forecasting multiple time series with one sided dynamic principal components abstractwe define one sided dynamic principal components odpc for time series as linear combinations of the present and past values of the series that minimize the reconstruction mean squared err

a transference principle for general groups and functional calculus on umd spaces let ia be the generator of a c 0 group u s s is an element of r on a banach space x and omega theta u the group type of u we prove a transference principle that allows to estimate parallel to f a parallel to in terms of the l p r x fourier multiplier norm of f i omega if x is a hilbert space this yields new proofs of important results of mcintosh and boyadzhiev de laubenfels if x is a umd space one obtains a bounded h 1 infinity calculus of a on horizontal strips related results for sectorial and parabola type operators follow finally it is proved that each generator of a cosine function on a umd space has bounded h infinity calculus on sectors

analytic solutions for a stefan problem with gibbs thomson correction we provide existence of a unique smooth solution for a class of oneand two phase stefan problems with gibbs thomson correction in arbitrary space dimensions in addition it is shown that the moving interface depends analytically on the temporal and spatial variables of crucial importance for the analysis is the property of maximal lpregularity for the linearized problem which is fully developed in this paper as well

determining the number of factors in the general dynamic factor model this article develops an information criterion for determining the number q of common shocks in the general dynamic factor model developed by forni et al as opposed to the restricted dynamic model considered by bai and ng and by amengual and watson our criterion is based on the fact that this number q is also the number of diverging eigenvalues of the spectral density matrix of the observations as the number n of series goes to infinity we provide sufficient conditions for consistency of the criterion for large n and t where t is the series length we show how the method can be implemented and provide simulations and empirics illustrating its very good finite sample performance application to real data adds a new empirical facet to an ongoing debate on the number of factors driving the u s economy

the generalized dynamic factor model consistency and rates abstract a factor model generalizing those proposed by geweke in d j aigner and a s goldberger latent variables in socio economic models north holland amsterdam 1977 sargent and sims new methods in business research federal reserve bank of minneapolis minneapolis 1977 engle and watson j amer statist assoc 76 1981 774 and stock and watson j business econom statist 20 2002 147 has been introduced in forni et al rev econ statist 80 2000 540 where consistent as the number n of series and the number t of observations both tend to infinity along appropriate paths n t n estimation methods for the common component are proposed rates of convergence associated with these methods are obtained here as functions of the paths n t n along which n and t go to infinity these results show that under suitable assumptions consistency requires t n to be at least of the same order as n whereas an optimal rate of n is reached for t n of the order of n2 if convergence to the space of common components is considered consistency holds irrespective of the path t n thus can be arbitrarily slow the optimal rate is still n but only requires t n to be of the order of n

generalized dynamic factor models and volatilities consistency rates and prediction intervals abstract volatilities in high dimensional panels of economic time series with a dynamic factor structure on the levels or returns typically also admit a dynamic factor decomposition we consider a two stage dynamic factor model method recovering the common and idiosyncratic components of both levels and log volatilities specifically in a first estimation step we extract the common and idiosyncratic shocks for the levels from which a log volatility proxy is computed in a second step we estimate a dynamic factor model which is equivalent to a multiplicative factor structure for volatilities for the log volatility panel by exploiting this two stage factor approach we build one step ahead conditional prediction intervals for large n t panels of returns those intervals are based on empirical quantiles not on conditional variances they can be either equal or unequal tailed we provide uniform consistency and consistency rates results for the proposed estimators as both n and t tend to infinity we study the finite sample properties of our estimators by means of monte carlo simulations finally we apply our methodology to a panel of asset returns belonging to the s p100 index in order to compute one step ahead conditional prediction intervals for the period 2006 2013 a comparison with the componentwise garch benchmark which does not take advantage of cross sectional information demonstrates the superiority of our approach which is genuinely multivariate and high dimensional nonparametric and model free

