variation and efficiency of high frequency betas abstract this paper studies the efficient estimation of betas from high frequency return data on a fixed time interval under an assumption of equal diffusive and jump betas we derive the semiparametric efficiency bound for estimating the common beta and develop an adaptive estimator that attains the efficiency bound we further propose a hausman type test for deciding whether the common beta assumption is true from the high frequency data in our empirical analysis we provide examples of stocks and time periods for which a common market beta assumption appears true and ones for which this is not the case we further quantify empirically the gains from the efficient common beta estimation developed in the paper

inference theory for volatility functional dependencies we develop inference theory for models involving possibly nonlinear transforms of the elements of the spot covariance matrix of a multivariate continuous time process observed at high frequency the framework can be used to study the relationship among the elements of the latent spot covariance matrix and processes defined on the basis of it such as systematic and idiosyncratic variances factor betas and correlations on a fixed interval of time the estimation is based on matching model implied moment conditions under the occupation measure induced by the spot covariance process we prove consistency and asymptotic mixed normality of our estimator of the random coefficients in the volatility model and further develop model specification tests we apply our inference methods to study variance and correlation risks in nine sector portfolios comprising the s p 500 index we document sector specific variance risks in addition to that of the market and time varying heterogeneous correlation risk among the market neutral components of the sector portfolio returns

the realized empirical distribution function of stochastic variance with application to goodness of fit testing abstract we propose a nonparametric estimator of the empirical distribution function edf of the latent spot variance of the log price of a financial asset we show that over a fixed time span our realized edf or redf inferred from noisy high frequency data is consistent as the mesh of the observation grid goes to zero in a double asymptotic framework with time also increasing to infinity the redf converges to the cumulative distribution function of volatility if it exists we exploit these results to construct some new goodness of fit tests for stochastic volatility models in a monte carlo study the redf is found to be accurate over the entire support of volatility this leads to goodness of fit tests that are both correctly sized and relatively powerful against common alternatives in an empirical application we recover the redf from stock market high frequency data we inspect the goodness of fit of several two parameter marginal distributions that are inherent in standard stochastic volatility models the inverse gaussian offers the best overall description of random equity variation but the fit is less than perfect this suggests an extra parameter as available in e g the generalized inverse gaussian is required to model stochastic variance

statistical analysis of a multiply twisted helix abstract a multiply twisted helix in which a one dimensional array of components is twisted producing a helix which if twisted itself produces a doubly twisted helix and so on in which there are couplings between adjacent rounds of helices was investigated using a cellular automaton and the spectral statistics of a quantum particle a useful distance between the components of the structure is measured using a cellular automaton the dynamics of which is simulated for a number of initial conditions in order to determine the degree of connectivity between the components the area of the sphere with radius r on the basis of the above distance is shown to be proportional to r2 when r is small the anderson transition was investigated based on the spectral statistics of a quantum particle in a multiply twisted helix with on site random potentials as the strength of the on site random potentials increases the anderson transition occurs both results support our conclusion that the number of dimensions is always three for every multiply twisted helix if the couplings between adjacent rounds are strong enough

anderson transition driven by running fractal dimensions in a fractal shaped structure abstract anderson transition in a fractal shaped structure is driven by running fractal dimension from two to three we analyzed the spectral statistics of a quantum particle confined in a fractal shaped structure generated using the dielectric breakdown model in three dimensions when the fractal dimension is almost three the spectral statistics of low energy states are similar to those of a gaussian orthogonal ensemble as the fractal dimension decreases to two the spectral statistics become poissonian this indicates the onset of quantum localization in the fractal shaped structure so the anderson transition takes place as the fractal dimension changes the effects of introducing random potentials are also analyzed when a random magnetic field affects quantum states extended over our fractal shaped structure the spectral statistics are similar to those of a gaussian unitary ensemble on the other hand a random on site potential encourages quantum localization in our fractal shaped structure

