second order perturbation theory for embedded eigenvalues we study second order perturbation theory for embedded eigenvalues of an abstract class of self adjoint operators using an extension of the mourre theory under assumptions on the regularity of bound states with respect to a conjugate operator we prove upper semicontinuity of the point spectrum and establish the fermi golden rule criterion our results apply to massless pauli fierz hamiltonians for arbitrary coupling

weighted decomposition construction for perfect secret sharing schemes abstract the purpose of this paper is to present a new decomposition technique called the weighted decomposition construction for perfect secret sharing schemes with general access structures this construction is more general than previous constructions based on the weighted decomposition construction we improve the information rates in four cases out of the 18 cases of secret sharing schemes left unsolved for connected graphs on six vertices

efficiency bounds implied by multiperiod conditional moment restrictions abstract in this article we study a class of econometric models that imply a set of multiperiod conditional moment restrictions these restrictions depend on an unknown parameter vector we construct an extensive class of consistent asymptotically normal estimators of this parameter vector and calculate the greatest lower bound for the asymptotic covariance matrices of estimators in this class in so doing we extend results reported by hansen 1985 and stoica soderstrom and friedlander 1985 by allowing for more general forms of nonlinearities and temporal dependence many dynamic econometric models imply that the expectation of a function of a currently observed data vector and an unknown parameter vector conditioned on information available at some point in the past is 0 we focus on models in which the conditioning information is lagged more than one time period as in the models considered by barro 1981 dunn and singleton 1986 eichenbaum and hansen 1987 eichenbaum hansen and singleto

financial asset returns direction of change forecasting and volatility dynamics we consider three sets of phenomena that feature prominently in the financial economics literature 1 conditional mean dependence or lack thereof in asset returns 2 dependence and hence forecastability in asset return signs and 3 dependence and hence forecastability in asset return volatilities we show that they are very much interrelated and explore the relationships in detail among other things we show that 1 volatility dependence produces sign dependence so long as expected returns are nonzero so that one should expect sign dependence given the overwhelming evidence of volatility dependence 2 it is statistically possible to have sign dependence without conditional mean dependence 3 sign dependence is not likely to be found via analysis of sign autocorrelations runs tests or traditional market timing tests because of the special nonlinear nature of sign dependence so that traditional market timing tests are best viewed as tests for sign dependence arising from variation in expected returns rather than from variation in volatility or higher moments 4 sign dependence is not likely to be found in very high frequency e g daily or very low frequency e g annual returns instead it is more likely to be found at intermediate return horizons and 5 the link between volatility dependence and sign dependence remains intact in conditionally non gaussian environments for example with time varying conditional skewness and or kurtosis

temporal aggregation of garch processes the authors derive low frequency say weekly models implied by high frequency say daily arma models with symmetric garch errors they show that low frequency models exhibit conditional heteroskedasticity of the garch form as well the parameters in the conditional variance equation of the low frequency model depend upon mean variance and kurtosis parameters of the corresponding high frequency model moreover strongly consistent estimators of the parameters in the high frequency model can be derived from low frequency data the common assumption in applications that rescaled innovations are independent is disputable since it depends upon the available data frequency copyright 1993 by the econometric society

spiraling attractors and quantum dynamics for a class of long range magnetic fields abstract we consider the long time behavior of a quantum particle in a 2d magnetic field which is homogeneous of degree 1 if the field never vanishes above a certain energy the associated classical dynamical system has a globally attracting periodic orbit in a reduced phase space for that energy regime we construct a simple approximate evolution based on this attractor and prove that it completely describes the quantum dynamics of our system

scattering metrics and geodesic flow at infinity any compact manifold with boundary admits a riemann metric on its interior taking the form x 4 dx 2 x 2 h near the boundary where x is a boundary defining function and h is a smooth symmetric 2 cotensor restricting to be positive definite and hence a metric h on the boundary the scattering theory associated to the laplacian for such a scattering metric was discussed by the first author and here it is shown as conjectured that the scattering matrix is a fourier integral operator which quantizes the geodesic flow on the boundary for the metric h at time to prove this the poisson operator of the associated generalized boundary problem is constructed as a fourier integral operator associated to a singular legendre manifold