maximal regularity of the stokes operator in an exterior domain with moving boundary and application to the navier stokes equations consider the navier stokes system on an exterior domain with moving boundary and dirichlet boundary conditions in 2003 saal proved that the stokes operator in a domain with moving boundary has the property of maximal regularity provided that the operator is invertible hence his result can be applied if the domain is bounded or by adding a shift to the stokes operator if the domain is unbounded or the time interval is finite in this paper we will generalize his result to a result global in time if the reference domain is an exterior domain finally we will apply this result to the navier stokes equations to obtain a global in time existence theorem for small data

forecasting using principal components from a large number of predictors this article considers forecasting a single time series when there are many predictors n and time series observations t when the data follow an approximate factor model the predictors can be summarized by a small number of indexes which we estimate using principal components feasible forecasts are shown to be asymptotically efficient in the sense that the difference between the feasible forecasts and the infeasible forecasts constructed using the actual values of the factors converges in probability to 0 as both n and t grow large the estimated factors are shown to be consistent even in the presence of time variation in the factor model

completely positive measures and feller semigroups on donne d abord une approche unifiee aux mesures completement positives qui jouent un role important dans la theorie des equations de volterra a travers le theoreme de bernstein puis on etudie la solution d une equation de transport liee par une mesure non negative qu elle definit a l equation qui caracterise les noyaux completement positifs on obtient une desorption complete des generateurs de semigroupes de feller induits par de telles mesures on donne une application aux equations de flux thermique lineaire dans des materiaux avec memoire

a theorem of the dore venni type for noncommuting operators a theorem of the dore venni type for the sum of two closed linear operators is proved where the operators are noncommuting but instead satisfy a certain commutator condition this result is then applied to obtain optimal regularity results for parabolic evolution equations u t l t u t f t and evolutionary integral equations u t t 0 a t s l s u s ds g t which are nonautonomous the domains of the involved operators l t may depend on t but l t 1 is required to satisfy a certain smoothness property the results are then applied to parabolic partial differential and integro differential equations

global smooth solutions for a class of parabolic integrodifferential equations the existence and uniqueness of smooth global large data solutions of a class of quasilinear partial integrodifferential equations in one space and one time dimension are proved if the integral kernel behaves like t near t 0 o with a 2 3 an existence and regularity theorem for linear equations with variable coefficients that are related to this type is also proved in arbitrary space dimensions and with no restrictions for o

pointwise convergence for semigroups in vector valued l p spaces suppose that tt t 0 is a symmetric diffusion semigroup on l2 x and denote by widetilde t t t geq0 its tensor product extension to the bochner space l p x mathcal b where mathcal b belongs to a certain broad class of umd spaces we prove a vector valued version of the hopf dunford schwartz ergodic theorem and show that this extends to a maximal theorem for analytic continuations of widetilde t t t geq 0 on l p x mathcal b as an application we show that such continuations exhibit pointwise convergence

some results about complex powers of closed operators the aim of this paper is to give some further results about complex powers of operators a tool that the authors already employed in 2 and s to study some questions of operator theory our first result is essentially a completion of corollary 2 9 of 2 since it gives an estimate for the rate of decrease of a a at infinity when a is a positive operator with bounded imaginary powers we remark that the converse question i e the estimate of the imaginary powers in terms of the amplitude of the spectrum remains open next we prove a result of pertubation if we add to a positive operator

nonlinear system theory another look at dependence based on the nonlinear system theory we introduce previously undescribed dependence measures for stationary causal processes our physical and predictive dependence measures quantify the degree of dependence of outputs on inputs in physical systems the proposed dependence measures provide a natural framework for a limit theory for stationary processes in particular under conditions with quite simple forms we present limit theorems for partial sums empirical processes and kernel density estimates the conditions are mild and easily verifiable because they are directly related to the data generating mechanisms

