spectral gmm estimation of continuous time processes abstract this paper derives a methodology for the estimation of continuous time stochastic models based on the characteristic function the estimation method does not require discretization of the stochastic process and it is simple to apply in practice the method is essentially generalized method of moments on the complex plane hence it shares the efficiency and distribution properties of gmm estimators we illustrate the method with some applications to relevant estimation problems in continuous time finance we estimate a model of stochastic volatility a jump diffusion model with constant volatility and a model that nests both the stochastic volatility model and the jump diffusion model we find that negative jumps are important to explain skewness and asymmetry in excess kurtosis of the stock return distribution while stochastic volatility is important to capture the overall level of this kurtosis positive jumps are not statistically significant once we allow for stochastic volatility in the model we also estimate a non affine model of stochastic volatility and find that the power of the diffusion coefficient appears to be between one and two rather than the value of one half that leads to the standard affine stochastic volatility model however we find that including jumps into this non affine stochastic volatility model reduces the power of the diffusion coefficient to one half finally we offer an explanation for the observation that the estimate of persistence in stochastic volatility increases dramatically as the frequency of the observed data falls based on a multiple factor stochastic volatility model

efficient minimum distance estimation with multiple rates of convergence abstract this paper extends the asymptotic theory of gmm inference to allow sample counterparts of the estimating equations to converge at multiple rates different from the usual square root of the sample size in this setting we provide consistent estimation of the structural parameters in addition we define a convenient rotation in the parameter space or reparametrization to disentangle the different rates of convergence more precisely we identify special linear combinations of the structural parameters associated with a specific rate of convergence finally we demonstrate the validity of usual inference procedures like the overidentification test and wald test with standard formulas it is important to stress that both estimation and testing work without requiring the knowledge of the various rates however the assessment of these rates is crucial for asymptotic power considerations possible applications include econometric problems with two dimensions of asymptotics due to trimming tail estimation infill asymptotic social interactions kernel smoothing or any kind of regularization

bounds and expansions for fisher information when the moments are known summary an expansion of the score statistic as a polynomial in the random variable can be used to provide a nondecreasing sequence of lower bounds for the fisher information when the moments are known as functions of the parameter if the random variable is asymptotically normal the first three bounds provide the first three terms in the asymptotic expansion for the fisher information this leads to a definition of efficiency which may be used to advantage with small sample sizes providing lower bounds for the efficiency of any statistic whose moments are known but whose exact distribution is intractable fisher 1925 suggested that the efficiency of a statistic be measured by its squared correlation with the maximum likelihood estimate this idea was extended by rao 1962 who defined first and second order efficiency by considering how well a linear or quadratic function of the statistic correlated with the derivative of the log likelihood in 2 of the present paper we develop this further by looking at polynomial expansions of the score statistic to obtain a nondecreasing sequence of lower bounds for the fisher information 4y 0 of a statistic y y x which is some function of the data x these bounds may be expressed in terms of the moments of the statistic and their first derivatives with respect to the unknown parameter 0 if we return to fisher s 1925 definition of efficiency as the ratio of fy 0 ox 0 whre ox 0 is the fisher information in the whole sample we can use this to obtain an efficiency for y which is invariant under one one transformations and which does not need to appeal to asymptotic arguments the results are particularly useful for random variables whose moments are known but whose exact sampling distribution is either unknown or intractable in 3 we consider other implications such as the possibility of using different sequences of functions and the question of convergence a recent application of these results by brockwell brown 1981 is given as an example rao 1962 pointed out that the limit of the ratio fy 0 fx o in large samples was the asymptotic squared correlation between the statistic y and the derivative of the log likelihood function lx o alx 0 ao for the full data set when this ratio tends to one both fisher and rao suggested using lim fx 0 fy 0 as n oo as a means of discriminating between alternative statistics this asymptotic concept of second order

nonparametric estimation for a class of levy processes we consider estimation for a class of levy processes modelled as a sum of a drift a symmetric stable process and a compound poisson process we propose a nonparametric approach to estimating unknown parameters of our model including the drift the scale and index parameters in the stable law the mean of the poisson process and the underlying jump size distribution we show that regression and nonparametric deconvolution methods based on the empirical characteristic function can be used for inference interesting connections are shown to exist between properties of our estimators and of those found in conventional deconvolution

estimation of stable distributions by indirect inference this article deals with the estimation of the parameters of an stable distribution by the indirect inference method with the skewed t distribution as an auxiliary model the latter distribution appears as a good candidate for an auxiliary model since it has the same number of parameters as the stable distribution with each parameter playing a similar role to improve the properties of the estimator in finite sample we use a variant of the method called constrained indirect inference in a monte carlo study we show that this method delivers estimators with good properties in finite sample in particular they are much more efficient than two other prevalent methods based on the characteristic function and the empirical quantiles we provide an empirical application to hedge fund returns

