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

finite dimensional approximation in infinite dimensional mathematical programming we consider the problem of approximating an optimal solution to a separable doubly infinite mathematical program p with lower staircase structure by solutions to the programs p n obtained by truncating after the first n variables and n constraints of p viewing the surplus vector variable associated with the nth constraint as a state and assuming that all feasible states are eventually reachable from any feasible state we show that the efficient set of all solutions optimal to all possible feasible surplus states for p n converges to the set of optimal solutions to p a tie breaking algorithm which selects a nearest point efficient solution for p n is shown for convex programs to converge to an optimal solution to p a stopping rule is provided for discovering a value of n sufficiently large to guarantee any prespecified level of accuracy the theory is illustrated by an application to production planning

infinite horizon optimization we consider the general problem of choosing a discounted cost minimizing infinite sequence of decisions from a closed subset of the product space formed by a sequence of arbitrary compact metric spaces examples include equipment replacement production planning and more generally infinite stage mathematical programs it is shown that the optimal costs for finite horizon approximating problems converge to the optimal infinite horizon cost as the horizons diverge to infinity moreover the existence of a unique algorithmically optimal i e accumulation point solution is shown to be a necessary and sufficient condition for convergence in the product topology i e policy convergence of all finite horizon optima under the weaker condition of hausdorff convergence of the sets of finite horizon optima to the set of infinite horizon optima we show how to force policy convergence through a natural tie breaking rule finally a forward algorithm is presented which in the presence of a unique infinite horizon optimum is guaranteed to converge

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

pull backs of algebras and crossed products by certain diagonal actions let g be a locally compact group and p q t a principal g bundle if a is a c algebra with primitive ideal space t the pull back p a of a along p is the balanced tensor product co q c t a if 3 g aut a consists of c t module automorphisms and y g aut co q is the natural action then the automorphism group y 0x 3 of co q 0 a respects the balancing and induces the diagonal action p 3 of g on p a we discuss some examples of such actions and study the crossed product p a x p g we suggest a substitute d for the fixed point algebra prove p a x g is strongly morita equivalent to d and investigate the structure of d in various cases in particular we ask when d is strongly morita equivalent to a sometimes but by no means always and investigate the case where a has continuous trace let b be a c algebra and g a locally compact group acting on b as a strongly continuous automorphism group a our goal here is to study the crossed product c algebra b x g for two classes of diagonal actions for which the induced action of g on b is free the first class includes actions of the form y 0x3 on b co q 0 a where p q t is a principal g bundle y is the dual action of g on co q and 3 g aut a is an action of g on another c algebra a we also consider diagonal actions on algebras which are the pull backs of another algebra a along a principal bundle p q t if a is a c algebra with primitive ideal space t then the pull back p a is the balanced tensor product co q cb t a when 3 g aut a consists of c t module automorphisms the product action ty 0 3 preserves the balancing and the diagonal action p 3 is by definition the induced action on p a in general if f x y and q prima y are continuous then cb y acts on co x by composition with f and on a by composition with q and the daunshofmann theorem we can therefore define the pull back f a of a along f as the c algebraic tensor product co x cb y a the reason for the name is that when a is the algebra of sections of some c bundle e over y there is a natural isomorphism of f a onto the algebra of sections of the pull back f e in 1 we discuss this and other basic properties of pull backs and give some evidence to show they are likely to be of interest in particular we show that if g is abelian and a g aut a is locally unitary in the sense of 18 then the crossed product received by the editors october 20 1983 and in revised form february 15 1984 1980 mathematics subject classification primary 46l40 46l55

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

discrete time pontryagin principles with infinite horizon we establish necessary conditions of optimality for problems of optimal control theory in the discrete time framework with infinite horizon our necessary conditions are in the form of pontryagin principles we treat smooth and partially nonsmooth settings without concavity a strong motivation to the study of such problems comes from dynamical macroeconomic theory and there exist also some motivations provided by physics

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

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

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

group actions on c algebras 3 cocycles and quantum field theory we study group extensions where acts on a c algebraa given a twisted covariant representation v of the paira we construct 3 cocycles on with values in the centre of the group generated byv these 3 cocycles are obstructions to the existence of an extension of byv which acts ona compatibly with the main theorems of the paper introduce a subsidiary invariant which classifies actions of onv and in terms of which a necessary and sufficient condition for the the cohomology class of the 3 cocycle to be non trivial may be formulated examples are provided which show how non trivial 3 cocycles may be realised the framework we choose to exhibit these essentially mathematical results is influenced by anomalous gauge field theories we show how to interpret our results in that setting in two ways one motivated by an algebraic approach to constrained dynamics and the other by the descent equation approach to constructing cocycles on gauge groups in order to make comparisons with the usual approach to cohomology in gauge theory we conclude with a lie algebra version of the invariant and the 3 cocycle

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

symmetry groups and non abelian cohomology we consider the implementation of symmetry groups of automorphisms of an algebra of observables in a reducible representation whose multipliers in general are non commuting operators in the commutant of the representation the multipliers obey a non abelian cocycle relation which generalizes the 2 cohomology of the group examples are given from the theory of spin algebras and continuous tensor products for typei representations we show that the multiplier can be chosen to lie in the centre giving an isomorphism with abelian theory