effects of nonlocal stress on the determination of shear banding flow we analyze the steady planar shear flow of the modified johnson segalman model which has an added nonlocal term we find that the new term allows for unambiguous selection of the stress at which two phases coexist in contrast to the original model for general differential constitutive models we show the singular nature of stress selection in terms of a saddle connection between fixed points in the equivalent dynamical system the result means that stress selection is unique under most conditions for space nonlocal models finally illustrated by simple models we show that stress selection generally depends on the form of the nonlocal terms weak universality

dynamic factor models with infinite dimensional factor space asymptotic analysis abstract factor models all particular cases of the generalized dynamic factor model gdfm introduced in forni et al 2000 have become extremely popular in the theory and practice of large panels of time series data the asymptotic properties consistency and rates of the corresponding estimators have been studied in forni et al 2004 those estimators however rely on brillinger s concept of dynamic principal components and thus involve two sided filters which leads to rather poor forecasting performances no such problem arises with estimators based on standard static principal components which have been dominant in this literature on the other hand the consistency of those static estimators requires the assumption that the space spanned by the factors has finite dimension which severely restricts their generality prohibiting for instance autoregressive factor loadings this paper derives the asymptotic properties of a semiparametric estimator of the loadings and common shocks based on one sided filters recently proposed by forni et al 2015 consistency and exact rates of convergence are obtained for this estimator under a general class of gdfms that does not require a finite dimensional factor space a monte carlo experiment and an empirical exercise on us macroeconomic data corroborate those theoretical results and demonstrate the excellent performance of those estimators in out of sample forecasting

jamming hysteresis and oscillation in scalar models for shear thickening we investigate shear thickening and jamming within the framework of a family of spatially homogeneous scalar rheological models these are based on the soft glassy rheology model of sollich et al phys rev lett 78 2020 1997 but with an effective temperature x that is a decreasing function of either the global stress ensuremath sigma or the local strain l for appropriate x x ensuremath sigma it is shown that the flow curves include a region of negative slope around which the stress exhibits hysteresis under a cyclically varying imposed strain rate stackrel ifmmode dot else fi ensuremath gamma a subclass of these x ensuremath sigma have flow curves that touch the stackrel ifmmode dot else fi ensuremath gamma 0 axis for a finite range of stresses imposing a stress from this range jams the system in the sense that the strain ensuremath gamma creeps only logarithmically with time t ensuremath gamma t ensuremath sim mathrm ln t these same systems may produce a finite asymptotic yield stress under an imposed strain in a manner that depends on the entire stress history of the sample a phenomenon we refer to as history dependent jamming in contrast when x x l the flow curves are always monotonic but we show that some x l generate an oscillatory strain response for a range of steady imposed stresses similar spontaneous oscillations are observed in a simplified model with fewer degrees of freedom we discuss this result in relation to the temporal instabilities observed in rheological experiments and stick slip behavior found in other contexts and comment on the possible relationship with delay differential equations that are known to produce oscillations and chaos

strong feller property and irreducibility for diffusions on hilbert spaces it is shown that the transition semigroup p t t 0 corresponding to a nonlinear stochastic evolution equation is strong feller and irreducible provided the nonlinearities are lipschitz continuous and the diffusion term is nondegenerate this result ensures the uniqueness of the invariant measure for p t t 0

universality classes for extreme value statistics the equilibrium low temperature physics of disordered systems is governed by the statistics of extremely low energy states it is thus relevant to discuss the possible universality classes for extreme value statistics we compare the usual probabilistic classification to the results of the replica approach we show in detail for several problems including the random energy model and the decaying burgers turbulence that one class of independent variables corresponds exactly to the so called one step replica symmetry breaking solution in the replica language we argue that this universality class holds if the correlations are sufficiently weak and propose a conjecture on the level of correlations which leads to different universality classes