boundedness empty channel detection and synchronization for communicating finite automata abstract in this paper we consider networks of communicating finite state machines cfsm s that explicitly allow zero testing i e empty channel detection in our main result we show that the boundedness problem is decidable for the class of fifo networks consisting of two such cfsm s where one of the two machines is allowed to send only a single type of message to the other this result we feel is somewhat surprising since the zero testing capability is precisely the required extension needed in order to render the problem undecidable for the related class of vector addition systems with states vass s of dimension two note that both have the ability to store two nonnegative integers which can be conditionally tested for zero the reason for the disparity appears to be that such a class of extended vass s would be capable of more synchronized behaviour since the actions of the two counters can be controlled by a single finite state control the rest of the paper examines other classes of networks which allow empty channel detection these results seem to indicate that our main result cannot be extended

fisher s information for discretely sampled levy processes this paper studies the asymptotic behavior of the fisher information for a levy process discretely sampled at an increasing frequency we show that it is possible to distinguish not only the continuous part of the process from its jumps part but also different types of jumps and derive the rates of convergence of efficient estimators

efficient estimation of general dynamic models with a continuum of moment conditions there are two difficulties with the implementation of the characteristic function based estimators first the optimal instrument yielding the ml efficiency depends on the unknown probability density function second the need to use a large set of moment conditions leads to the singularity of the covariance matrix we resolve the two problems in the framework of gmm with a continuum of moment conditions a new optimal instrument relies on the double indexing and as a result has a simple exponential form the singularity problem is addressed via a penalization term we introduce hac type estimators for non markov models a simulated method of moments is proposed for non analytical cases

estimating the jump activity index under noisy observations using high frequency data it is widely accepted that the high frequency data are contaminated by microstructure noise whose effect on the statistical inference has been of increasing interest in the literature much of it however has focused on the integrated volatility in this article we investigate another important characteristic namely the jump activity index jai of a discretely sampled semi martingale corrupted by microstructure noise we point out that ignoring the microstructure noise can have a disastrous effect on the estimation of the jai consequently we propose a two stage procedure to estimate the jai it first reduces the effect of noise by local smoothing and then estimates the index from the smoothed data the asymptotic properties such as consistency and asymptotic normality are given simulations are conducted to evaluate the performance of the procedure finally we implement our estimators to some real datasets

nonparametric inference of discretely sampled stable levy processes abstract we study nonparametric inference of stochastic models driven by stable levy processes we introduce a nonparametric estimator of the stable index that achieves the parametric n rate of convergence for the volatility function due to the heavy tailedness the classical least squares method is not applicable we then propose a nonparametric least absolute deviation or median quantile estimator and study its asymptotic behavior including asymptotic normality and maximal deviations by establishing a representation of bahadur kiefer type the result is applied to several major foreign exchange rates

diverging moments and parameter estimation heavy tailed distributions are enjoying increased popularity and are becoming more readily applicable as the arsenal of analytical and numerical tools grows they play key roles in modeling approaches in networking finance and hydrology to name but a few areas the tail parameter is of central importance because it governs both the existence of moments of positive order and the thickness of the tails of the distribution some of the best known tail estimators such as those of koutrouvelis and hill are either parametric or show a lack of robustness or accuracy this article develops a shift and scale invariant nonparametric estimator for both upper and lower bounds for orders with finite moments the estimator builds on the equivalence between tail behavior and the regularity of the characteristic function at the origin and achieves its goal by deriving a simplified wavelet analysis that is particularly suited to characteristic functions

undecidable problems in unreliable computations lossy counter machines are defined as minsky counter machines where the values in the counters can spontaneously decrease at any time while termination is decidable for lossy counter machines structural termination termination for every input is undecidable this undecidability result has far reaching consequences lossy counter machines can be used as a general tool to prove the undecidability of many problems for example 1 the verification of systems that model communication through unreliable channels e g model checking lossy fifo channel systems and lossy vector addition systems 2 several problems for reset petri nets like structural termination boundedness and structural boundedness 3 parameterized problems like fairness of broadcast communication protocols

a new approach to function based hypothesis testing in location scale families motivated by two applications in the mining industry we introduce a new approach to testing the hypothesis that two sampled distributions are simply location and scale changes of one another the test applicable to both paired data and two sample data is based on the empirical characteristic function more conventional techniques founded on the empirical distribution function suffer from serious drawbacks when used to test for location scale families in the motivating applications knowing that the distributions differ only in location and scale has significant operational and economic advantages enabling protocols for one type of data to be applied directly to another supplementary material in the form of matlab code is available online