on estimating a density using hellinger distance and some other strange facts on s interesse ici aux possibles vitesses d estimation d une densite a support compact dans m sous des hypotheses de regularite lorsque la perte est mesuree par le carre de la distance de hellinger on regardera aussi le cas connu des normes mathbb l q pour 1 q 2 et le risque est le risque minimax sur la famille on donne une methode generale permettant de traiter les problemes dans le cadre de la theorie de l approximation sous des conditions concernant l entropie metrique et l e capacite des familles a estimer les rapports entre regularite et entropie metrique etant bien connus nous pourrons aussi traiter les cas classiques et d autres qui le sont moins sous des conditions de bornes inferieures les vitesses sont celles observees pour la norme mathbb l q mais elles different dans le cas general on montre aussi que les restrictions sur la compacite du support ou la regularite sont indispensables et que leur absence mene a l impossibilite d obtenir une estimation raisonnable en ce sens que n importe quelle suite d estimateurs sera arbitrairement mauvaise en un point au moins un resultat analogue est vrai sous des conditions de regularite

the algebra of two scales estimation and the s tsrv high frequency estimation that is robust to sampling times abstract in this paper we derive a new algebraic property of two scales estimation in high frequency data under which the effect of sampling times is canceled to high order this is a particular robustness property of the two scales construction in general irregular asynchronous or endogenous times can cause problems in estimators based on equidistant observation of trade or quote times the new algebraic property can be combined with pre averaging giving rise to the smoothed two scales realized volatility s tsrv we derive a finite sample solution to controlling edge effects and for handling irregular and endogenous observation times and asynchronously observed multivariate data in connection with this development we use the algebraic approach to define a version of the s tsrv which has particularly small edge effect in microstructure noise the main result of the paper is a representation of the statistical error of the estimator in terms of simple components as an application of this representation the paper develops a central limit theory for multivariate volatility estimators the approach can also handle leads and lags in the signal process

entropy based tests of uniformity abstract the power properties of an entropy based test are investigated when used for testing uniformity on 0 1 percentage points and power against seven alternatives are reported compared with other tests of uniformity the entropy based test possesses good power properties for many alternatives some asymptotic null and alternative distributions are derived for sample sizes up to 100 the table of percentage points provides a practical guide for using this test a theory of entropy based tests of distributional hypotheses other than uniformity is outlined

bootstrapping volatility functionals a local and nonparametric perspective summaryvolatility functionals are widely used in financial econometrics in the literature they are estimated with realized volatility functionals using high frequency data in this paper we introduce a nonparametric local bootstrap method that resamples the high frequency returns with replacement in local windows shrinking to zero while the block bootstrap in time series hall et al 1995 aims to reduce correlation the local bootstrap is intended to eliminate the heterogeneity of volatility we prove that the local bootstrap distribution of the studentized realized volatility functional is first order accurate we present edgeworth expansions of the studentized realized variance with and without local bootstrapping in the absence of the leverage effect and jumps the expansions show that the local bootstrap distribution of the studentized realized variance is second order accurate extensive simulation studies verify the theory

on the number of common factors with high frequency data summaryin this paper we introduce a local principal component analysis approach to determining the number of common factors of a continuous time factor model with time varying factor loadings using high frequency data the model is approximated locally on shrinking blocks using discrete time factor models the number of common factors is estimated by minimizing the penalized aggregated mean squared residual error over all shrinking blocks while the local mean squared residual error on each block converges at rate min n 1 4 p where n is the sample size and p is the dimension the aggregated mean squared residual error converges at rate min n 1 2 p this achieves the convergence rate of the penalized criterion function of the global principal component analysis method assuming restrictive constant factor loading an estimator of the number of factors based on the local principal component analysis is consistent simulation results justify the performance of our estimator a real financial dataset is analysed

critical helix of hierarchical structures abstract electronic structures in a hierarchical helix with inter round couplings i e a multiply twisted helix are investigated using the spectral statistics of a quantum particle the hierarchical structure is constructed using a procedure in which a helical chain of components is twisted producing a doubly twisted helix which if itself is twisted produces a triply twisted helix and so on we compare three types of inter round couplings which enable electrons to return to their original positions when the strength of inter round couplings is sufficiently smaller than that along a basal helix the type of inter round couplings can be distinguished by the behavior of spectral statistics the multiply twisted helix of inter round couplings through a single site is unique in the sense that its electronic structure is robust against any change in the basal helix so is called a critical helix

efficient estimation of integral functionals of a density bickel and ritov s estimator is a quite intricate expression based on kernel estimators of the density in this paper we propose an alternative and somehow simpler method of estimation based on orthogonal projections this