whittle estimation of egarch and other exponential volatility models abstract the strong consistency and asymptotic normality of the whittle estimate of the parameters in a class of exponential volatility processes are established our main focus here are the egarch model of nelson d 1991 conditional heteroscedasticity in asset pricing a new approach econometrica 59 347 370 and other one shock models such as the gjr model of glosten l jaganathan r runkle d 1993 on the relation between the expected value and the volatility of the nominal excess returns on stocks journal of finance 48 1779 1801 but two shock models such as the sv model of taylor s 1986 modelling financial time series wiley chichester uk are also comprised by our assumptions the variable of interest might not have finite fractional moment of any order and so in particular finite variance is not imposed we allow for a wide range of degrees of persistence of shocks to conditional variance allowing for both short and long memory

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

marginalization and contemporaneous aggregation in multivariate garch processes abstract we first of all show that contemporaneous aggregation of independent univariate garch processes yields a weak garch process as introduced by drost and nijman 1993 subsequently we analyze the dependence of the parameters in the aggregate on the parameters in the underlying models and show that the variance parameters after aggregation depend on the underlying variance and kurtosis parameters then we generalize the results by showing that a linear combination of variables generated by a multivariate garch process will also be weak garch finally we derive the marginal weak garch processes implied by several multivariate garch processes

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

global solutions to the eikonal equation we study structural stability of smoothness of the maximal solution to the geometric eikonal equation on rd g d 2 this is within the framework of order zero metrics g for a subclass of these metrics we show existence stability as well as precise asymptotics for derivatives of the solution these results are applicable to examples arising in schrodinger operator theory

time dependent scattering theory on manifolds abstract this is the third and the last paper in a series of papers on spectral and scattering theory for the schrodinger operator on a manifold possessing an escape function for example a manifold with asymptotically euclidean and or hyperbolic ends here we discuss the time dependent scattering theory a long range perturbation is allowed and scattering by obstacles possibly non smooth and or unbounded in a certain way is included in the theory we also resolve a conjecture by hempel post weder on cross ends transmissions between two or more ends formulated in a time dependent manner

asymptotic filtering theory for univariate arch models this paper builds on this earlier work by deriving the asymptotic distribution of the measurement error this allows us to approximate the measurement accuracy of arch conditional variance estimates and compare the efficiency achieved by different arch models we are also able to characterize the relative importance of different kinds of misspecification for example we show that misspecifying conditional means adds only trivially at least asymptotically to measurement error while other factors for example capturing the leverage effect accommodating thick tailed residuals and correctly modelling the variability of the conditional variance process are potentially much more important third we are able to characterize a class of asymptotically optimal arch conditional variance estimates

estimating stochastic volatility diffusion using conditional moments of integrated volatility we exploit the distributional information contained in high frequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions the estimator is based on the analytical solutions of the first two conditional moments for the latent integrated volatility the realization of which is effectively approximated by the sum of the squared high frequency increments of the process our simulation evidence indicates that the resulting gmm estimator is highly reliable and accurate our empirical implementation based on high frequency five minute foreign exchange returns suggests the presence of multiple latent stochastic volatility factors and possible jumps

absence of singular continuous spectrum for certain self adjoint operators we give a sufficient condition for a self adjoint operator to have the following properties in a neighborhood of a pointe of its spectrum a its point spectrum is finite b its singular continuous spectrum is empty c its resolvent satisfies a class of a priori estimates

on open scattering channels for manifolds with ends abstract in the framework of time dependent geometric scattering theory we study the existence and completeness of the wave operators for perturbations of the riemannian metric for the laplacian on a complete manifold of dimension n the smallness condition for the perturbation is expressed intrinsically and coordinate free in purely geometric terms using the harmonic radius therefore the size of the perturbation can be controlled in terms of local bounds on the injectivity radius and the ricci curvature as an application of these ideas we obtain a stability result for the scattering matrix with respect to perturbations of the riemannian metric this stability result implies that a scattering channel which interacts with other channels preserves this property under small perturbations