a recursive algorithm for mixture of densities estimation recursive algorithms for the estimation of mixtures of densities have attracted a lot of attention in the last 10 years here an algorithm for recursive estimation is studied it complements existing approaches in the literature as it is based on conditions that are usually very weak for example the parameter space over which the mixture is taken does not need to be necessarily bounded the essence of the procedure is to combine density estimation via empirical characteristic function together with an iterative hilbert space approximation algorithm the conditions for consistency of the estimator are verified for three important statistical problems a simulation study is also included

on some fourier methods for inference abstract common statistical procedures such as maximum likelihood and m estimation admit generalized representations in the fourier domain the fourier domain provides fertile ground for approaching a number of difficult problems in inference in particular the empirical characteristic function and its extension for stationary time series are shown to be fundamental tools which support numerically simple inference procedures having arbitrarily high asymptotic efficiency and certain robustness features as well a numerical illustration involving the symmetric stable laws is given

estimation of affine asset pricing models using the empirical characteristic function abstract the known functional form of the conditional characteristic function ccf of discretely sampled observations from an affine diffusion is used to develop computationally tractable and asymptotically efficient estimators of the parameters of affine diffusions and of asset pricing models in which the state vectors follow affine diffusions both time domain estimators based on fourier inversion of the ccf and frequency domain estimators based directly on the ccf are constructed a method of moments estimator based on the ccf is shown to approximate the efficiency of maximum likelihood for affine diffusion and asset pricing models

estimation for multivariate stable distributions with generalized empirical likelihood abstract this paper considers the generalized empirical likelihood gel method for estimating the parameters of the multivariate stable distribution the gel method is considered to be an extension of the generalized method of moments gmm the multivariate stable distributions are widely applicable as they can accommodate both skewness and heavy tails we treat the spectral measure which summarizes scale and asymmetry by discretization in order to estimate all the model parameters simultaneously we apply the estimating function constructed by equating empirical and theoretical characteristic functions the efficacy of the proposed gel method is demonstrated in monte carlo studies an illustrative example involving daily returns of market indexes is also included

increased correlation among asset classes are volatility or jumps to blame or both abstract we develop estimators and asymptotic theory to decompose the quadratic covariation between two assets into its continuous and jump components in a manner that is robust to the presence of market microstructure noise using high frequency data on different assets classes we find that the recent financial crisis led to an increase in both the quadratic variations of the assets and their correlations however we find little evidence to suggest a change between the relative contributions of the brownian and jump components as both comove co jumps stem from surprising news announcements that occur primarily before the opening of the us market and are also accompanied by an increase in brownian driven correlations

volatility estimators for discretely sampled levy processes this paper studies the estimation of the volatility parameter in a model where the driving process is a brownian motion or a more general symmetric stable process that is perturbed by another levy process we distinguish between a parametric case where the law of the perturbing process is known and a semiparametric case where it is not in the parametric case we construct estimators which are asymptotically efficient in the semiparametric case we can obtain asymptotically efficient estimators by sampling at a sufficiently high frequency and these estimators are efficient uniformly in the law of the perturbing process

best nonlinear three stage least squares estimation of certain econometric models a method is presented for estimating nonlinear simultaneous equations and transformation models in the presence of disturbance distribution of unknown form it asymptotically achieves the lower variance bound for instrumental variables estimates the author avoids smoothed nonparametric estimation his instruments averaging over the unsmoothed empirical distribution of preliminary residuals he allows for stationary serial dependence in various settings estimates are proposed and large sample inference rules justified these being unaffected if the optimal instruments use only an arbitrarily small vanishing fraction of the residuals the author investigates theoretically the effect of such computational savings on the goodness of the normal approximation copyright 1991 by the econometric society

a numerical criterion for very ample line bundles let x be a projective algebraic manifold of dimension n and let l be an ample line bundle over x we give a numerical criterion ensuring that the adjoint bundle kx l is very ample the sufficient conditions are expressed in terms of lower bounds for the intersection numbers l y over subvarieties y of x in the case of surfaces our criterion gives universal bounds and is only slightly weaker than i reider s criterion when dimx 3 and codimy 2 the lower bounds for l y involve a numerical constant which depends on the geometry of x by means of an iteration process it is finally shown that 2kx ml is very ample form 12n our approach is mostly analytic and based on a combination of hormander s l estimates for the operator lelong number theory and the aubin calabi yau theorem

asymptotic error distributions for the euler method for stochastic differential equations we are interested in the rate of convergence of the euler scheme approximation of the solution to a stochastic differential equation driven by a general possibly discontinuous semimartingale and by the asymptotic behavior of the associated normalized error it is well known that for ito s equations the rate is 1 sqrt n we provide a necessary and sufficient condition for this rate to be 1 sqrt n when the driving semimartingale is a continuous martingale or a continuous semimartingale under a mild additional assumption we also prove that in these cases the normalized error processes converge in law the rate can also differ from 1 sqrt n this is the case for instance if the driving process is deterministic or if it is a levy process without a brownian component it is again 1 sqrt n when the driving process is levy with a nonvanishing brownian component but then the normalized error processes converge in law in the finite dimensional sense only while the discretized normalized error processes converge in law in the skorohod sense and the limit is given an explicit form