models of intermediate spectral statistics based on numerical results it is conjectured that the spectral statistics of certain pseudointegrable billiards have a special form similar to that of the anderson model at the transition point a simple theoretical model where such statistics can be obtained analytically is briefly discussed a few models with similar behavior are considered in particular we analytically found the eigenvalue statistics of a poisson distributed matrix perturbed by a rank one matrix which is a good model for spectral statistics of a singular billiard

multiple periodic solutions of a class of p laplacian by using the recent generalization of coincidence degree method the existence of multiple periodic solutions for a class of p laplacian is obtained under the existence of strict upper and lower solutions

a rank test for the number of factors with high frequency data abstract in the literature consistency of the estimates of the number of factors for large dimensional factor models had been extensively studied recently but the second order property of the estimator has long been unsolved due to lack of limiting distribution of the estimators in this paper we propose a rank test of the number of factors using large panel high frequency data contaminated with microstructure noise the rank test is realized by forming a fixed number of portfolios which reduce the dimension to a finite number in the process of constructing portfolios the number of factors is equal to the rank of the volatility matrix of the diversified portfolios asymptotically via estimating the volatility rank of a low dimensional price dynamics of the portfolios we establish a central limit theorem of the estimated factor number we then apply the asymptotic normality to testing on the number of factors numerical experiments including the monte carlo simulations and real data analysis justify our theory

estimating divergence functionals and the likelihood ratio by convex risk minimization we develop and analyze m estimation methods for divergence functionals and the likelihood ratios of two probability distributions our method is based on a nonasymptotic variational characterization of f divergences which allows the problem of estimating divergences to be tackled via convex empirical risk optimization the resulting estimators are simple to implement requiring only the solution of standard convex programs we present an analysis of consistency and convergence for these estimators given conditions only on the ratios of densities we show that our estimators can achieve optimal minimax rates for the likelihood ratio and the divergence functionals in certain regimes we derive an efficient optimization algorithm for computing our estimates and illustrate their convergence behavior and practical viability by simulations

estimation of integral functionals of a density let be a smooth function of k 2 variables we shall investigate in this paper the rates of convergence of estimators of t f f f x f x f k x x dx when f belongs to some class of densities of smoothness s we prove that when 2k 1 4 one can define an estimator t n of t f based on n i i d observations of density f on the real line which converges at the semiparametric rate 1 n on the other hand when s 2k 1 4 t f cannot be estimated at a rate faster than n with 4 s k 4s 1 we shall also provide some extensions to the multidimensional case those results extend previous works of levit of bickel and ritov and of donoho and nussbaum on estimation of quadratic functionals

generalized method of integrated moments for high frequency data we propose a semiparametric two step inference procedure for a finite dimensional parameter based on moment conditions constructed from high frequency data the population moment conditions take the form of temporally integrated functionals of state variable processes that include the latent stochastic volatility process of an asset in the first step we nonparametrically recover the volatility path from high frequency asset returns the nonparametric volatility estimator is then used to form sample moment functions in the second step gmm estimation which requires the correction of a high order nonlinearity bias from the first step we show that the proposed estimator is consistent and asymptotically mixed gaussian and propose a consistent estimator for the conditional asymptotic variance we also construct a bierens type consistent specification test these infill asymptotic results are based on a novel empirical process type theory for general integrated functionals of noisy semimartingale processes

volatility regressions with fat tails abstract nowadays a common method to forecast integrated variance is to use the fitted value of a simple ols autoregression of the realized variance however non parametric estimates of the tail index of this realized variance process reveal that its second moment is possibly unbounded in this case the behavior of the ols estimators and the corresponding statistics are unclear we prove that when the second moment of the spot variance is unbounded the slope of the spot variance s autoregression converges to a random variable as the sample size diverges the same result holds when one uses the integrated or realized variance instead of the spot variance we then consider the class of diffusion variance models with an affine drift a class which includes garch and cev processes and we prove that iv estimation with adequate instruments provide consistent estimators of the drift parameters as long as the variance process has a finite first moment regardless of the existence of the second moment in particular for the garch diffusion model with fat tails an iv estimation where the instrument equals the sign of the centered lagged value of the variable of interest provides consistent estimators simulation results corroborate the theoretical findings of the paper

