new results on global stability analysis of discontinuous cohen grossberg neural networks of neutral type in hale s form in this paper we aim to investigate the globally asymptotic stability of the equilibrium point for the discontinuous cohen grossberg neural networks of neutral type in hale s form to deal with th

nonlinear shrinkage estimation of large integrated covariance matrices integrated covariance matrices arise in intra day models of asset returns which allow volatility to change across the trading day when the number of assets is large the natural estimator of such a matrix suffers from bias contributed from extreme eigenvalues we introduce a novel nonlinear shrinkage estimator for the integrated covariance matrix which shrinks the extreme eigenvalues of a realized covariance matrix back to an acceptable level and enjoys a certain asymptotic efficiency when the number of assets is of the same order as the number of data points novel maximum exposure and actual risk bounds are derived when our estimator is used in constructing the minimum variance portfolio compared to other methods our estimator performs favorably in both simulations and a real data analysis

a local stable bootstrap for power variations of pure jump semimartingales and activity index estimation abstract we provide a new resampling procedure the local stable bootstrap that is able to mimic the dependence properties of realized power variations for pure jump semimartingales observed at different frequencies this allows us to propose a bootstrap estimator and inference procedure for the activity index of the underlying process as well as bootstrap tests for whether it obeys a jump diffusion or a pure jump process that is of the null hypothesis h 0 2 against the alternative h 1 2 we establish first order asymptotic validity of the resulting bootstrap power variations activity index estimator and diffusion tests for h 0 moreover the finite sample size and power properties of the proposed diffusion tests are compared to those of benchmark tests using monte carlo simulations unlike existing procedures our bootstrap tests are correctly sized in general settings finally we illustrate the use and properties of the new bootstrap diffusion tests using high frequency data on three fx series the s p 500 and the vix

covariance matrix estimation and linear process bootstrap for multivariate time series of possibly increasing dimension multivariate time series present many challenges especially when they are high dimensional the paper s focus is twofold first we address the subject of consistently estimating the autocovariance sequence this is a sequence of matrices that we conveniently stack into one huge matrix we are then able to show consistency of an estimator based on the so called flat top tapers most importantly the consistency holds true even when the time series dimension is allowed to increase with the sample size secondly we revisit the linear process bootstrap lpb procedure proposed by mcmurry and politis journal of time series analysis 2010 for univariate time series based on the aforementioned stacked autocovariance matrix estimator we are able to define a version of the lpb valid for multivariate time series under rather general assumptions we show that our multivariate linear process bootstrap mlpb has asymptotic validity for the sample mean in two important cases a when the time series dimension is fixed and b when it is allowed to increase with sample size as an aside in case a we show that the mlpb works also for spectral density estimators which is a novel result even in the univariate case we conclude with a simulation study that demonstrates the superiority of the mlpb in some important cases

a moving blocks empirical likelihood method for longitudinal data summary in the analysis of longitudinal or panel data neglecting the serial correlations among the repeated measurements within subjects may lead to inefficient inference in particular when the number of repeated measurements is large it may be desirable to model the serial correlations more generally an appealing approach is to accommodate the serial correlations nonparametrically in this article we propose a moving blocks empirical likelihood method for general estimating equations asymptotic results are derived under sequential limits simulation studies are conducted to investigate the finite sample performances of the proposed methods and compare them with the elementwise and subject wise empirical likelihood methods of wang et al 2010 biometrika 97 79 93 and the block empirical likelihood method of you et al 2006 can j statist 34 79 96 an application to an aids longitudinal study is presented

two stage stationary bootstrapping for bivariate average realized volatility matrix under market microstructure noise and asynchronicity abstract under the two important modern financial market features of noise and non synchronicity for multiple assets for consistent estimators of the integrated covariations we adopt the two time scale average realized volatility matrix arvm which is a matrix extension of the two time scale realized volatilities of zhang et al 2005 an asymptotic normal theory is provided for the two time scale arvm and resulting realized covariations the asymptotic normality is not directly applicable in practice to construct statistical methods owning to nuisance parameters to bypass the nuisance parameter problem two stage stationary bootstrapping is proposed we establish consistencies of the bootstrap distributions and construct confidence intervals and hypothesis tests for the integrated covariance regression coefficient and correlation coefficient the validity of the stationary bootstrap for the high frequency heterogeneous returns is proved by showing that there exist parameters of the stationary bootstrap blocks so that the bootstrap consistencies hold the proposed bootstrap methods extend the i i d bootstrapping methods for realized covariations by dovonon et al 2013 that are confined to synchronous noise free sampling for high frequency noisy asynchronous samples a monte carlo experiment shows better finite sample performances of the proposed stationary bootstrap methods based on the two time scale arvm estimator than the wild blocks of blocks bootstrap methods of hounyo 2017 based on pre averaged truncated estimator