estimating the degree of activity of jumps in high frequency data we define a generalized index of jump activity propose estimators of that index for a discretely sampled process and derive the estimators properties these estimators are applicable despite the presence of brownian volatility in the process which makes it more challenging to infer the characteristics of the small infinite activity jumps when the method is applied to high frequency stock returns we find evidence of infinitely active jumps in the data and estimate their index of activity

convexity of complements of tropical varieties and approximations of currents the goal of this note is to affirm a local version of conjecture of nisse sottile 19 on higher convexity of complements of tropical varieties while providing a family of counter examples for the global nisse sottle conjecture in any codimension and dimension higher than one moreover it is shown that surprisingly this family also provides a family of counter examples for the generalized hodge conjecture for positive currents in these dimensions and gives rise to further approximability obstruction

realized laplace transforms for pure jump semimartingales we consider specification and inference for the stochastic scale of discretely observed pure jump semimartingales with locally stable levy densities in the setting where both the time span of the data set increases and the mesh of the observation grid decreases the estimation is based on constructing a nonparametric estimate for the empirical laplace transform of the stochastic scale over a given interval of time by aggregating high frequency increments of the observed process on that time interval into a statistic we call realized laplace transform the realized laplace transform depends on the activity of the driving pure jump martingale and we consider both cases when the latter is known or has to be inferred from the data

the method of simulated quantiles we introduce an inference method based on quantiles matching which is useful for situations where the density function does not have a closed form but it is simple to simulate and or moments do not exist functions of theoretical quantiles which depend on the parameters of the assumed probability law are matched with sample quantiles which depend on observations since the theoretical quantiles may not be available analytically the optimization is based on simulations we illustrate the method with the estimation of stable distributions a thorough monte carlo study and an illustration to 22 nancial indexes show

impact of jumps on returns and realised variances econometric analysis of time deformed levy processes in order to assess the effect of jumps on realised variance calculations we study some of the econometric properties of time changed levy processes we show that in general realised variance is an inconsistent estimator of the time change however we can derive the second order properties of realised variances and use these to estimate the parameters of such models our analytic results give a first indication of the degrees of inconsistency of realised variance as an estimator of the time change in the non brownian case further our results suggest volatility is even more predictable than has been shown by the recent econometric work on realised variance

is brownian motion necessary to model high frequency data this paper considers the problem of testing for the presence of a continuous part in a semimartingale sampled at high frequency we provide two tests one where the null hypothesis is that a continuous component is present the other where the continuous component is absent and the model is then driven by a pure jump process when applied to high frequency individual stock data both tests point toward the need to include a continuous component in the model

assessment of uncertainty in high frequency data the observed asymptotic variance the availability of high frequency financial data has generated a series of estimators based on intra day data improving the quality of large areas of financial econometrics however estimating the standard error of these estimators is often challenging the root of the problem is that traditionally standard errors rely on estimating a theoretically derived asymptotic variance and often this asymptotic variance involves substantially more complex quantities than the original parameter to be estimated standard errors are important they are used to assess the precision of estimators in the form of confidence intervals to create feasible statistics for testing to build forecasting models based on say daily estimates and also to optimize the tuning parameters the contribution of this paper is to provide an alternative and general solution to this problem which we call observed asymptotic variance it is a general nonparametric method for assessing asymptotic variance avar it provides consistent estimators of avar for a broad class of integrated parameters t dt where the spot parameter process can be a general semimartingale with continuous and jump components the observed avar is implemented with the help of a two scales method its construction works well in the presence of microstructure noise and when the observation times are irregular or asynchronous in the multivariate case the methodology is valid for a wide variety of estimators including the standard ones for variance and covariance and also for more complex estimators such as of leverage effects high frequency betas and semivariance

estimation of location and scale in cauchy distributions using the empirical characteristic function summary the iterative method for the parameter estimation of stable laws proposed by koutrouvelis 1981 is modified to handle the case where the distribution is assumed to belong to a cauchy family with location and or scale parameter unknown it is shown that the determination of optimum values at which the empirical characteristic function needs to be evaluated reduces in this case to the determination of the asymptotically optimum quantiles for the parameter estimation of an exponential distribution by linear functions of order statistics the estimators of the scale and location parameters are asymptotically independent and normally distributed and achieve asymptotic efficiencies close to unity the proposed procedure is compared to a method of estimation using linear functions of order statistics