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

topological invariants associated with the spectrum of crossed product c algebras a separable c dynamical system a g in which a is a continuous trace c algebra and g is abelian is called n principal if n is a closed subgroup of g such that restricted to n is locally unitary and the action of g on defines a principal bundle p a g in this event it is known that the spectrum of a g is a principal n bundle q over g in this article we show that a pair p q where p x z is a principal g n bundle and q y z is principal nbundle determines a class in h4 z which vanishes if and only if there is a continuous trace c algebra a with spectrum x and a n principal system a g with p p more generally given a g and p as above we consider the question of when systems a g with p p exist

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

convex infinite horizon programs we establish conditions under which a sequence of finite horizon convex programs monotonically increases in value to the value of the infinite program a subsequence of optimal solutions converges to the optimal solution of the infinite problem if the conditions we impose fail then roughtly the optimal value of the infinite horizon problem is an improper convex function under more restrictive conditions we establish the necessary and sufficient conditions for optimality this constructive procedure gives us a way to solve the infinite long range problem by solving a finite short range problem it appears to work well in practice

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

large volatility matrix inference via combining low frequency and high frequency approaches it is increasingly important in financial economics to estimate volatilities of asset returns however most of the available methods are not directly applicable when the number of assets involved is large due to the lack of accuracy in estimating high dimensional matrices therefore it is pertinent to reduce the effective size of volatility matrices in order to produce adequate estimates and forecasts furthermore since high frequency financial data for different assets are typically not recorded at the same time points conventional dimension reduction techniques are not directly applicable to overcome those difficulties we explore a novel approach that combines high frequency volatility matrix estimation together with low frequency dynamic models the proposed methodology consists of three steps i estimate daily realized covolatility matrices directly based on high frequency data ii fit a matrix factor model to the estimated daily covolatility matrices and iii fit a vector autoregressive mo

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

shadow prices in infinite dimensional linear programming we consider the class of linear programs that can be formulated with infinitely many variables and constraints but where each constraint has only finitely many variables this class includes virtually all infinite horizon planning problems modeled as infinite stage linear programs examples include infinite horizon production planning under time varying demands and equipment replacement under technological change we provide under a regularity condition conditions that are both necessary and sufficient for strong duality to hold moreover we show that under these conditions the lagrangean function corresponding to any pair of primal and dual optimal solutions forms a linear support to the optimal value function thus extending the shadow price interpretation of an optimal dual solution to the infinite dimensional case we illustrate the theory through an application to production planning under time varying demands and costs where strong duality is established

duality gaps in semi infinite linear programming an approximation problem this paper builds upon the relationship between the objective function of a semi infinite linear program and its constraints to identify a class of semi infinite linear programs which do not have a duality gap the key idea is to guarantee the approximation of the primal program by a sequence of linear programs where thenth approximating program is to minimize the objective function subject to the firstn constraints the paper goes on to show that any program not in the identified class can be linearly perturbed into it with the optimal value of the perturbed program converging to the optimal value of the original program the results are then extended to the case when an uncountable number of constraints are present by reducing this case to the countable case

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

the quantum theory of second class constraints kinematics the problem of second class quantum constraints is here set up in the context ofc algebras utilizing the connection with state conditions as given by the heuristic quantization rules that is a constraint set is said to be first class if all its members can satisfy the same state condition and second class otherwise several heuristic models are examined and they all agree with this definition given then a second class constraint set we separate out its first class part as all those constraints which are compatible with the others and we propose an algebraic construction for imposition of the constraints this construction reduces to the normal one when the constraints are first class moreover the physical automorphisms assumed as conserving the constraints will also respect this construction the final physical algebra obtained is free of constraints gauge invariant unital and with the right choice simple thisc algebra also contains a factor algebra of the usual observables i e the commutator algebra of the constraints the general theory is applied to two examples the elimination of a canonical pair from a boson field theory as in the two dimensional anomalous chiral schwinger model of rajaraman 14 and the imposition of quadratic second class constraints on a linear boson field theory

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

model building techniques for the correction of end effects in multistage convex programs this paper considers model building procedures that can be used to reduce end effects in multistage planning models in particular it emphasizes some problems that are peculiar to energy planning applications the paper presents and compares four methods for mitigating end effects it concludes that one of these four methods the dual equilibrium procedure is best the major drawback of the dual equilibrium procedure is its lack of simplicity if it is to be widely used then it must be widely understood