the jackknife and the bootstrap for general stationary observations we extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence we do not attempt a reduction to i i d values the jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of l consecutive data once in the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero under appropriate conditions consistency is obtained if l l n rightarrow infty and l n n rightarrow 0 general statistics are approximated by an arithmetic mean in regular cases this approximation determines the asymptotic behavior bootstrap replicates are constructed by selecting blocks of length l randomly with replacement among the blocks of observations the procedures are illustrated by using the sunspot numbers and some simulated data

the asymptotic behavior of quadratic forms in φ mixing random variables let z i i 1 be a linear process defined by z email protected j 0 d email protected t j with d j j 0 being a regular varying sequence of real numbers and x t

subsampling high frequency data the main contribution of this paper is to propose a novel way of conducting inference for an important general class of estimators that includes many estimators of integrated volatility a subsampling scheme is introduced that consistently estimates the asymptotic variance for an estimator thereby facilitating inference and the construction of valid confidence intervals the new method does not rely on the exact form of the asymptotic variance which is useful when the latter is of complicated form the method is applied to the volatility estimator of ait sahalia et al 2011 in the presence of autocorrelated and heteroscedastic market microstructure noise

bootstrapping integrated covariance matrix estimators in noisy jump diffusion models with non synchronous trading abstract we propose a bootstrap method for estimating the distribution and functionals of it such as the variance of various integrated covariance matrix estimators in particular we first adapt the wild blocks of blocks bootstrap method suggested for the pre averaged realized volatility estimator to a general class of estimators of integrated covolatility we then show the first order asymptotic validity of this method in the multivariate context with a potential presence of jumps dependent microstructure noise irregularly spaced and non synchronous data our results justify using the bootstrap to estimate the covariance matrix of a broad class of covolatility estimators the bootstrap variance estimator is positive semi definite by construction an appealing feature that is not always shared by existing variance estimators of the integrated covariance estimator as an application of our results we also consider the bootstrap for regression coefficients we show that the wild blocks of blocks bootstrap appropriately centered is able to mimic both the dependence and heterogeneity of the scores we provide a proof of construction of bootstrap percentile and percentile t intervals as well as variance estimates in this context this contrasts the traditional pairs bootstrap which is not able to mimic the score heterogeneity even in the simple case where no microstructure noise is present our monte carlo simulations show that the wild blocks of blocks bootstrap improve the finite sample properties of the alternative approach based on the gaussian approximation we illustrate its practical use on high frequency equity data

bootstrapping realized volatility we propose bootstrap methods for a general class of nonlinear transformations of realized volatility which includes the raw version of realized volatility and its logarithmic transformation as special cases we consider the independent and identically distributed i i d bootstrap and the wild bootstrap wb and prove their first order asymptotic validity under general assumptions on the log price process that allow for drift and leverage effects we derive edgeworth expansions in a simpler model that rules out these effects the i i d bootstrap provides a second order asymptotic refinement when volatility is constant but not otherwise the wb yields a second order asymptotic refinement under stochastic volatility provided we choose the external random variable used to construct the wb data appropriately none of these methods provides third order asymptotic refinements both methods improve upon the first order asymptotic theory in finite samples

monotone viable trajectories for functional differential inclusions this paper is a study on functional differential inclusions with memory which represent the multivalued version of retarded functional differential equations the main result gives a necessary and sufficient equations the main result gives a necessary and sufficient condition ensuring the existence of viable trajectories that means trajectories remaining in a given nonempty closed convex set defined by given constraints the system must satisfy to be viable some motivations for this paper can be found in control theory where f t f t u u u is the set of possible velocities of the system at time t depending on the past history represented by the function and on a control u ranging over a set u of controls other motivations can be found in planning procedures in microeconomics and in biological evolutions where problems with memory do effectively appear in a multivalued version all these models require viability constraints represented by a closed convex set

least squares variogram fitting by spatial subsampling summary least squares methods are popular for fitting valid variogram models to spatial data the paper proposes a new least squares method based on spatial subsampling for variogram model fitting we show that the method proposed is statistically efficient among a class of least squares methods including the generalized least squares method further it is computationally much simpler than the generalized least squares method the method produces valid variogram estimators under very mild regularity conditions on the underlying random field and may be applied with different choices of the generic variogram estimator without analytical calculation an extension of the method proposed to a class of spatial regression models is illustrated with a real data example results from a simulation study on finite sample properties of the method are also reported

maximum likelihood and the bootstrap for nonlinear dynamic models we provide a unified framework for analyzing bootstrapped extremum estimators of nonlinear dynamic models for heterogeneous dependent stochastic processes we apply our results to the moving blocks bootstrap of kunsch ann stat 17 1989 1217 and liu and singh in r lepage l billiard eds exploring the limits of the bootstrap wiley new york 1992 and prove the first order asymptotic validity of the bootstrap approximation to the true distribution of quasi maximum likelihood estimators we also consider bootstrap testing in particular we prove the first order asymptotic validity of the bootstrap distribution of suitable bootstrap analogs of wald and lagrange multiplier statistics for testing hypotheses