maximum likelihood estimation of stochastic frontier models by the fourier transform the paper is concerned with several kinds of stochastic frontier models whose likelihood function is not available in closed form first with output oriented stochastic frontier models whose one sided errors have a distribution other than the standard ones exponential or half normal the gamma and beta distributions are leading examples second with input oriented stochastic frontier models which are common in theoretical discussions but not in econometric applications third with two tiered stochastic frontier models when the one sided error components follow gamma distributions fourth with latent class models with gamma distributed one sided error terms fifth with models whose two sided error component is distributed as stable paretian and the one sided error is gamma the principal aim is to propose approximations to the density of the composed error based on the inversion of the characteristic function which turns out to be manageable using the fourier transform procedures that are based on the asymptotic normal form of the log likelihood function and have arbitrary degrees of asymptotic efficiency are also proposed implemented and evaluated in connection with output oriented stochastic frontiers the new methods are illustrated using data for us commercial banks electric utilities and a sample from the national youth longitudinal survey

inference for continuous semimartingales observed at high frequency the econometric literature of high frequency data often relies on moment estimators which are derived from assuming local constancy of volatility and related quantities we here study this local constancy approximation as a general approach to estimation in such data we show that the technique yields asymptotic properties consistency normality that are correct subject to an ex post adjustment involving asymptotic likelihood ratios these adjustments are derived and documented several examples of estimation are provided powers of volatility leverage effect and integrated betas the first order approximations based on local constancy can be over the period of one observation or over blocks of successive observations it has the advantage of gaining in transparency in defining and analyzing estimators the theory relies heavily on the interplay between stable convergence and measure change and on asymptotic expansions for martingales

verification of programs with half duplex communication we consider the analysis of infinite half duplex systems made of finite state machines that communicate over unbounded channels the half duplex property for two machines and two channels one in each direction says that each reachable configuration has at most one channel non empty we prove in this paper that such half duplex systems have a recognizable reachability set we show how to compute in polynomial time a symbolic representation of this reachability set and how to use that description to solve several verification problems furthermore though the model of communicating finite state machines is turing powerful we prove that membership of the class of half duplex systems is decidable unfortunately the natural generalization to systems with more than two machines is turing powerful we also prove that the model checking of those systems against pltl propositional linear temporal logic or ctl computational tree logic is undecidable finally we show how to apply the previous decidability results to the regular model checking we propose a new symbolic reachability semi algorithm with accelerations which successfully terminates on half duplex systems of two machines and some interesting non half duplex systems

algorithmic analysis of programs with well quasi ordered domains over the past few years increasing research effort has been directed towards the automatic verification of infinite state systems this paper is concerned with identifying general mathematical structures which can serve as sufficient conditions for achieving decidability we present decidability results for a class of systems called well structured systems which consist of a finite control part operating on an infinite data domain the results assume that the data domain is equipped with a preorder which is a well quasi ordering such that the transition relation is monotonic a simulation with respect to the preorder we show that the following properties are decidable for well structured systems reachability whether a certain set of control states is reachable other safety properties can be reduced to the reachability problem eventuality whether all executions eventually reach a given set of control states represented as afp in ctl simulation whether there exists a simulation between a finite automaton and a well structured system the simulation problem will be shown to be decidable in both directions we also describe how these general principles subsume several decidability results from the literature about timed automata relational automata petri nets and lossy channel systems

empirical likelihood methods based on characteristic functions with applications to levy processes levy processes have been receiving increasing attention in financial modeling one distinctive feature of such models is that their characteristic functions are readily available inference based on characteristic functions is very useful for studying levy processes by incorporating the recent advances in nonparametric approaches empirical likelihood methods based on characteristic functions are developed in this paper for parameter estimation testing a particular parametric class including the presence of a jump component in the levy process and testing for symmetry of a distribution simulation and case studies confirm the effectiveness of the proposed method

efficient estimation and filtering for multivariate jump diffusions abstract this paper develops estimators of the transition density filters and parameters of multivariate jump diffusion models the drift volatility jump intensity and jump magnitude are allowed to be state dependent and non affine it is not necessary to diagonalize the volatility matrix our density and filter estimators converge at the canonical rate typically associated with exact monte carlo estimation our parameter estimators have the same asymptotic distribution as maximum likelihood estimators which are often intractable for the class of models we consider the results of this paper enable the empirical analysis of previously intractable models of asset prices and economic time series

convergence of gaussian quasi likelihood random fields for ergodic levy driven sde observed at high frequency this paper investigates the gaussian quasi likelihood estimation of an exponentially ergodic multidimensional markov process which is expressed as a solution to a levy driven stochastic differential equations whose coefficients are supposed to be known except for the finite dimensional parameters to be estimated we suppose that the process is observed under the condition for the rapidly increasing experimental design by means of the polynomial type large deviation inequality the mighty convergence of the corresponding statistical random fields is derived which especially leads to the asymptotic normality at rate p nhn for all the target parameters and also to the convergence of their moments in our results the diffusion coefficient may be degenerate or even null although the resulting estimator is not asymptotically efficient in the presence of jumps we do not require any specific form of the driving levy measure rendering that the proposed estimation procedure is practical and somewhat robust to underlying model specification