eigenvalue ratio test for the number of factors this paper proposes two new estimators for determining the number of factors r in static approximate factor models we exploit the well known fact that the r largest eigenvalues of the variance matrix of n response variables grow unboundedly as n increases while the other eigenvalues remain bounded the new estimators are obtained simply by maximizing the ratio of two adjacent eigenvalues our simulation results provide promising evidence for the two estimators

determining the number of factors in approximate factor models in this paper we develop some econometric theory for factor models of large dimensions the focus is the determination of the number of factors r which is an unresolved issue in the rapidly growing literature on multifactor models we first establish the convergence rate for the factor estimates that will allow for consistent estimation of r we then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria the theory is developed under the framework of large cross sections n and large time dimensions t no restriction is imposed on the relation between n and t simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice

maximal lp regularity of parabolic problems with boundary dynamics of relaxation type in this paper we investigate vector valued parabolic initial boundary value problems of relaxation type typical examples for such boundary conditions are dynamic boundary conditions or linearized free boundary value problems like in the stefan problem we present a complete lp theory for such problems which is based on maximal regularity of certain model problems

interpolation embeddings and traces of anisotropic fractional sobolev spaces with temporal weights we investigate the properties of a class of weighted vector valued lp spaces and the corresponding an isotropic sobolev slobodetskii spaces these spaces arise naturally in the context of maximal lp regularity for parabolic initial boundary value problems our main tools are operators with a bounded h calculus interpolation theory and operator sums

optimal relaxed control of dissipative stochastic partial differential equations in banach spaces we study an optimal relaxed control problem for a class of semilinear stochastic pdes on banach spaces perturbed by multiplicative noise and driven by a cylindrical wiener process the state equation is controlled through the nonlinear part of the drift coefficient which satisfies a dissipative type condition with respect to the state variable the main tools of our study are the factorization method for stochastic convolutions in umd type 2 banach spaces and certain compactness properties of the factorization operator and of the class of young measures on suslin metrizable control sets

asymptotic spectral theory for nonlinear time series we consider asymptotic problems in spectral analysis of stationary causal processes limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given instead of the commonly used strong mixing conditions in our asymptotic spectral theory we impose conditions only involving conditional moments which are easily verifiable for a variety of nonlinear time series

stochastic maximal lp regularity in this article we prove a maximal lp regularity result for stochastic convolutions which extends krylov s basic mixed lp lq inequality for the laplace operator on d to large classes of elliptic operators both on d and on bounded domains in d with various boundary conditions our method of proof is based on mcintosh s h functional calculus r boundedness techniques and sharp lp lq square function estimates for stochastic integrals in lq spaces under an additional invertibility assumption on a a maximal space time lp regularity result is obtained as well

solvability of a parabolic problem with non smooth data abstract we study a weak solvability of one linear parabolic problem with a summable right hand side and non smooth coefficients we consider this problem as appropriate operator equation in some banach space methods of the semigroups theory fractional powers of operators and integral operators for solvability of this operator equation are used

d cca a decomposition based canonical correlation analysis for high dimensional datasets a typical approach to the joint analysis of two high dimensional datasets is to decompose each data matrix into three parts a low rank common matrix that captures the shared information across dat

a joint functional calculus for sectorial operators with commuting resolvents 1 introduction in this paper we are concerned with h 1 functional calculus in the sense of the construction introduced by mcintosh 23 and developed recently by cowling doust mcintosh and yagi 8 given v in 0 p we will use the notation sv fz 2 c n f0g jarg z j vg to denote the open sector of angle 2v around the half line r let x be a complex banach space given a linear operator a on x we denote by d a n a and r a the domain the kernel and the range of a respectively we also denote by j a the spectrum of a and by r a the resolvent set of a

examples of unbounded imaginary powers of operators two examples are given the first one consists of an operator of positive type in hilbert space without bounded imaginary powers the second one is concerned with the closedness of the sum of two closed operators in a hilbert space