inference for autocorrelations under weak assumptions abstract in this article we consider the large sample behavior of estimates of autocorrelations and autoregressive moving average arma coefficients as well as their distributions under weak conditions specifically the usual text book formulas for variances of these estimates are based on strong assumptions and should not be routinely applied without careful consideration such is the case when the time series follows an arma process with uncorrelated innovations that may not be assumed to be independent and identically distributed as a specific case it is well known that if the process is independent and identically distributed then the sample autocorrelation estimates scaled by the square root of the sample size are asymptotically standard normal this result is used extensively as a diagnostic check on the residuals of a fitted model or as an initial test on the observed time series to determine whether further model fitting is warranted in this article we show that this result can be quite

consistency of the jackknife after bootstrap variance estimator for the bootstrap quantiles of a studentized statistic efron j roy statist soc ser b 54 1992 83 1111 proposed a computationally efficient method called the jackknife after bootstrap for estimating the variance of a bootstrap estimator for independent data for dependent data a version of the jackknife after bootstrap method has been recently proposed by lahiri econometric theory 18 2002 79 98 in this paper it is shown that the jackknife after bootstrap estimators of the variance of a bootstrap quantile are consistent for both dependent and independent data results from a simulation study are also presented

asymptotic expansions for sums of block variables under weak dependence let x i be a sequence of random vectors and y in f in x i l be zero mean block variables where x i l x i x i l 1 i 1 are overlapping blocks of length l and where f in are borel measurable functions this paper establishes valid joint asymptotic expansions of general orders for the joint distribution of the sums n i 1 x i and n i 1 y in under weak dependence conditions on the sequence x i i when the block length t grows to infinity in contrast to the classical edgeworth expansion results where the terms in the expansions are given by powers of n 1 2 the expansions derived here are mixtures of two series one in powers of n 1 2 and the other in powers of n l 1 2 applications of the main results to i expansions for studentized statistics of time series data and ii second order correctness of the blocks of blocks bootstrap method are given

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

an investigation of ideals in the set of fuzzy measures this work is devoted to the investigation of sets of fuzzy measures that are closed with respect to convex sum and product of fuzzy measures which we call ideals it is shown that the basic convex families of fuzzy measures which are interpreted as lower probabilities possess such properties

subsampling for heteroskedastic time series abstract in this article a general theory for the construction of confidence intervals or regions in the context of heteroskedastic dependent data is presented the basic idea is to approximate the sampling distribution of a statistic based on the values of the statistic computed over smaller subsets of the data this method was first proposed by politis and romano 1994b for stationary observations we extend their results to heteroskedastic observations and prove a general asymptotic validity result under minimal conditions in contrast the usual bootstrap and moving blocks bootstrap are typically valid only for asymptotically linear statistics and their justification requires a case by case analysis our general asymptotic results are applied to a regression setting with dependent heteroskedastic errors

inference in vars with conditional heteroskedasticity of unknown form we derive a framework for asymptotically valid inference in stable vector autoregressive var models with conditional heteroskedasticity of unknown form we prove a joint central limit theorem for the var slope parameter and innovation covariance parameter estimators and address bootstrap inference as well our results are important for correct inference on var statistics that depend both on the var slope and the variance parameters as e g in structural impulse response functions irfs we also show that wild and pairwise bootstrap schemes fail in the presence of conditional heteroskedasticity if inference on functions of the unconditional variance parameters is of interest because they do not correctly replicate the relevant fourth moments structure of the error terms in contrast the residual based moving block bootstrap results in asymptotically valid inference we illustrate the practical implications of our theoretical results by providing simulation evidence on the finite sample properties of different inference methods for irfs our results point out that estimation uncertainty may increase dramatically in the presence of conditional heteroskedasticity moreover most inference methods are likely to understate the true estimation uncertainty substantially in finite samples

semiparametric normal transformation models for spatially correlated survival data there is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiologic studies in this article we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data this class of models assumes that survival outcomes marginally follow a cox proportional hazard model with unspecified baseline hazard and their joint distribution is obtained by transforming survival outcomes to normal random variables whose joint distribution is assumed to be multivariate normal with a spatial correlation structure a key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields we study the relationship of the spatial correlation structure of the transformed no

multivariate realised kernels consistent positive semi definite estimators of the covariation of equity prices with noise and non synchronous trading we propose a multivariate realised kernel to estimate the ex post covariation of log prices we show this new consistent estimator is guaranteed to be positive semi definite and is robust to measurement noise of certain types and can also handle non synchronous trading it is the first estimator which has these three properties which are all essential for empirical work in this area we derive the large sample asymptotics of this estimator and assess its accuracy using a monte carlo study we implement the estimator on some us equity data comparing our results to previous work which has used returns measured over 5 or 10 minutes intervals we show the new estimator is substantially more precise