realized laplace transforms for estimation of jump diffusive volatility models a b s t r a c t we develop an efficient and analytically tractable method for estimation of parametric volatility models that is robust to price level jumps the method entails first integrating intra day data into the realized laplace transform of volatility which is a model free estimate of the daily integrated empirical laplace transform of the unobservable volatility the estimation is then done by matching moments of the integrated joint laplace transform with those implied by the parametric volatility model in the empirical application the best fitting volatility model is a non diffusive two factor model where low activity jumps drive its persistent component and more active jumps drive the transient one

embedding and asymptotic expansions for martingales the paper develops a way of embedding general martingales in continuous ones in such a way that the quadratic variation of the continuous martingale has conditional cumulants given the original martingale that are explicitly given in terms of optional and predictable variations of the original process bartlett identities for the conditional cumulants are also found a main corollary to these results is the establishment of second and in some cases higher order asymptotic expansions for martingales

a test of exponentiality vs monotone hazard alternatives derived from the empirical characteristic function on propose un test d exponentialite qui est consistant pour des alternatives a taux de panne monotone

deciding bisimulation equivalences for a class of non finite state programs traditionally many automatic program verification techniques have been applicable only to finite state programs in this paper we extend some of these techniques to a class of infinite state programs that in addition to having a finite state control component may read store and write but not perform any other computations on data such programs are data independent in the sense that their behavior does not depend on the actual data values supplied we consider the problems of deciding strong equivalence and observation equivalence defined by bisimulations as in ccs between such programs these equivalences have major applications in verification of communication protocols we present reductions of these problems to the problem of deciding strong equivalence and observation equivalence between finite state programs for which polynomial time algorithms exist the equivalence problems on data independent programs are shown to be np hard in the size of the programs

estimation for levy processes from high frequency data within a long time interval in this paper we study nonparametric estimation of the levy density for levy processes first without then with brownian component for this we consider 2n resp 3n discrete time observations with step delta the asymptotic framework is n tends to infinity delta delta n tends to zero while n delta n tends to infinity we use a fourier approach to construct an adaptive nonparametric estimator and to provide a bound for the global l2 risk estimators of the drift and of the variance of the gaussian component are also studied we discuss rates of convergence and give examples and simulation results for processes fitting in our framework

high efficiency estimation for the positive stable laws abstract a moment method based on the sample averages of x t and x 2t with suitably chosen t is suggested for estimating the index a and scale parameter c 1 of the positive stable distribution with laplace transform e exp x exp c the corresponding cramer rao lower bounds are computed by using a new and simple fourier technique which is based on an idea of jarrett it is found that the asymptotic efficiencies of the proposed estimators exceed 97 for all values of between zero and 994 a comparison is made with the optimal asymptotic efficiencies attainable by using a different moment method based on e t 1 x and e 2 t 2 x

spectral estimation of the fractional order of a levy process we consider the problem of estimating the fractional order of a levy process from low frequency historical and options data an estimation methodology is developed which allows us to treat both estimation and calibration problems in a unified way the corresponding procedure consists of two steps the estimation of a conditional characteristic function and the weighted least squares estimation of the fractional order in spectral domain while the second step is identical for both calibration and estimation the first one depends on the problem at hand minimax rates of convergence for the fractional order estimate are derived the asymptotic normality is proved and a data driven algorithm based on aggregation is proposed the performance of the estimator in both estimation and calibration setups is illustrated by a simulation study

reliability of mobile processes with noisy channels to model the behavior of channels in real world mobile systems ying introduced an extension of the calculus by taking channel noise into account unfortunately this extension is not faithful in the sense that its semantics does not coincide with the standard one for the calculus in the noise free case in this paper we consider a simple variant of the calculus the asynchronous calculus a which has been used for modeling some concurrent systems with asynchronous communication to model these systems with noisy channels we propose a faithful extension of a called the a n calculus after giving a probabilistic transitional semantics of a n we introduce bisimilarity in a n and show that it is a partial input congruence if a specification of a system is described as a process p in a and we view the behavior of p in a n as an implementation of the specification then it is interesting to measure how far the behavior in a n is from that in a we thus introduce the notion of reliability degree which is based upon a new approximate bisimulation we find that bisimilar agents may have different reliability degrees and even the agent with the greatest reliability degree may not be satisfactory we thus appeal to shannon s noisy channel coding theorem and show that reliability degrees can be improved by employing coding techniques

forward analysis and model checking for trace bounded wsts abstract we investigate a subclass of well structured transition systems wsts the trace bounded in the sense of ginsburg and spanier 1964 1 complete deterministic ones which we claim provide an adequate basis for the study of forward analyses as developed by finkel and goubault larrecq 2012 2 indeed we prove that unlike other conditions considered previously for the termination of forward analysis trace boundedness is decidable trace boundedness turns out to be a valuable restriction for wsts verification as we show that it further allows to decide all regular properties on the set of infinite traces of the system