generalized ornstein uhlenbeck semigroups littlewood paley stein inequalities and the p a meyer equivalence of norms abstract let be a nondegenerate gaussian measure on a hilbert space h for an arbitrary selfadjoint nonnegative operator a we consider the semigroup e tl e ta on l p where stands for the second quantization operator we provide an explicit characterization of the domains of i l m 2 in l p in terms of gaussian sobolev spaces thus extending the p a meyer result on equivalence of norms the main tools are the littlewood paley stein inequalities which are proved under minimal assumptions by a purely analytic method following e stein 1970 topics in harmonic analysis princeton univ press princeton nj

positivity and regularity of hyperbolic volterra equations in banach spaces soit x un espace de banach a un operateur lineaire clos non borne dans x a domaine dense d a a l loc 1 r f c j x avec j 0 t et on considere l equation de volterra de type scalaire u t f t 0 t a t au d t j on etudie l existence la positivite la regularite et la compacite ainsi que l integrabilite de l operateur resolvant s t defini par s t x x 0 t a t as xd t 0 x d a pour deux classes particulieres de noyaux a et d operateurs a

existence of analytic solutions for the classical stefan problem we prove that under mild regularity assumptions on the initial data the two phase classical stefan problem admits a unique solution that is analytic in space and time

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

abstract lp estimates for the cauchy problem with applications to the navier stokes equations in exterior domains abstract we apply an abstract perturbation theorem to derive global in time lq estimates for the cauchy problem and lq ls estimates for the nonstationary stokes equations in exterior domains this will be applied to obtain various new global in time estimates for weak solutions of the navier stokes equations

on the regularity of a generalized diffusion problem arising in population dynamics set in a cylindrical domain abstract in this paper we consider a generalized diffusion problem arising in population dynamics to this end we study a fourth order operational equation of elliptic type with various boundary conditions we show existence uniqueness and regularity of a classical solution on a cylindrical domain under some necessary and sufficient conditions on the data this elliptic problem is solved in l p a b x p 1 where a b r and x is a umd banach space our techniques use essentially the functional calculus and the semigroup theory

a conserved phase field system with memory and relaxed chemical potential abstract in this paper we propose a conserved phase field model with memory and relaxed chemical potential our model could be considered also in the frame of cahn hilliard s theory of spinodal decomposition of a binary mixture where there is a coupling to a slowly relaxing variable e g in phase separation of polymer mixtures near a glass transition the global well posedness in an l p setting is obtained under suitable relaxation functions and under homogeneous conditions

strong solutions of the navier stokes equations for a compressible fluid of allen cahn type in this work we study the navier stokes allen cahn system a combination of the compressible navier stokes equations with an allen cahn phase field description this model describes two phase patterns in a flowing liquid including phase transformations our purpose is to show the existence and uniqueness of local strong solutions for arbitrary initial data part of the proof is based on methods used in a companion paper which investigated the compressible navier stokes equations

h infty calculus for the sum of non commuting operators a recent result of kalton and weis is extended to the case of non commuting operators employing the commutator condition of labbas and terreni or of da prato and grisvard under appropriate assumptions it is shown that the sum of two non commuting operators admits an h calculus the main results are then applied to a parabolic problem on a wedge domain

domains of fractional powers of the stokes operator in lr spaces soit d un domaine borne de r n n 2 a frontiere lisse s soit 1 r et soit x r la fermeture dans l r d n de tous les champs vectoriels solenoidaux lisses a support compact dans d soit w r m d l espace de sobolev d ordre m et soit le laplacien on considere l operateur de stokes a r p r de domaine d a r w w r 2 d n w 5 0 mx 2 soit a un nombre reel positif pour chaque positif il y a une constante ce a telle que a r z ce a exp im z pour tout z satisfaisant a rez 0 ou a r z est la norme operateur de a r z