monotone method for second order periodic boundary value problems in recent years there has been an extensive study of the existence of periodic solutions l s 11 14 151 in 8 111 the existence of solutions of first and second order pbvp period boundary value problems has been obtained by a novel approach of combining the classical method of lower and upper solutions and the method of alternative problems lyapunovschmidt method which provide conditions that are easily verifiable and which covers previous known results of other authors as a constructive method for obtaining extremal solutions of initial and boundary value problems the monotone iterative procedure has been employed by several researchers 5 7 11 13 151 the objective of this paper is to employ this useful technique for second order pbvp to obtain the minimal and maximal solutions as limits of monotone iterates our method can be used to study semilinear parabolic initial boundary value problems and other problems at resonance

multiple nontrivial solutions for nonlinear periodic problems with the p laplacian abstract we consider a nonlinear periodic problem driven by the scalar p laplacian with a nonsmooth potential hemivariational inequality using the degree theory for multivalued perturbations of s operators and the spectrum of a class of weighted eigenvalue problems for the scalar p laplacian we prove the existence of at least three distinct nontrivial solutions two of which have constant sign

on the existence of harmonic solutions of lie nard systems we discuss the existence of harmonic solutions of lienard systems of the form x d dtgradf x gradg x p t where f c 2 r n r g c 1 r n r p c 0 r r n and p t t p t for a constant t 0

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

nonparametric estimators which can be plugged in we consider nonparametric estimation of an object such as a probability density or a regression function can such an estimator achieve the ratewise minimax rate of convergence on suitable function spaces while at the same time when plugged in estimate efficiently at a rate of n 1 2 with the best constant many functionals of the object for example can we have a density estimator whose definite integrals are efficient estimators of the cumulative distribution function we show that this is impossible for very large sets for example expectations of all functions bounded by m however we also show that it is possible for sets as large as indicators of all quadrants that is distribution functions we give appropriate constructions of such estimates

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

anderson transition in fractal based complexes abstract we investigated the anderson transition in fractal based complexes which were generated using the dielectric breakdown model when parameter in the model was changed from 1 to 2 at time 1 during the growth when 1 2 our nerve cell like complex can be considered a dendritic fractal grown on a somatic fractal on the other hand when 1 2 our nebula like complex cannot be divided into two regions the spectral statistics of a quantum particle in these fractal based complexes were analyzed and the result indicates the existence of an anderson transition an extended electron showing quantum chaos becomes localized when 1 decreases in a nerve cell like complex and when 1 increases in a nebula like complex it is shown that these two types of fractal based complexes can be distinguished by the type of anderson transition the features of which are characterized based on the berry robnik distribution

principal component analysis of high frequency data we develop the necessary methodology to conduct principal component analysis at high frequency we construct estimators of realized eigenvalues eigenvectors and principal components and provide

efficient asymptotic variance reduction when estimating volatility in high frequency data abstract this paper shows how to carry out efficient asymptotic variance reduction when estimating volatility in the presence of stochastic volatility and microstructure noise with the realized kernels rk from barndorff nielsen et al 2008 and the quasi maximum likelihood estimator qmle studied in xiu 2010 to obtain such a reduction we chop the data into b blocks compute the rk or qmle on each block and aggregate the block estimates the ratio of asymptotic variance over the bound of asymptotic efficiency converges as b increases to the ratio in the parametric version of the problem i e 1 0025 in the case of the fastest rk tukey hanning 16 and 1 for the qmle the impact of stochastic sampling times and jump in the price process is examined carefully the finite sample performance of both estimators is investigated in simulations while empirical work illustrates the gain in practice

statistical inferences for price staleness abstract this paper proposes a nonparametric theory for statistical inferences on zero returns of high frequency asset prices using an infill asymptotic design we derive limit theorems for the percentage of zero returns observed on a finite time interval and for other related quantities within this framework we develop two nonparametric tests first we test whether intra day zero returns are independent and identically distributed second we test whether intra day variation of the likelihood of occurrence of zero returns can be solely explained by a deterministic diurnal pattern in an empirical application to ten representative stocks of the nyse we provide evidence that the null of independent and identically distributed intra day zero returns can be conclusively rejected we further find that a deterministic diurnal pattern is not sufficient to explain the intra day variability of the distribution of zero returns

an extension of mawhin s continuation theorem and its application to boundary value problems with a p laplacain abstract in order to study boundary value problems bvps with a p laplacian an extension of mawhin s continuation theorem is given then some existence theorems for bvps with a p laplacian at resonance are proved