model checking of systems with many identical timed processes over the last years there has been an increasing research effort directed towards the automatic verification of infinite state systems such as timed automata hybrid automata data independent systems relational automata petri nets lossy channel systems context free and push down processes we present a method for deciding reachability properties of networks of timed processes such a network consists of an arbitrary set of identical timed automata each with a single real valued clock using a standard reduction from safety properties to reachability properties we can use our algorithm to decide general safety properties of timed networks to our knowledge this is the first decidability result concerning verification of systems that are infinite state in two dimensions they contain an arbitrary set of identical processes and they use infinite data structures viz real valued clocks we illustrate our method by showing how it can be used to automatically verify fischer s protocol a timer based protocol for enforcing mutual exclusion among an arbitrary number of processes finally we show undecidability of the recurrent state problem given a state in a timed network check whether there is a computation of the network visiting the state infinitely often this implies undecidability of model checking for any temporal logic which is sufficiently expressive to encode the recurrent state problem such as ptl ctl etc

chebyshev polynomial approximations and characteristic function estimation on developpe une nouvelle procedure pour estimer les fonctions caracteristiques basee sur un developpement en polynomes de chebyshev pour la densite du cosinus des resultats de simulation confirment l utilite de la methode

simulated likelihood estimators for discretely observed jump diffusions abstract this paper develops an unbiased monte carlo approximation to the transition density of a jump diffusion process with state dependent drift volatility jump intensity and jump magnitude the approximation is used to construct a likelihood estimator of the parameters of a jump diffusion observed at fixed time intervals that need not be short the estimator is asymptotically unbiased for any sample size it has the same large sample asymptotic properties as the true but uncomputable likelihood estimator numerical results illustrate its properties

econometric analysis of realized volatility and its use in estimating stochastic volatility models summary the availability of intraday data on the prices of speculative assets means that we can use quadratic variation like measures of activity in financial markets called realized volatility to study the stochastic properties of returns here under the assumption of a rather general stochastic volatility model we derive the moments and the asymptotic distribution of the realized volatility error the difference between realized volatility and the discretized integrated volatility which we call actual volatility these properties can be used to allow us to estimate the parameters of stochastic volatility models without recourse to the use of simulation intensive methods

empirical transform estimation for indexed stochastic models we present a method for estimating the parameters in indexed stochastic models via a least squares approach based on empirical transforms asymptotic approximations are derived for the distribution of the resulting estimators an explicit expression for the mean squared error provides a natural way of selecting the transform variable and a numerical example illustrates the performance of the resulting method a common finding which we term diagonal optimization occurs when multiparameter models are fitted by using transforms diagonal optimization arises when optimal performance results from equating the elements of the transform vector and we provide a heuristic explanation of why this occurs

identifying the successive blumenthal getoor indices of a discretely observed process this paper studies the identification of the levy jump measure of a discretely sampled semimartingale we define successive blumenthal getoor indices of jump activity and show that the leading index can always be identified but that higher order indices are only identifiable if they are sufficiently close to the previous one even if the path is fully observed this result establishes a clear boundary on which aspects of the jump measure can be identified on the basis of discrete observations and which cannot we then propose an estimation procedure for the identifiable indices and compare the rates of convergence of these estimators with the optimal rates in a special parametric case which we can compute explicitly 1 introduction let x be a one dimensional semimartingale defined on a finite time interval 0 t our objective is to make some progress toward the identification of the jump measure of x at high frequency the motivation for what follows has its roots in a family of econometric problems which can be stated as follows we observe a single path of x but not fully although other observation

variation based tests for volatility misspecification abstract we provide a simple and easy to use goodness of fit test for the misspecification of the volatility function in diffusion models the test uses power variations constructed as functionals of discretely observed diffusion processes we introduce an orthogonality condition which stabilizes the limit law in the presence of parameter estimation and avoids the necessity for a bootstrap procedure that reduces performance and leads to complications associated with the structure of the diffusion process the test has good finite sample performance as we demonstrate in numerical simulations

jump robust volatility estimation using nearest neighbor truncation abstract we propose two new jump robust estimators of integrated variance that allow for an asymptotic limit theory in the presence of jumps specifically our medrv estimator has better efficiency properties than the tripower variation measure and displays better finite sample robustness to jumps and small zero returns we stress the benefits of local volatility measures using short return blocks as this greatly alleviates the downward biases stemming from rapid fluctuations in volatility including diurnal intraday u shape patterns an empirical investigation of the dow jones 30 stocks and extensive simulations corroborate the robustness and efficiency properties of our nearest neighbor truncation estimators

