditional heteroskedasticity model abstract in many applications it has been found that the autoregressive conditional heteroskedasticity arch model under the conditional normal or student s t distributions are not general enough to account for the excess kurtosis in the data moreover asymmetry in the financial data is rarely modeled in a systematic way in this paper we suggest a general density function based on the maximum entropy me approach that takes account of asymmetry excess kurtosis and also of high peakedness the me principle is based on the efficient use of available information and as is well known many of the standard family of distributions can be derived from the me approach we demonstrate how we can extract information functional from the data in the form of moment functions we also propose a test procedure for selecting appropriate moment functions our procedure is illustrated with an application to the nyse stock returns the empirical results reveal that the me approach with a fewer moment functions leads to a model that captures the stylized facts quite effectively

a simple r estimation method for semiparametric duration models modeling nonnegative financial variables e g durations between trades traded volumes or asset volatilities is central to a number of studies across financial econometrics and despite the efforts still poses several statistical challenges among them the efficiency aspects of semiparametric estimation in this paper we concentrate on estimation problems in autoregressive conditional duration acd models with unspecified innovation densities exponential quasi likelihood estimators qmle are the usual practice in that context the efficiency of those qmles the only fisher consistent qmles unfortunately rapidly deteriorates away from the reference exponential density a phenomenon that has been emphasized earlier by drost and werker 2003 who propose various semiparametrically efficient procedures to palliate that phenomenon those procedures rely on a general semiparametric approach which typically requires kernel estimation of the underlying innovation density we propose rank based estimators r estimators as a substitute just as the qmle r estimators remain root n consistent irrespective of the underlying density and rely on the choice of a reference density under which they achieve semiparametric efficiency that density however needs not be the exponential one contrary to the semiparametric estimators proposed by drost and werker 2003 r estimators neither require tangent space calculations nor kernel based density estimation numerical results moreover indicate that r estimators based on exponential reference densities uniformly outperform the exponential qmle under such families of innovations as the weibull or burr densities a real data example about modeling the price range of the swiss stock market index concludes the paper

mobility of a class of perforated polyhedra a class of over braced but typically flexible body hinge frameworks is described they are based on polyhedra with rigid faces where an independent subset of faces has been replaced by a set of holes the contact polyhedron c describing the bodies vertices of c and their connecting joints edges of c is derived by subdivision of the edges of an underlying cubic polyhedron symmetry calculations detect flexibility not revealed by counting alone a generic symmetry extended version of the grubler kutzbach mobility counting rule accounts for the net mobilities of infinite families of this type based on subdivisions of prisms wedges barrels and some general inflations of a parent polyhedron the prisms with all faces even and all barrels are found to generate flexible perforated polyhedra under the subdivision construction the investigation was inspired by a question raised by walter whiteley about a perforated polyhedron with a unique mechanism reducing octahedral to tetrahedral symmetry it turns out that the perforated polyhedron with highest oh point group symmetry based on subdivision of the cube is mechanically equivalent to the hoberman switch pitch toy both objects exhibit an exactly similar mechanism that preserves td subgroup symmetry over a finite range this mechanism survives in two variants suggested by bob connelly and barbara heys that have the same contact graph but lower initial maximum symmetry

filtering and forecasting with misspecified arch models i getting the right variance with the wrong model this paper investigates the properties of the conditional covariance estimates generated by a misspecified arch model for example suppose that we observe a diffusion process at discrete time intervals of length h for each h we use a garch 1 1 model to estimate the instantaneous conditional covariance matrix of the diffusion under mild regularity conditions the difference between these conditional covariance estimates and the true conditional covariance converges to zero in probability as h 0 many other arch models for example exponential arch have similar consistency properties this may well account for the success of arch models in short term forecasting using high frequency data since even misspecified arch models can produce good estimates of volatility

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

bootstrap refinements for qml estimators of the garch 1 1 parameters a b s t r a c t this paper reconsiders a block bootstrap procedure for quasi maximum likelihood estimation of garch models based on the resampling of the likelihood function as proposed by goncalves and white 2004 maximum likelihood and the bootstrap for nonlinear dynamic models journal of econometrics 119 199 219 first we provide necessary conditions and sufficient conditions in terms of moments of the innovation process for the existence of the edgeworth expansion of the garch 1 1 estimator up to the k th term second we provide sufficient conditions for higher order refinements for equally tailed and symmetric test statistics in particular the bootstrap estimator based on resampling the likelihood has the same higher order improvements in terms of error in the rejection probabilities as those in andrews 2002 higher order improvements of a computationally attractive k step bootstrap for extremum estimators econometrica 70 119 162

a first passage time problem for many random walkers abstract the passage of ions through membrane channels plays an important role in many fields of biology an earlier paper m boguna a m berezhkovskii g h weiss phys rev e 62 2000 3250 developed a toy model for statistical properties of the occupancy of a single site by different numbers of lattice random walkers chosen from an infinite set it was assumed there that the residence time in one sojourn at the origin differed from the residence time of points elsewhere in this paper we derive some properties of the corresponding first passage time to the occupancy of the special site by k 1 random walkers in one or two dimensions results of our study were obtained from an extensive set of simulations