commutators c0 semigroups and resolvent estimates abstract we study the existence and the continuity properties of the boundary values on the real axis of the resolvent of a self adjoint operator h in the framework of the conjugate operator method initiated by mourre we allow the conjugate operator a to be the generator of a c 0 semigroup finer estimates require a to be maximal symmetric and we consider situations where the first commutator h i a is not comparable to h the applications include the spectral theory of zero mass quantum field models

a method for calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators abstract for many time series estimation problems there is an infinite dimensional class of generalized method of moments estimators that are consistent and asymptotically normal this paper suggests a procedure for calculating the greatest lower bound for the asymptotic covariance matrices of such estimators the analysis focuses on estimation problems in which the data are generated by a stochastic process that is stationary and ergodic the calculation of the bound uses martingale difference approximations as suggested by gordon 1969 and a matrix version of hilbert space methods

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

scattering theory for riemannian laplacians we introduce a notion of scattering theory for the laplace beltrami operator on non compact connected and complete riemannian manifolds a principal condition is given by a certain positive lower bound of the second fundamental form of angular submanifolds at infinity another condition is certain bounds of derivatives up to order one of the trace of this quantity these conditions are shown to be optimal for existence and completeness of a wave operator our theory does not involve prescribed asymptotic behavior of the metric at infinity like asymptotic euclidean or hyperbolic metrics studied previously in the literature a consequence of the theory is spectral theory for the laplace beltrami operator including identification of the continuous spectrum and absence of singular continuous spectrum

temporal aggregation of multivariate garch processes this paper derives results for the temporal aggregation of multivariate garch 1 1 processes in the general vector specification it is shown that the class of weak multivariate garch 1 1 processes is closed under temporal aggregation fourth moment characteristics turn out to be crucial for the low frequency dynamics for both stock and flow variables in some aspects the aggregation characteristics of multivariate garch processes are shown to be different from those of vector autoregressive moving average processes a numerical example illustrates some of the results

asymptotic completeness for n body short range quantum systems a new proof we give an alternative geometrical proof of asymptotic completeness for an arbitrary number of quantum particles interacting through shortrange pair potentials it relies on an estimate showing that the intercluster motion concentrates asymptotically on classical trajectories

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

asymptotically optimal smoothing with arch models suppose an observed time series is generated by a stochastic volatility model i e there is an unobservable state variable controlling the volatility of the innovations in the series as shown by nelson 1992 and nelson and foster 1994 a misspecified arch model will often be able to consistently as a continuous time limit is approached estimate the unobserved volatility process using information in the lagged residuals this paper shows how to more efficiently estimate such a volatility process using information in both lagged and led residuals in particular this paper expands the optimal filtering results of nelson and foster 1994 and nelson 1994 to smoothing and to filtering with a random initial condition

on the use of high frequency measures of volatility in midas regressions abstract many empirical studies link mixed data frequency variables such as low frequency macroeconomic or financial variables with high frequency financial indicators volatilities especially within a predictive regression model context the objective of this paper is threefold first we relate the standard least squares ls regression model with high frequency volatility predictors with the corresponding mixed data sampling nonlinear ls midas nls regression model ghysels et al 2005 ghysels et al 2006 and evaluate the properties of the regression estimators of these models we also consider alternative high frequency volatility measures as well as various continuous time models using their corresponding relevant higher order moments to further analyze the properties of these estimators second we derive the relative mse efficiency of the slope estimator in the standard ls and midas regressions we provide conditions for relative efficiency and present the numerical results for different continuous time models third we extend the analysis of the bias of the slope estimator in standard ls regressions with alternative realized measures of risk such as the realized covariance realized beta and the realized skewness when the true dgp is a midas model