on the closedness of the sum of two closed operators o t t 1 where e g a is the infinitesimal generator of an analytic semigroup in a complex banach space x we find that in general it is false that for every fe lp 0 t x problem 1 has a solution uewi p o t x c lp o t a usually it is necessary to impose some further regularity conditions on f consider for instance the way in which problem 1 is studied in the paper 8 and compare th 3 7 and 3 14 which are applied in w 4 of the same paper to solve problem 1 we find that in general we have only strong solutions while in the hilbert space setting we have strict solutions this corresponds to the fact that in general the operator a b where b u u is only closable while in a hilbert space it is closed this remark suggests that the better result may depend on the nicer geometric properties of a hilbert space with respect to a general banach space and it is natural to ask which conditions should be imposed on the banach space to force the sum of two suitable closed opera tors to be closed the above considerations motivate the manifold aim of the present paper a to find conditions on a banach space x and on closed linear operators a and b acting in x which ensure that a b is closed b to apply the result of a to problem 1 it seems that the convenient property for the banach space x is convexity or otherwise stated the umd condition for information about these equiva lent conditions we refer to 4 in which it is also proved that if x is convex and l p oe then the hilbert transform is continuous from lp r x into lp r x on the other hand it is also known see 2 that if there exists pe 1 oe such that the hilbert transform is continuous from lp r x into itself

stability properties of stochastic maximal l p regularity in this paper we consider lp regularity estimates for solutions to stochastic evolution equations which is called stochastic maximal lp regularity our aim is to find a theory which is analogously to dore s theory for deterministic evolution equations he has shown that maximal lp regularity is independent of the length of the time interval implies analyticity and exponential stability of the semigroup is stable under perturbation and many more properties we show that the stochastic versions of these results hold

dynamical behavior of a complex fluid near an out of equilibrium transition approaching simple rheological chaos we report here an extensive study of sustained oscillations of the viscosity of a complex fluid near an out of equilibrium transition using well defined protocols we perform rheological measurements of the onion texture near a layering transition in a couette flow this complex fluid exhibits sustained oscillations of the viscosity on a large time scale 500 s at controlled stress these oscillations are directly correlated to an oscillating microstructural change of the texture of the fluid we observe a great diversity of dynamical behavior and show that there is a coupling with spatial effects in the inverted delta v direction this is in agreement with a careful analysis of the temporal series of the viscosity with the dynamical system theory this analysis indicates that the observed dynamical responses do not strictly correspond to three dimensional chaotic states probably because some spatiotemporal effects are present and are likely to play an important role

dynamical stability of non constant equilibria for the compressible navier stokes equations in eulerian coordinates in this paper we establish global existence and uniqueness of strong solutions to the non isothermal compressible navier stokes equations in bounded domains the initial data have to be near equilibria that may be non constant due to considering large external forces we are able to show exponential stability of equilibria in the phase space and above all to study the problem in eulerian coordinates the latter seems to be a novelty since in works by other authors global strong lp solutions have been investigated only in lagrangian coordinates eulerian coordinates are even declared as impossible to deal with the proof is based on a careful derivation and study of the associated linear problem

dynamic factor models with infinite dimensional factor spaces one sided representations abstract factor model methods recently have become extremely popular in the theory and practice of large panels of time series data those methods rely on various factor models which all are particular cases of the generalized dynamic factor model gdfm introduced in forniet al 2000 that paper however rests on brillinger s dynamic principal components the corresponding estimators are two sided filters whose performance at the end of the observation period or for forecasting purposes is rather poor no such problem arises with estimators based on standard principal components which have been dominant in this literature on the other hand those estimators require the assumption that the space spanned by the factors has finite dimension in the present paper we argue that such an assumption is extremely restrictive and potentially quite harmful elaborating upon recent results by anderson and deistler 2008a b on singular stationary processes with rational spectrum we obtain one sided representations for the gdfm without assuming finite dimension of the factor space construction of the corresponding estimators is also briefly outlined in a companion paper we establish consistency and rates for such estimators and provide monte carlo results further motivating our approach