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

forecasting volatility of ssec in chinese stock market using multifractal analysis abstract in this paper taking about 7 years high frequency data of the shanghai stock exchange composite index ssec as an example we propose a daily volatility measure based on the multifractal spectrum of the high frequency price variability within a trading day an arfima model is used to depict the dynamics of this multifractal volatility mfv measures the one day ahead volatility forecasting performances of the mfv model and some other existing volatility models such as the realized volatility model stochastic volatility model and garch are evaluated by the superior prediction ability spa test the empirical results show that under several loss functions the mfv model obtains the best forecasting accuracy

a symmetry analysis of mechanisms in rotating rings of tetrahedra rotating rings of tetrahedra are well known from recreational mathematics rings of n tetrahedra with n even are analysed by symmetry adapted versions of classical counting rules of mechanism analysis for n 6 a single state of self stress is found together with n 5 symmetry distinct mechanisms which include the eponymous rotating mechanism for n 4 in a generic configuration a single mechanism remains together with three states of self stress but uniquely in this case the mechanism path passes through a bifurcation at which the number of mechanisms and states of self stress is raised by one

estimating semiparametric arch models by kernel smoothing methods we investigate a class of semiparametric arch models that includes as a special case the partially nonparametric pnp model introduced by engle and ng 1993 and which allows for both flexible dynamics and flexible function form with regard to the news impact function we show that the functional part of the model satisfies a type ii linear integral equation and give simple conditions under which there is a unique solution we propose an estimation method that is based on kernel smoothing and profiled likelihood we establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model we also discuss efficiency of both the parametric part and the nonparametric part we investigate the performance of our procedures on simulated data and on a sample of s p500 index returns we find evidence of asymmetric news impact functions consistent with the parametric analysis

estimation for partially nonstationary multivariate autoregressive models with conditional heteroscedasticity this paper investigates a partially nonstationary multivariate autoregressive model which allows its innovations to be generated by a multivariate arch autoregressive conditional heteroscedastic process three estimators including the least squares estimator a full rank maximum likelihood estimator and a reduced rank maximum likelihood estimator are considered and their asymptotic distributions are derived when the multivariate arch process reduces to the innovation with a constant covariance matrix these asymptotic distributions are the same as those given by ahn reinsel 1990 however in the presence of multivariate arch innovations the asymptotic distributions of the full rank maximum likelihood estimator and the reduced rank maximum likelihood estimator involve two correlated multivariate brownian motions which are different from those given by ahn reinsel 1990 simulation results show that the full rank and reduced rank maximum likelihood estimator are more efficient than the least squares estimator an empirical example shows that the two features of multivariate conditional heteroscedasticity and partial nonstationarity may be present simultaneously in a multivariate time series

kernel estimators of asymptotic variance for adaptive markov chain monte carlo we study the asymptotic behavior of kernel estimators of asymptotic variances or long run variances for a class of adaptive markov chains the convergence is studied both in l p and almost surely the results also apply to markov chains and improve on the existing literature by imposing weaker conditions we illustrate the results with applications to the garch 1 1 markov model and to an adaptive mcmc algorithm for bayesian logistic regression

properties of moments of a family of garch processes this paper considers the moments of a family of first order garch processes first a general condition for the existence of any integer moment of the absolute values of the observations is given second a general expression for this moment as a function of lower order moments is derived third the kurtosis and the autocorrelation function of the squared and absolute valued observations are derived the results apply to a number of different garch parameterizations finally the existence or lack thereof of the theoretical counterpart to the so called taylor effect in some members of this garch family is discussed possibilities of extending the results to higher order garch processes are indicated and potential applications of the statistical theory proposed

bayesian inference in econometric models using monte carlo integration methods for the systematic application of monte carlo integration with importance sampling to bayesian inference in econometric models are developed conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of monte carlo replications increases and the numerical accuracy of this approximation may be assessed reliably are set forth methods for the analytical verification of these conditions are discussed

modelling high frequency economic time series abstract the minute by minute move of the hang seng index hsi data over a 4 yr period is analysed and shown to possess similar statistical features as those of other markets based on a mathematical theorem pope ching phys fluids a 5 1993 1529 we derive an analytic form for the probability distribution function pdf of index moves from fitted functional forms of certain conditional averages of the time series furthermore following a recent work by stolovitzky and ching phys lett a 255 1999 11 we show that the observed pdf can be reproduced by a langevin process with a move dependent noise amplitude the form of the langevin equation can be determined directly from the market data

quasi maximum likelihood estimation for conditional quantiles in this paper we derive the asymptotic distribution of a new class of quasi maximum likelihood estimators qmle based on a tick exponential family of densities we show that the tick exponential assumption is a necessary and sufficient condition for a qmle to be consistent for the parameters of a correctly specified model of a given conditional quantile hence the role of this family of densities in the conditional quantile estimation is analog to the role of the linear exponential family in the conditional mean estimation the tick exponential qmles are shown to be asymptotically normal with an asymptotic covariance matrix that has a novel form not seen in earlier work and which accounts for possible model misspecification for practical purposes we show that the maximization of the tick exponential quasi log likelihood can conveniently be carried out by using standard gradient based optimization techniques more importantly we provide a consistent estimator for the asymptotic covariance matrix based on the scores of the log likelihood which allows us to compute the conditional quantile confidence intervals