testing for jumps in a discretely observed process we propose a new test to determine whether jumps are present in asset returns or other discretely sampled processes as the sampling interval tends to 0 our test statistic converges to 1 if there are jumps and to another deterministic and known value such as 2 if there are no jumps the test is valid for all ito semimartingales depends neither on the law of the process nor on the coefficients of the equation which it solves does not require a preliminary estimation of these coefficients and when there are jumps the test is applicable whether jumps have finite or infinite activity and for an arbitrary blumenthal getoor index we finally implement the test on simulations and asset returns data

on the efficiency of empirical characteristic function procedures summary the asymptotic normality and arbitrarily high efficiency of some new statistical procedures based on the empirical characteristic function is established under general conditions

on the jump activity index for semimartingales hk rgc hkust6011 07p hkust6015 08p hkust6019 10p national nature science foundation of china 71071155 fundamental research funds for the central universities renmin university of china 10xnl007 nsfc 71071155

anova for diffusions and ito processes ito processes are the most common form of continuous semimartingales and include diffusion processes this paper is concerned with the nonparametric regression relationship between two such ito processes we are interested in the quadratic variation integrated volatility of the residual in this regression over a unit of time such as a day a main conceptual finding is that this quadratic variation can be estimated almost as if the residual process were observed the difference being that there is also a bias which is of the same asymptotic order as the mixed normal error term the proposed methodology anova for diffusions and ito processes can be used to measure the statistical quality of a parametric model and non parametrically the appropriateness of a one regressor model in general on the other hand it also helps quantify and characterize the trading hedging error in the case of financial applications

value passing ccs with noisy channels value passing ccs a full version of milner s ccs is a process algebra in which actions consist of sending and receiving values through noiseless communication channels the full calculus is a succinct yet expressive language for the specification and verification of reactive systems taking into account the reality of channel noise in reactive systems in this paper we introduce an extension of value passing ccs called value passing ccs with noisy channels vccs n in which noise is described by a probability distribution over the values after presenting the reduction operational semantics and labelled operational semantics of vccs n we develop the theory of behavioural equivalence by introducing barbed equivalence barbed congruence bisimilarity and full bisimilarity in particular we show that barbed equivalence and barbed congruence coincide with bisimilarity and full bisimilarity respectively based upon the labelled operational semantics of vccs n we establish a probabilistic modal logic for expressing system properties and show its connection with the notion of bisimilarity finally we use vccs n to model a communication protocol for ensuring the reliable transmission of data across an error prone channel

on the asymptotic efficiency of distributed estimation systems with constant modulus signals over multiple access channels a distributed estimation problem is considered with multiple access channels between sensors and a fusion center the sensors phase modulate their noisy observations before transmitting them to the fusion center where a signal parameter is estimated the asymptotic efficiency of this estimator is then determined by using two inequalities that relate the fisher information and the characteristic function a necessary and sufficient condition for equality is found for the first time in the literature the loss in efficiency of the distributed estimation scheme relative to the centralized approach is quantified for different sensing noise distributions it is shown that this distributed estimation system does not incur an efficiency loss if and only if the sensing noise distribution is gaussian

continuous record asymptotics for rolling sample variance estimators it is widely known that conditional covariances of asset returns change over time researchers doing empirical work have adopted many strategies for accommodating conditional heteroskedasticity among the popular strategies are a chopping the available data into short blocks of time and assuming homoskedasticity within the blocks b performing one sided rolling regressions in which only data from say the preceding five year period is used to estimate the conditional covariance of returns at a given date and c performing two sided rolling regressions in which covariances are estimated for each date using say five years of lags and five years of leads another model garch amounts to a one sided weighted rolling regression we develop continuous record asymptotic approximations for the measurement error in conditional variances and covariances when using these methods we derive asymptotically optimal window lengths for standard rolling regressions and optimal weights for weighted rolling regressions as an empirical example we estimate volatility on the s p 500 stock index using daily data from 1928 to 1990

estimation of regression coefficients with the help of characteristic functions abstract in this paper some easily applicable estimators of the regression coefficient in a simple regression model with errors in variables are derived usually one uses sample moments to estimate the regression coefficient however we use empirical characteristic functions in several points besides theoretical derivations a small study with generated data is discussed this study compares our method with estimating methods which use higher order moments

undecidable verification problems for programs with unreliable channels we consider the class of finite state systems communicating through unbounded butlossyfifo channels calledlossy channel systems these systems have infinite state spaces due to the unboundedness of the channels in an earlier paper we showed that the problems of checking reachability safety properties and eventuality properties are decidable for lossy channel systems in this paper we show that the following problems are undecidable the model checking problem in propositional temporal logics such as propositional linear time temporal logic ptl and computation tree logic ctl the problem of deciding eventuality properties with fair channels do all computations eventually reach a given set of states if the unreliable channels satisfy fairness assumptions the results are obtained through reduction from a variant of the post correspondence problem