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

three cocycle in mathematics and physics it is shown that the three cocycle arises when a representation of a transformation group is nonassociative so that the jacobi identity fails a physical setting is given when the translation group in the presence of a magnetic monopole is represented by gauge invariant operators a trivial three cocycle occurs insisting that finite translations be associative leads to dirac s monopole quantization condition attention is called to the possible relevance of three cocycles in the quark model s u 6 ensuremath bigotimes u 6 algebra

optimal sparse volatility matrix estimation for high dimensional ito processes with measurement errors stochastic processes are often used to model complex scientiflc problems in flelds ranging from biology and flnance to engineering and physical science this paper investigates rate optimal estimation of the volatility matrix of a high dimensional it o process observed with measurement errors at discrete time points the minimax rate of convergence is established for estimating sparse volatility matrices by combining the multi scale and threshold approaches we construct a volatility matrix estimator to achieve the optimal convergence rate the minimax lower bound is derived by considering a subclass of it o processes for which the minimax lower bound is obtained through a novel equivalent model of covariance matrix estimation for independent but non identically distributed observations and through a delicate construction of the least favorable parameters in addition a simulation study was conducted to test the flnite sample performance of the optimal estimator and the simulation results were found to support the established asymptotic theory

circumventing the slater conundrum in countably infinite linear programs abstract duality results on countably infinite linear programs are scarce subspaces that admit an interior point which is a sufficient condition for a zero duality gap yield a dual where the constraints cannot be expressed using the ordinary transpose of the primal constraint matrix subspaces that permit a dual with this transpose do not admit an interior point this difficulty has stumped researchers for a few decades it has recently been called the slater conundrum we find a way around this hurdle we propose a pair of primal dual spaces with three properties the series in the primal and dual objective functions converge the series defined by the rows and columns of the primal constraint matrix converge and the order of sums in a particular iterated series of a double sequence defined by the primal constraint matrix can be interchanged so that the dual is defined by the ordinary transpose weak duality and complementary slackness are then immediate instead of using interior point conditions to establish a zero duality gap we call upon the planning horizon method when the series in the primal and dual constraints are continuous we prove that strong duality holds if a sequence of optimal solutions to finite dimensional truncations of the primal and dual cilps has an accumulation point we show by counterexample that the requirement that such an accumulation point exist cannot be relaxed our results are illustrated using several examples and are applied to countable state markov decision processes and to a problem in robust optimization

a shadow simplex method for infinite linear programs we present a simplex type algorithm that is an algorithm that moves from one extreme point of the infinite dimensional feasible region to another not necessarily adjacent extreme point for solving a class of linear programs with countably infinite variables and constraints each iteration of this method can be implemented in finite time whereas the solution values converge to the optimal value as the number of iterations increases this simplex type algorithm moves to an adjacent extreme point and hence reduces to a true infinite dimensional simplex method for the important special cases of nonstationary infinite horizon deterministic and stochastic dynamic programs

duality in infinite dimensional linear programming we consider the class of linear programs with infinitely many variables and constraints having the property that every constraint contains at most finitely many variables while every variable appears in at most finitely many constraints examples include production planning and equipment replacement over an infinite horizon we form the natural dual linear programming problem and prove strong duality under a transversality condition that dual prices are asymptotically zero that is we show under this transversality condition that optimal solutions are attained in both primal and dual problems and their optimal values are equal the transversality condition and hence strong duality is established for an infinite horizon production planning problem

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

existence results and finite horizon approximates for infinite horizon optimization problems the paper deals with infinite horizon optimization problems the existence of optimal solutions is obtained as a consequence of an asymptotic growth condition we also exhibit finite horizon approximates that yield upper and lower bounds for the optimal values and whose optimal solutions converge to the long term optimal trajectories

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

on the mickelsson faddeev extension and unitary representations the mickelsson faddeev extension is a 3 space analogue of a kac moody group where the central charge is replaced by a space of functions of the gauge potential this extension is a pullback of a universal extension where the gauge potentials are replaced by operators in a schatten ideal as in non commutative differential geometry our main result is that the universal extension cannot be faithfully represented by unitary operators on a separable hilbert space we also examine potential consequences of the existence of unitary representations for the mickelsson faddeev extension

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

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

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

algebraic quantization of systems with a gauge degeneracy systems with a gauge degeneracy are characterized either by supplementary conditions or by a set of generators of gauge transformations or by a set of constraints deriving from dirac s canonical constraint method these constraints can be expressed either as conditions on the field algebra or on the states on in ac algebra framework we show that the state conditions give rise to a factor algebra of a subalgebra of the field algebra this factor algebra is free of state conditions in this formulation we show also that the algebraic conditions can be treated in the same way as the state conditions the connection between states on and states on is investigated further within this framework as is also the set of transformations which are compatible with the set of constraints it is also shown that not every set of constraints can give rise to a nontrivial system finally as an example the abstract theory is applied to the electromagnetic field and this treatment can be generalized to all systems of bosons with linear constraints the question of dynamics is not discussed

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

realizing 3 cocycles as obstructions the occurrence of a 3 cocycle in quantum mechanics or quantum field theory has been interpreted somewhat paradoxically as a breakdown of the jacobi identity the main result of this paper is that the 3 cocycle in chiral qcd arises as an obstruction which prevents the existence of a certain extension of one lie algebra by another this obstruction may be avoided by constructing a modified lie algebra extension consisting of derivations on the algebra generated by the fields however the 3 cocycle then appears when an attempt is made to implement these derivations by commutation with unbounded operators in the canonical equal time formalism assuming the existence of these unbounded operators is what leads to the violation of the jacobi identity

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