bootstrapping realized multivariate volatility measures we study bootstrap methods for statistics that are a function of multivariate high frequency returns such as realized regression coefficients and realized covariances and correlations for these measures of covariation the monte carlo simulation results of barndorff nielsen and shephard 2004 show that finite sample distortions associated with their feasible asymptotic theory approach may arise if sampling is not too frequent this motivates our use of the bootstrap as an alternative tool of inference for covariation measures we consider an i i d bootstrap applied to the vector of returns we show that the finite sample performance of the bootstrap is superior to the existing first order asymptotic theory nevertheless and contrary to the existing results in the bootstrap literature for regression models subject to heteroskedasticity in the error term the edgeworth expansion for the i i d bootstrap that we develop here shows that this method is not second order accurate we argue that this is due to the fact that the conditional mean parameters of realized regression models are heterogeneous under stochastic volatility

bootstrapping the box pierce q test a robust test of uncorrelatedness abstract this paper describes a test of the null hypothesis that the first k autocorrelations of a covariance stationary time series are zero in the presence of statistical dependence the test is based on the box pierce q statistic with bootstrap based p values the bootstrap is implemented using a double blocks of blocks procedure with prewhitening the finite sample performance of the bootstrap q test is investigated by simulation in our experiments the performance is satisfactory for samples of n 500 at this sample size the differences between the empirical and nominal rejection probabilities are essentially eliminated

generalized halanay inequalities and their applications to neural networks with unbounded time varying delays in this brief we discuss some variants of generalized halanay inequalities that are useful in the discussion of dissipativity and stability of delayed neural networks integro differential systems and volterra functional differential equations we provide some generalizations of the halanay inequality which is more accurate than the existing results as applications we discuss invariant set dissipative synchronization and global asymptotic stability for the hopfield neural networks with infinite delays we also prove that the dynamical systems with unbounded time varying delays are globally asymptotically stable

estimating the quadratic covariation matrix from noisy observations local method of moments and efficiency an efficient estimator is constructed for the quadratic covariation or integrated covolatility matrix of a multivariate continuous martingale based on noisy and non synchronous observations under high frequency asymptotics our approach relies on an asymptotically equivalent continuous time observation model where a local generalised method of moments in the spectral domain turns out to be optimal asymptotic semiparametric efficiency is established in the cramer rao sense main findings are that non synchronicity of observation times has no impact on the asymptotics and that major efficiency gains are possible under correlation simulations illustrate the finite sample behaviour

limit theorems for nonlinear functionals of a stationary gaussian sequence of vectors limit theorems for functions of stationary mean zero gaussian sequences of vectors satisfying long range dependence conditions are considered depending on the rate of decay of the coefficients the limit law can be either gaussian or the law of a multiple ito wiener integral we prove the bootstrap of these limit theorems in the case when the limit is normal a sufficient bracketing condition for these limit theorems to happen uniformly over a class of functions is presented

razumikhin type theorems for hybrid system with memory in this paper we address the stability problem of hybrid systems with memory which are newly developed to model hybrid dynamic systems affected by delays for such systems stability criteria are developed based on razumikhin type conditions which are usually applied in the delay systems we prove that the hybrid system with memory is uniformly globally pre asymptotically stable by small gain theorem besides a relaxed razumikhin type stability criterion is also proposed which does not require strict decrease of the lyapunov razumikhin function during jumps several examples are given to illustrate the effectiveness and generality of the proposed results

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

bootstrapping high frequency jump tests the main contribution of this article is to propose a bootstrap test for jumps based on functions of realized volatility and bipower variation bootstrap intraday returns are randomly generated fro

econometric analysis of realized covariation high frequency based covariance regression and correlation in financial economics this paper analyses multivariate high frequency financial data using realized covariation we provide a new asymptotic distribution theory for standard methods such as regression correlation analysis and covariance it will be based on a fixed interval of time e g a day or week allowing the number of high frequency returns during this period to go to infinity our analysis allows us to study how high frequency correlations regressions and covariances change through time in particular we provide confidence intervals for each of these quantities

bootstrap confidence regions computed from autoregressions of arbitrary order summary given a linear time series e g an autoregression of infinite order we may construct a finite order approximation and use that as the basis for bootstrap confidence regions the sieve or autoregressive bootstrap as this method is often called is generally seen as a competitor with the better understood block bootstrap approach however in the present paper we argue that for linear time series the sieve bootstrap has significantly better performance than blocking methods and offers a wider range of opportunities in particular since it does not corrupt second order properties then it may be used in a double bootstrap form with the second bootstrap application being employed to calibrate a basic percentile method confidence interval this approach confers secondorder accuracy without the need to estimate variance that offers substantial benefits since variances of statistics based on time series can be difficult to estimate reliably and partly because of the relatively small amount of information contained in a dependent process are notorious for causing problems when used to studentize other advantages of the sieve bootstrap include considerably greater robustness against variations in the choice of the tuning parameter here equal to the autoregressive order and the fact that in contradistinction to the case of the block bootstrap the percentile t version of the sieve bootstrap may be based on the raw estimator of standard error in the process of establishing these properties we show that the sieve bootstrap is second order correct