arch models as diffusion approximations abstract this paper investigates the convergence of stochastic difference equations e g arch to stochastic differential equations as the length of the discrete time intervals between observations goes to zero these results are applied to the garch 1 1 model of bollerslev 1986 and to the ar 1 exponential arch model of nelson 1989 in their continuous time limits the conditional variance processes in these models have stationary distributions that are inverted gamma and lognormal respectively in addition a class of diffusion approximations based on the exponential arch model is developed

spectral analysis of second order elliptic operators on noncompact manifolds on demontre l estimation de mourre et les bornes qui y sont reliees pour une classe d operateurs elliptiques qui inclut des laplaciens pour des quotients cofinis et coinfinis d espaces hyperboliques

unobserved component time series models with arch disturbances abstract this paper considers how arch effects may be handled in time series models formulated in terms of unobserved components a general model is formulated but this includes as special cases a random walk plus noise model with both disturbances subject to arch effects an arch m model with a time varying parameter and a latent factor model with arch effects in the factors although the model is not conditionally gaussian an approximate filter can be obtained and used as the basis for estimation the performance of this method is examined on real data sets and monte carlo experiments are carried out the method is extended to handle garch and a latent factor model based on the t distribution

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

spectral theory of time periodic many body systems we study the spectrum of the monodromy operator for an n body quantum system in a time periodic external field with time mean equal to zero this includes ac stark and circularly polarized fields and pair potentials with a local singularity up to and including the coulomb singularity in the framework of floquet theory we prove a local commutator estimate and use it to prove a limiting absorption principle for the floquet hamiltonian as well as exponential decay estimates on non threshold eigenfunctions these two results are then used to obtain a second order perturbation theory for embedded eigenvalues the principal tool is a new extended mourre theory

radiation condition bounds on manifolds with ends abstract we study spectral theory for the schrodinger operator on manifolds possessing an escape function a particular class of examples are manifolds with euclidean and or hyperbolic ends certain exterior domains for possibly unbounded obstacles are included we prove rellich s theorem the limiting absorption principle radiation condition bounds and the sommerfeld uniqueness result striving to extending and refining previously known spectral results on manifolds the proofs are given by an extensive use of commutator arguments these arguments have a classical spirit essentially not involving energy cutoffs or microlocal analysis and require presumably minimum regularity and decay properties of perturbations this paper has interest of its own right but it also serves as a basis for the stationary scattering theory developed fully in the sequel 19

absence of embedded eigenvalues for riemannian laplacians in this paper we study absence of embedded eigenvalues for schrodinger operators on non compact connected riemannian manifolds a principal example is given by a manifold with an end possibly more than one in which geodesic coordinates are naturally defined in this case one of our geometric conditions is a positive lower bound of the second fundamental form of angular submanifolds at infinity inside the end another condition is an upper bound of the trace of this quantity while a third one is a bound of the derivatives of part of the trace some oscillatory behaviour of the trace is allowed in addition to geometric bounds we need conditions on the potential a regularity property of the domain of the schrodinger operator and the unique continuation property examples include ends endowed with asymptotic euclidean or hyperbolic metrics

non gaussian ornstein uhlenbeck based models and some of their uses in financial economics non gaussian processes of ornstein uhlenbeck ou type offer the possibility of capturing important distributional deviations from gaussianity and for flexible modelling of dependence structures this paper develops this potential drawing on and extending powerful results from probability theory for applications in statistical analysis their power is illustrated by a sustained application of ou processes within the context of finance and econometrics we construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive ou processes and we study these models in relation to financial data and theory