structural computations with the singular value decomposition of the equilibrium matrix abstract the singular value decomposition of the equilibrium matrix makes it possible to answer any question of a static kinematic or static kinematic nature for any structural assembly within a unified computational framework the paper introduces this decomposition relates it to the physical properties of a given assembly and derives formulae for stresses displacements etc a simple example illustrates the calculations

the fine structure of volatility feedback i multi scale self reflexivity abstract we attempt to unveil the fine structure of volatility feedback effects in the context of general quadratic autoregressive qarch models which assume that today s volatility can be expressed as a general quadratic form of the past daily returns the standard arch or garch framework is recovered when the quadratic kernel is diagonal the calibration of these models on us stock returns reveals several unexpected features the off diagonal non arch coefficients of the quadratic kernel are found to be highly significant both in sample and out of sample although all these coefficients turn out to be one order of magnitude smaller than the diagonal elements this confirms that daily returns play a special role in the volatility feedback mechanism as postulated by arch models the feedback kernel exhibits a surprisingly complex structure incompatible with all models proposed so far in the literature its spectral properties suggest the existence of volatility neutral patterns of past returns the diagonal part of the quadratic kernel is found to decay as a power law of the lag in line with the long memory of volatility finally qarch models suggest some violations of time reversal symmetry in financial time series which are indeed observed empirically although of much smaller amplitude than predicted we speculate that a faithful volatility model should include both arch feedback effects and a stochastic component

occupancy of a single site by many random walkers we consider an infinite number of noninteracting lattice random walkers with the goal of determining statistical properties of the time out of a total time t that a single site has been occupied by n random walkers initially the random walkers are assumed uniformly distributed on the lattice except for the target site at the origin which is unoccupied the random walk model is taken to be a continuous time random walk and the pausing time density at the target site is allowed to differ from the pausing time density at other sites we calculate the dependence of the mean time of occupancy by n random walkers as a function of n and the observation time t we also find the variance for the cumulative time during which the site is unoccupied the large t behavior of the variance differs according as the random walk is transient or recurrent it is shown that the variance is proportional to t at large t in three or more dimensions it is proportional to t 3 2 in one dimension and to t ln t in two dimensions

multivariate functional coefficient regression models for nonlinear vector time series data summary vector time series data are widely found in practice in this paper we propose a multivariate functional coefficient regression model with heteroscedasticity for modeling such data the local linear smoother is employed to estimate the unknown coefficient matrices asymptotic normality 10 of the proposed estimators is established and bandwidth selection is considered to deal with cointegration widely observed in financial markets we propose an error corrected multivariate functional coefficient model simulations show that the proposed estimation procedures capture nonlinear structures of coefficients well analysis of united states interest rates illustrates the proposed methodology 15

efficient estimation in semiparametric garch models abstract it is well known that financial data sets exhibit conditional hereroskedasticity garch type models are often used to model this phenomenon since the distribution of the rescaled innovations is generally far from a normal distribution a semiparametric approach is advisable several publications observed that adaptive estimation of the euclidean parameters is not possible in the usual parametrization when the distribution of the rescaled innovations is the efficient score functions in the parametric model of the autoregression parameters are orthogonal to the tangent space generated by the nuisance parameter thus suggesting that adaptive estimation of the autoregression parameters is possible indeed we construct adaptive and hence efficient estimators in a general garch in mean type context including integrated garch models our analysis is based on a general lan theorem for time series models published elsewhere in contrast to recent literature about arch models we do not need moment condition

speckle suppression in sar images using the 2 d garch model a novel bayesian based speckle suppression method for synthetic aperture radar sar images is presented that preserves the structural features and textural information of the scene first the logarithmic transform of the original image is analyzed into the multiscale wavelet domain we show that the wavelet coefficients of sar images have significantly non gaussian statistics that are best described by the 2 d garch model by using the 2 d garch model on the wavelet coefficients we are capable of taking into account important characteristics of wavelet coefficients such as heavy tailed marginal distribution and the dependencies between the coefficients furthermore we use a maximum a posteriori map estimator for estimating the clean image wavelet coefficients finally we compare our proposed method with various speckle suppression methods applied on synthetic and actual sar images and we verify the performance improvement in utilizing the new strategy

on the relation between garch and stable processes stable and garch processes have been advocated for modeling financial data the aim of this note is to compare the two processes it is shown that the unconditional distribution of variaties from a garch like process which explicity models the clustering of volatility and exhibits the fat tail property as well can be stable given suitable conditions the conditional distributions are stable as well while it is generally realized that processes with variates that have unconditional nonnormal stable densities have a high frequency of outliers it is less well known that they can exhibit the clustering phenomenon too the clustering is obtained through stable subordination with conditional scaling