generalized lyapunov approach for functional differential inclusions abstract this paper is concerned with the generalized lyapunov approach for functional differential inclusions fdi at first we prove a class of generalized halanay s inequalities then by applying the generalization of halanay s inequalities we investigate the uniformly ultimate boundedness and uniformly asymptotic stability of fdi

quasi maximum likelihood estimation of volatility with high frequency data this paper investigates the properties of the well known maximum likelihood estimator in the presence of stochastic volatility and market microstructure noise by extending the classic asymptotic results of quasi maximum likelihood estimation when trying to estimate the integrated volatility and the variance of noise this parametric approach remains consistent efficient and robust as a quasi estimator under misspecified assumptions moreover it shares the model free feature with nonparametric alternatives for instance realized kernels while being advantageous over them in terms of finite sample performance in light of quadratic representation this estimator behaves like an iterative exponential realized kernel asymptotically comparisons with a variety of implementations of the tukey hanning2 kernel are provided using monte carlo simulations and an empirical study with the euro us dollar future illustrates its application in practice

designing realised kernels to measure the ex post variation of equity prices in the presence of noise this paper shows how to use realised kernels to carry out efficient feasible inference on the expost variation of underlying equity prices in the presence of simple models of market frictions the issue is subtle with only estimators which have symmetric weights delivering consistent estimators with mixed gaussian limit theorems the weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem realised kernels can also be selected to i be analysed using endogenously spaced data such as that in databases on transactions ii allow for market frictions which are endogenous iii allow for temporally dependent noise the finite sample performance of our estimators is studied using simulation while empirical work illustrates their use in practice

generalized lyapunov method for discontinuous systems abstract nonlinear dynamical systems described by differential equations with discontinuous right hand side and solutions intended in filippov sense are considered based on filippov differential inclusion and a new chain rule for differentiating regular functions along filippov solution trajectories different kinds of stability and convergence results are presented moreover we investigate the stability and convergence for the corresponding perturbation system of the discontinuous system and some new criteria are addressed

on saturation discontinuities and delays in iiss and iss feedback control redesign this paper addresses input to state stability iss and integral iss iiss redesign to enhance robustness of feedback control systems in the face of actuator disturbances the idea of the redesign is to modify control laws available for disturbance free systems a priori in order to achieve robustness against the disturbance in practice control system design often encounters time delays discontinuities and actuator limitations at the same time the purpose of this paper is to propose a unified treatment of these issues in the redesign for actuator disturbances for the new class of systems we pursue lgv type formulas which are widely used for ordinary differential equations in addition we incorporate saturation into the lgv type control for implementation in the presence of actuator limitations to derive such a redesign formula we develop a framework of iss iiss lyapunov krasovskii functionals allowing for the krasovskii solutions this paper demonstrates that the notion of invariantly differentiable functionals is useful for deriving lgv type control laws and dealing with discontinuities directly the iiss formulation which includes the iss as a special case allows us to address actuator limitations in the redesign problem in a flexible manner

generalized halanay inequalities for dissipativity of volterra functional differential equations abstract this paper is concerned with the dissipativity of theoretical solutions to nonlinear volterra functional differential equations vfdes at first we give some generalizations of halanay s inequality which play an important role in study of dissipativity and stability of differential equations then by applying the generalization of halanay s inequality the dissipativity results of vfdes are obtained which provides unified theoretical foundation for the dissipativity analysis of systems in ordinary differential equations odes delay differential equations ddes integro differential equations ides volterra delay integro differential equations vdides and vfdes of other type which appear in practice

pre averaging estimators of the ex post covariance matrix in noisy diffusion models with non synchronous data we show how pre averaging can be applied to the problem of measuring the ex post covariance of financial asset returns under microstructure noise and non synchronous trading a pre averaged realised covariance is proposed and we present an asymptotic theory for this new estimator which can be configured to possess an optimal convergence rate or to ensure positive semi definite covariance matrix estimates we also derive a noise robust hayashi yoshida estimator that can be implemented on the original data without prior alignment of prices we uncover the finite sample properties of our estimators with simulations and illustrate their practical use on high frequency equity data

jackknife bootstrap and other resampling methods in regression analysis motivated by a representation for the least squares estimator we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time they are unbiased for homoscedastic errors and a special case the delete one jackknife is almost unbiased for heteroscedastic errors the method is extended to cover nonlinear parameters regression m estimators nonlinear regression and generalized linear models interval estimators can be constructed from the jackknife histogram three bootstrap methods are considered two are shown to give biased variance estimators and one does not have the bias robustness property enjoyed by the weighted delete one jackknife a general method for resampling residuals is proposed it gives variance estimators that are bias robust several bias reducing estimators are proposed some simulation results are reported

jumps and betas a new framework for disentangling and estimating systematic risks we provide a new theoretical framework for disentangling and estimating the sensitivity towards systematic diffusive and jump risks in the context of factor models our estimates of the sensitivities towards systematic risks or betas are based on the notion of increasingly finer sampled returns over fixed time intervals we show consistency and derive the asymptotic distributions of our estimators in an empirical application of the new procedures involving high frequency data for forty individual stocks we find that the estimated monthly diffusive and jump betas with respect to an aggregate market portfolio differ substantially for some of the stocks in the sample