closing the garch gap continuous time garch modeling abstract it is the purpose of this paper to build a bridge between continuous time models which are central in the modern finance literature and weak garch processes in discrete time which often provide parsimonious descriptions of the observed data the properties of continuous time processes which exhibit garch type behavior at all discrete frequencies will be discussed several examples of such processes illustrate the general theory the class of continuous time garch models can be divided into two subclasses in the first group garch diffusions the sample paths are smooth and in the other group garch jump diffusions the sample paths are erratic a simple complete characterization of both types is given in terms of the kurtosis of the observed discrete time data these two groups of garch processes can be described by three and four coefficients respectively explicit formulas of all implied discrete time weak garch parameters are available moreover knowledge of the discrete time garch parameters at only one frequency completely determines the continuous time coefficients of the garch process so in estimating a continuous time garch process it suffices to estimate the discrete time garch parameters for the available data frequency the analysis carries over to models with an autoregressive component

scattering theory for the laplacian on symmetric spaces of noncompact type and its application to a conjecture of strichartz abstract in this paper we develop the scattering theory for the laplacian on symmetric spaces of noncompact type we study the asymptotic properties of the resolvent in the framework of the agmon hormander space our approach is based on a detailed analysis of the helgason fourier transform and generalized spherical functions on symmetric spaces of noncompact type as an application of our scattering theory we prove a conjecture by strichartz concerning a characterization of a family of generalized eigenfunctions of the laplacian

estimation of continuous time markov processes sampled at random time intervals we introduce a family of generalized method of moments estimators of the parameters of a continuous time markov process observed at random time intervals the results include strong consistency asymptotic normality and a characterization of standard errors sampling is at an arrival intensity that is allowed to depend on the underlying markov process and on the parameter vector to be estimated we focus on financial applications including tick based sampling allowing for jump diffusions regime switching diffusions and reflected diffusions

temporal aggregation of volatility models in this paper we consider temporal aggregation of volatility models we introduce semiparametric volatility models termed square root stochastic autoregressive volatility sr sarv which are characterized by autoregressive dynamics of the stochastic variance our class encompasses the usual garch models and various asymmetric garch models moreover our stochastic volatility models are characterized by multiperiod conditional moment restrictions in terms of observables the sr sarv class is a natural extension of the class of weak garch models this extension has four advantages i we do not assume that fourth moments are finite ii we allow for asymmetries skewness leverage effect that are excluded from weak garch models iii we derive conditional moment restrictions and iv our framework allows us to study temporal aggregation of igarch models

the sample autocorrelations of heavy tailed processes with applications to arch we study the sample acvf and acf of a general stationary sequence under a weak mixing condition and in the case that the marginal distributions are regularly varying this includes linear and bilinear processes with regularly varying noise and arch processes their squares and absolute values we show that the distributional limits of the sample acf can be random provided that the variance of the marginal distribution is infinite and the process is nonlinear this is in contrast to infinite variance linear processes if the process has a finite second but infinite fourth moment then the sample acp is consistent with scaling rates that grow at a slower rate than the standard root n consequently asymptotic confidence bands are wider than those constructed in the classical theory we demonstrate the theory in full detail far an arch 1 process

spectral methods for identifying scalar diffusions this paper shows how to identify nonparametrically scalar stationary diffusions from discrete time data the local evolution of the diffusion is characterized by a drift and diffusion coefficient along with the specification of boundary behavior we recover this local evolution from two objects that can be inferred directly from discrete time data the stationary density and a conveniently chosen eigenvalue eigenfunction pair of the conditional expectation operator over a unit interval of time this construction also lends itself to a spectral characterization of the over identifying restrictions implied by a scalar diffusion model of a discrete time markov process

indirect estimation of large conditionally heteroskedastic factor models with an application to the dow 30 stocks we derive indirect estimators of conditionally heteroskedastic factor models in which the volatilities of common and idiosyncratic factors depend on their past unobserved values by calibrating the score of a kalman filter approximation with inequality constraints on the auxiliary model parameters we also propose alternative indirect estimators for large scale models and explain how to apply our procedures to many other dynamic latent variable models we analyse the small sample behaviour of our indirect estimators and several likelihood based procedures through an extensive monte carlo experiment with empirically realistic designs finally we apply our procedures to weekly returns on the dow 30 stocks