adaptive estimation of continuous time regression models using high frequency data abstract we derive the asymptotic efficiency bound for regular estimates of the slope coefficient in a linear continuous time regression model for the continuous martingale parts of two ito semimartingales observed on a fixed time interval with asymptotically shrinking mesh of the observation grid we further construct an estimator from high frequency data that achieves this efficiency bound and indeed is adaptive to the presence of infinite dimensional nuisance components the estimator is formed by taking optimal weighted average of local nonparametric volatility estimates that are constructed over blocks of high frequency observations the asymptotic efficiency bound is derived under a markov assumption for the bivariate process while the high frequency estimator and its asymptotic properties are derived in a general ito semimartingale setting to study the asymptotic behavior of the proposed estimator we introduce a general spatial localization procedure which extends known results on the estimation of integrated volatility functionals to more general classes of functions of volatility empirically relevant numerical examples illustrate that the proposed efficient estimator provides nontrivial improvement over alternatives in the extant literature

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

mixed scale jump regressions with bootstrap inference abstract we develop an efficient mixed scale estimator for jump regressions using high frequency asset returns a fine time scale is used to accurately identify the locations of large rare jumps in the explanatory variables such as the price of the market portfolio a coarse scale is then used in the estimation in order to attenuate the effect of trading frictions in the dependent variable such as the prices of potentially less liquid assets the proposed estimator has a non standard asymptotic distribution that cannot be made asymptotically pivotal via studentization we propose a novel bootstrap procedure for feasible inference and justify its asymptotic validity we show that the bootstrap provides an automatic higher order asymptotic approximation by accounting for the sampling variation in estimates of nuisance quantities that are used in efficient estimation the monte carlo analysis indicates good finite sample performance of the general specification test and confidence intervals based on the bootstrap we apply the method to a high frequency panel of dow stock prices together with the market index defined by the s p 500 index futures over the period 2007 2014 we document remarkable temporal stability in the way that stocks react to market jumps however this relationship for many of the stocks in the sample is significantly noisier and more unstable during sector specific jump events

nonparametric estimation of jump diffusion models abstract this paper develops the asymptotics for nonparametric kernel estimators of local time drift and volatilities and levy measure in jump diffusion models our asymptotics are developed in a very general set up allowing the sample span to increase as the sampling interval decreases and without assuming stationarity for drift and volatilities we analyze both local constant and local linear estimators we consider not only estimators for instantaneous conditional second moment but also threshold estimators to disentangle diffusive and jump volatilities the optimal bandwidths are provided for all these estimators

nonlinear resonant periodic problems with concave terms abstract we consider a nonlinear periodic problem driven by the scalar p laplacian with a concave term and a caratheodory perturbation we assume that this perturbation f t x is p 1 linear at and resonance can occur with respect to an eigenvalue m 1 m 2 of the negative periodic scalar p laplacian using a combination of variational techniques based on the critical point theory with morse theory we establish the existence of at least three nontrivial solutions useful in our considerations is an alternative minimax characterization of 1 0 the first nonzero eigenvalue that we prove in this work

geometrizing rates of convergence ii consider estimating a functional t f of an unknown distribution f in mathbf f from data x 1 cdots x n i i d f let omega varepsilon denote the modulus of continuity of the functional t over mathbf f computed with respect to hellinger distance for well behaved loss functions l t we show that inf t n sup mathbf f e fl t n t f is equivalent to l omega n 1 2 to within constants whenever t is linear and mathbf f is convex the same conclusion holds in three nonlinear cases estimating the rate of decay of a density estimating the mode and robust nonparametric regression we study the difficulty of testing between the composite infinite dimensional hypotheses h 0 t f leq t and h 1 t f geq t delta our results hold in the cases studied because the difficulty of the full infinite dimensional composite testing problem is comparable to the difficulty of the hardest simple two point testing subproblem

existence of multiple solutions for second order boundary value problems we give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y f x y y 0 x epsilon 0 1 y 0 0 y 1 in the special case f x y y f y greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions we give an example showing this latter result is sharp our results extend those of avery and of lakshmikantham et al

the method of lower and upper solutions for second third fourth and higher order boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u n t t u t u i a u i b i r i 0 n 1 where is a caratheodory function we obtain necessary and sufficient conditions in to guarantee the existence of solutions between a lower solution and an upper solution for n 2 if n 3 either or and n 4 if furthermore we obtain sufficient conditions in for n 2 k 6 when