is the diurnal pattern sufficient to explain intraday variation in volatility a nonparametric assessment abstract in this paper we propose a nonparametric way to test the hypothesis that time variation in intraday volatility is caused solely by a deterministic and recurrent diurnal pattern we assume that noisy high frequency data from a discretely sampled jump diffusion process are available the test is then based on asset returns which are deflated by the seasonal component and therefore homoskedastic under the null to construct our test statistic we extend the concept of pre averaged bipower variation to a general ito semimartingale setting via a truncation device we prove a central limit theorem for this statistic and construct a positive semi definite estimator of the asymptotic covariance matrix the t statistic after pre averaging and jump truncation diverges in the presence of stochastic volatility and has a standard normal distribution otherwise we show that replacing the true diurnal factor with a model free jump and noise robust estimator does not affect the asymptotic theory a monte carlo simulation also shows this substitution has no discernable impact in finite samples the test is however distorted by small infinite activity price jumps to improve inference we propose a new bootstrap approach which leads to almost correctly sized tests of the null hypothesis we apply the developed framework to a large cross section of equity high frequency data and find that the diurnal pattern accounts for a rather significant fraction of intraday variation in volatility but important sources of heteroskedasticity remain present in the data

bootstrap technology and applications bootstrap resampling methods have emerged as powerful tools for constructing inferential procedures in modern statistical data analysis although these methods depend on the availability of fast inexpensive computing they offer the potential for highly accurate methods of inference moreover they can even eliminate the need to impose a convenient statistical model that does not have a strong scientific basis in this article we review some bootstrap methods emphasizing applications through illustrations with some real data special attention is given to regression problems with dependent data and choosing tuning parameters for optimal performance

generalized lyapunov approach for convergence of neural networks with discontinuous or non lipschitz activations the paper considers a class of additive neural networks where the neuron activations are modeled by discontinuous functions or by continuous non lipschitz functions some tools are developed which enable us to apply a lyapunov like approach to differential equations with discontinuous right hand side modeling the neural network dynamics the tools include a chain rule for computing the time derivative along the neural network solutions of a nondifferentiable lyapunov function and a comparison principle for this time derivative which yields conditions for exponential convergence or convergence in finite time by means of the lyapunov like approach a general result is proved on global exponential convergence toward a unique equilibrium point of the neural network solutions moreover new results on global convergence in finite time are established which are applicable to neuron activations with jump discontinuities or neuron activations modeled by means of continuous non lipschitz holder functions

a goodness of fit test for arch models a goodness of fit test in the class of conditional heteroscedastic time series models is examined due to the nonstandard limiting distribution of the test we propose to bootstrap the test showing its asymptotic validity moreover we illustrate the finite sample performance of the test by a small monte carlo study

stability theorems for delay differential inclusions this technical note addresses stability problems of delay differential inclusions a chain rule is proposed for a wide class of lyapunov krasovskii functionals which are not necessarily invariantly differentiable we also obtain an invariance like theorem where the derivative of the candidate functional is bounded above by a continuous negative semidefinite function several examples are given to show the effectiveness of the results

a general resampling scheme for triangular arrays of alpha mixing random variables with application to the problem of spectral density estimation in 1989 kunsch introduced a modified bootstrap and jackknife for a statistic which is used to estimate a parameter of the m dimensional joint distribution of stationary and alpha mixing observations the modification amounts to resampling whole blocks of consecutive observations or deleting whole blocks one at a time liu and singh independently proposed in 1988 the same technique for observations that are m dependent however many time series statistics notably estimators of the spectral density function involve parameters of the whole infinite dimensional joint distribution and hence do not fit in this framework in this report we generalize the moving blocks resampling scheme of kunsch and liu and singh a still modified version of the nonparametric bootstrap and jackknife is seen to be valid for general linear statistics that are asymptotically normal and consistent for a parameter of the whole joint distribution we then apply this result to the problem of estimation of the spectral density

limit theorems for moving averages of discretized processes plus noise this paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise which are observed at high frequency our method generalizes the pre averaging approach see bernoulli15 2009 634 658 stochastic process appl 119 2009 2249 2276 and provides consistent estimates for various characteristics of general semimartingales furthermore we prove the associated multidimensional stable central limit theorems as expected we find central limit theorems with a convergence rate n 1 4 if n is the number of observations

the mean value of a fuzzy number abstract the notion of expectation is defined for fuzzy numbers of intervals viewing them as consonant random sets this expectation is interval valued and remains additive in the sense of fuzzy interval addition as a by product some light is shed on the debate between probability and possibility theory and the problem of how to carry measure theoretic notions into the field of possibility theory

a quasi maximum likelihood approach for integrated covariance matrix estimation with high frequency data estimating the integrated covariance matrix icm from high frequency financial trading data is crucial to reflect the volatilities and covariations of the underlying trading instruments such an objective is difficult due to contaminated data with microstructure noises asynchronous trading records and increasing data dimensionality in this paper we study a quasi maximum likelihood qml approach for estimating an icm from high frequency financial data we explore a novel multivariate moving average time series device that is convenient for evaluating the estimator both theoretically for its asymptotic properties and numerically for its practical implementations we demonstrate that the qml estimator is consistent to the icm and is asymptotically normally distributed efficiency gain of the qml approach is theoretically quantified and numerically demonstrated via extensive simulation studies an application of the qml approach is illustrated through analyzing a high frequency financial trading data set

estimating covariation epps effect microstructure noise abstract this paper is about how to estimate the integrated covariance x y t of two assets over a fixed time horizon 0 t when the observations of x and y are contaminated and when such noisy observations are at discrete but not synchronized times we show that the usual previous tick covariance estimator is biased and the size of the bias is more pronounced for less liquid assets this is an analytic characterization of the epps effect we also provide the optimal sampling frequency which balances the tradeoff between the bias and various sources of stochastic error terms including nonsynchronous trading microstructure noise and time discretization finally a two scales covariance estimator is provided which simultaneously cancels to first order the epps effect and the effect of microstructure noise the gain is demonstrated in data

empirical likelihood methods with weakly dependent processes this paper studies the method of empirical likelihood in models with weakly dependent processes in such cases if the likelihood function is formulated as if the data process were independent obviously empirical likelihood fails we propose to use empirical likelihood of blocks of observations to solve this problem in a nonparametric manner this method of blockwise empirical likelihood preserves the dependence of data and the resulting likelihood ratios can be used to construct asymptotically valid confidence intervals we consider general estimating equations for which an efficient estimator is derived by maximizing blockwise empirical likelihood we also introduce blocks of blocks empirical likelihood to conduct inference for parameters of the infinite dimensional joint distribution of data the smooth function model is used for such cases we show that blockwise empirical likelihood of the smooth function model with weakly dependent processes is bartlett correctable a wide variety of problems such as time series regressions and spectral densities can be treated using our methodology

on the closure of families of fuzzy measures under eventwise aggregations the paper contains some results on eventwise aggregation of fuzzy measures from the various families of lower probabilities this investigation includes coherent lower probabilities k monotone measures belief measures etc we study sufficient and necessary conditions on aggregation operators satisfying the closure property it is necessary to guarantee that the aggregation belongs to the same family as generating measures we also propose an efficient way for constructing aggregation operators using the found unique properties of multilinear extension this representation method for fuzzy measures generalizes to the n dimensional case the well known one giving distorted probabilities

high frequency covariance estimates with noisy and asynchronous financial data this article proposes a consistent and efficient estimator of the high frequency covariance quadratic covariation of two arbitrary assets observed asynchronously with market microstructure noise this estimator is built on the marriage of the quasi maximum likelihood estimator of the quadratic variation and the proposed generalized synchronization scheme and thus is not influenced by the epps effect moreover the estimation procedure is free of tuning parameters or bandwidths and is readily implementable monte carlo simulations show the advantage of this estimator by comparing it with a variety of estimators with specific synchronization methods the empirical studies of six foreign exchange future contracts illustrate the time varying correlations of the currencies during the 2008 global financial crisis demonstrating the similarities and differences in their roles as key currencies in the global market

market microstructure noise integrated variance estimators and the accuracy of asymptotic approximations a growing literature has been advocating consistent kernel estimation of integrated variance in the presence of financial market microstructure noise we find that for realistic sample sizes encountered in practice the asymptotic results derived for the proposed estimators may provide unsatisfactory representations of their finite sample properties in addition the existing asymptotic results might not offer sufficient guidance for practical implementations we show how to optimize the finite sample properties of kernel based integrated variance estimators empirically we find that their suboptimal implementation can in some cases lead to little or no finite sample gains when compared to the classical realized variance estimator significant statistical and economic gains can however be recovered by using our proposed finite sample methods

improved razumikhin type theorem for input to state stability of nonlinear time delay systems this note describes a lyapunov razumikhin function with an indefinite derivative that can be used to determine the input to state stability iss of a nonlinear time delay system first an extended comparison principle for estimating the solution of a differential inequality with an upper bound that is not semi negative definite is presented then that principle and a lyapunov razumikhin function with an indefinite derivative are employed to derive an iss criterion finally two examples show the effectiveness of our method and its superiority over others

finite time stabilization of delayed memristive neural networks discontinuous state feedback and adaptive control approach in this paper a general class of delayed memristive neural networks dmnns system described by functional differential equation with discontinuous right hand side is considered under the extended filippov framework we investigate the finite time stabilization problem for dmnns by using the famous finite time stability theorem and the generalized lyapunov functional method to do so we design two classes of novel controllers including discontinuous state feedback controller and discontinuous adaptive controller without assuming the boundedness and monotonicity of the activation functions several sufficient conditions are given to stabilize the states of this class of dmnns in finite time moreover the upper bounds of the settling time for stabilization are estimated finally numerical examples are provided to demonstrate the effectiveness of the developed method and the theoretical results

a tale of two time scales it is a common practice in finance to estimate volatility from the sum of frequently sampled squared returns however market microstructure poses challenges to this estimation approach as evidenced by recent empirical studies in finance the present work attempts to lay out theoretical grounds that reconcile continuous time modeling and discrete time samples we propose an estimation approach that takes advantage of the rich sources in tick by tick data while preserving the continuous time assumption on the underlying returns under our framework it becomes clear why and where the usual volatility estimator fails when the returns are sampled at the highest frequencies if the noise is asymptotically small our work provides a way of finding the optimal sampling frequency a better approach the two scales estimator works for any size of the noise

robust analysis of semiparametric renewal process models a rate model is proposed for a modulated renewal process comprising a single long sequence where the covariate process may not capture the dependencies in the sequence as in standard intensity models we consider partial likelihood based inferences under a semiparametric multiplicative rate model which has been widely studied in the context of independent and identical data under an intensity model gap times in a single long sequence may be used naively in the partial likelihood with variance estimation utilizing the observed information matrix under a rate model the gap times cannot be treated as independent and studying the partial likelihood is much more challenging we employ a mixing condition in the application of limit theory for stationary sequences to obtain consistency and asymptotic normality the estimator s variance is quite complicated owing to the unknown gap times dependence structure we adapt block bootstrapping and cluster variance estimators to the partial likelihood simulation studies and an analysis of a semiparametric extension of a popular model for neural spike train data demonstrate the practical utility of the rate approach in comparison with the intensity approach

the stationary bootstrap abstract this article introduces a resampling procedure called the stationary bootstrap as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on weakly dependent stationary observations previously a technique based on resampling blocks of consecutive observations was introduced to construct confidence intervals for a parameter of the m dimensional joint distribution of m consecutive observations where m is fixed this procedure has been generalized by constructing a blocks of blocks resampling scheme that yields asymptotically valid procedures even for a multivariate parameter of the whole i e infinite dimensional joint distribution of the stationary sequence of observations these methods share the construction of resampling blocks of observations to form a pseudo time series so that the statistic of interest may be recalculated based on the resampled data set but in the context of applying this method to stationary data it is natural

the moving blocks bootstrap and robust inference for linear least squares and quantile regressions abstract this paper presents the moving blocks bootstrap mbb as a new inference procedure for linear regression estimation which is robust to heteroskedasticity and autocorrelation of unknown forms the mbb covariance estimator is shown to provide heteroskedasticity and autocorrelation consistent hac standard errors for least squares ls and quantile regression qr coefficient estimators the mbb covariance estimator is shown to be asymptotically equivalent to the bartlett kernel estimator suggested by newey and west 1987 and the asymptotically optimal choice of the blocksize is discussed a monte carlo study is included showing that the mbb fares well in comparison to standard hac inference procedures considering strong mixing data generating processes the paper extends existing asymptotic results for the qr estimator the analogy to the ls case is stressed the paper analyzes both the cases of stochastic and of nonstochastic regressors and suggests two new grenander like conditions for the latter case the use of the mbb approach is illustrated for a practical example using a standard econometric package

testing for common arrivals of jumps for discretely observed multidimensional processes we consider a bivariate process xt x 1 t x 2 t which is observed on a flnite time interval 0 t at discrete times 0 n 2 n assuming that its two components x 1 and x 2 have jumps on 0 t we derive tests to decide whether they have at least one jump occurring at the same time common jumps or not disjoint jumps there are two difierent tests for the two possible null hypotheses common jumps or disjoint jumps those tests have a prescribed asymptotic level as the mesh n goes to 0 we show on some simulations that these tests perform reasonably well even in the flnite sample case and we also put them in use for some exchange rates data

bootstrap procedures under some non i i d models it is shown in this article that the classical i i d bootstrap remains a valid procedure for estimating the sampling distributions of certain symmetric estimators of location as long as the random observations are independently drawn from distributions with essentially a common location this may be viewed as a robust property of the classical i i d bootstrap also included is a study of the second order properties of a different bootstrap procedure proposed by wu in the context of heteroscedasticity in regression

tapered block bootstrap summary we introduce and study tapered block bootstrap methodology that yields an improvement over the well known block bootstrap for time series of kiinsch 1989 the asymptotic validity and the favourable bias properties of the tapered block bootstrap are shown the important practical issues of optimally choosing the window shape and the block size are addressed in detail while some finite sample simulations are presented validating the good performance of the tapered block bootstrap

when upper probabilities are possibility measures abstract a characteristic property is given for a pair of upper and lower probabilities induced by lower probability bounds on a finite set of events to coincide with possibility and necessity measures approximations of upper probabilities by possibility measures are discussed the problem of combining possibility distributions viewed as upper probabilities is investigated and the basic fuzzy set intersections are justified in this framework