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

high breakdown point and high efficiency robust estimates for regression a class of robust estimates for the linear model is introduced these estimates called mm estimates have simultaneously the following properties i they are highly efficient when the errors have a normal distribution and ii their breakdown point is 0 5 the mm estimates are defined by a three stage procedure in the first stage an initial regression estimate is computed which is consistent robust and with high breakdown point but not necessarily efficient in the second stage an m estimate of the errors scale is computed using residuals based on the initial estimate finally in the third stage an m estimate of the regression parameters based on a proper redescending psi function is computed consistency and asymptotical normality of the mm estimates assuming random carriers are proved a convergent iterative numerical algorithm is given finally the asymptotic biases under contamination of optimal bounded influence estimates and mm estimates are compared

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

asymptotic control and stabilization of nonlinear oscillators with non isolated equilibria let h r be a c1 function on a real hilbert space h and let 0 be a positive damping parameter for any control function e r r which tends to zero as t we study the asymptotic behavior of the trajectories of the damped nonlinear oscillator hbfc x t x t x t e t x t 0 we show that if e t does not tend to zero too rapidly as t then the term e t x t asymptotically acts as a tikhonov regularization which forces the trajectories to converge to a particular equilibrium indeed in the main result of this paper it is established that when is convex and s argmin under the key assumption that e is a slow control i e 0 e t dt then each trajectory of the hbfc system strongly converges as t to the element of minimal norm of the closed convex set s as an application we consider the damped wave equation with neumann boundary condition formula

asymptotic analysis of the exponential penalty trajectory in linear programming we consider the linear program min c x ax b and the associated exponential penalty functionfr x c x r exp aix bi r forr close to 0 the unconstrained minimizerx r offr admits an asymptotic expansion of the formx r x rd r wherex is a particular optimal solution of the linear program and the error term r has an exponentially fast decay using duality theory we exhibit an associated dual trajectory r which converges exponentially fast to a particular dual optimal solution these results are completed by an asymptotic analysis whenr tends to the primal trajectory has an asymptotic ray and the dual trajectory converges to an interior dual feasible solution

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

gabor representation of generalized functions this paper deals with gabor representation of generalized functions by this we mean that a given function is to be expanded in a series involving gabor functions that are located in the points of a given lattice in the time frequency plane we shall mainly consider lattices in which the area of the elementary cells of the lattice equals 1 in 1946 gabor used these expansions for the simultaneous analysis of signals in time and frequency cf 181 gabor stated that the above mentioned expansions exist for every reasonable signal and that the coefficients in the expansion are uniquely determined by the signal this statement is true when interpreted carefully and the aim of this paper is to find out what kind of generalized functions are sufficiently well behaved to allow a development in a gabor series we shall also consider the question of the uniqueness of the coefficients in the expansions as well as questions concerning convergence it turns out that the uniqueness questions can be handled with the aid of the main results of io in particular 2 12 and 2 13 the questions on the existence of expansions are harder to answer and require special care depending on the particular function we consider lpfunctions 1 p 2 in detail and show existence of gabor representation for tempered distribution in general

limited data x ray tomography using nonlinear evolution equations a novel approach to the x ray tomography problem with sparse projection data is proposed nonnegativity of the x ray attenuation coefficient is enforced by modelling it as max phi x 0 where phi is a smooth function the function phi is computed as the equilibrium solution of a nonlinear evolution equation analogous to the equations used in level set methods the reconstruction algorithm is applied to a simulated full and limited angle projection data of the shepp logan phantom with sparse angular sampling and b measured limited angle projection data of in vitro dental specimens the results are significantly better than those given by traditional backprojection based approaches and similar in quality but faster to compute compared to the algebraic reconstruction technique

strong asymptotic convergence of evolution equations governed by maximal monotone operators with tikhonov regularization abstract we consider the tikhonov like dynamics u t a u t e t u t where a is a maximal monotone operator on a hilbert space and the parameter function e t tends to 0 as t with 0 e t d t when a is the subdifferential of a closed proper convex function f we establish strong convergence of u t towards the least norm minimizer of f in the general case we prove strong convergence towards the least norm point in a 1 0 provided that the function e t has bounded variation and provide a counterexample when this property fails

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

asymptotic behavior of solutions to a class of nonlinear evolution equations on etudie les equations de la chaleur a controle de temperature a l interieur ou sur la frontiere du domaine pour cela on considere un type de problemes variationnels paraboliques avec obstacles

bilinear signal synthesis the authors discuss the signal synthesis problem in the general framework of bilinear signal representations bsrs thereby obtaining a unified treatment which encompasses e g the wigner distribution and ambiguity function as special cases the inclusion of a signal space constraint serves to impart flexibility to the signal synthesis process and to relax mathematical requirements the characterization of signal spaces either by orthogonal projection operators or by orthonormal bases leads to two different signal synthesis methods both methods assume the bsr to be unitary i e satisfy moyal s formula on the signal space on which signal synthesis is performed as an application of the general signal synthesis methods band limited signal synthesis in the case of the wigner distribution is considered

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

beam stacking a generalized preprocessing technique gaussian beams are well understood frequency domain entities combining the directional properties of plane waves with an effectively finite region of support these outstanding properties are retained not only on a prescribed observation plane but throughout the propagation path a preprocessing sequence aimed at transforming raw seismic data into beam stacks is proposed that is time harmonic gaussian beams are synthesized replacing the plane waves generated by conventional slant stacking procedures the suggested scheme is characterized by an open parameter essentially the beam width whose selection is critical to ultimate success specific criteria for choosing this parameter can be given in the limits of zero and infinite beam widths beam stacks degenerate to the original raw data and to the conventional slant stacks respectively although beam stacking is basically a frequency domain procedure a transformation into the time domain using frequency constituents within selected bands may be

a unified definition for the discrete time discrete frequency and discrete time frequency wigner distributions various discrete definitions of the wigner distribution wd for discrete time signals have been proposed in previous works the formulation developed in this paper leads to natural and unified definitions of discrete versions of the wd they are directly related to the continuous and preserve most of its properties the discretization is first considered in the time domain dtwd in the frequency domain dfwd and then in both domains simultaneously dtfwd in each case the aliasing problem is studied and generalized interpolation formulas allowing the reconstruction of the continuous wd are derived the dtfwd is particulary relevant for computer implementation of the wd

asymptotic behavior of nonautonomous monotone and subgradient evolution equations in a hilbert setting h we study the asymptotic behavior of the trajectories of nonautonomous evolution equations dot x t a t x t ni 0 where for each t geq 0 a t h rightrightarrows h denotes a maximal monotone operator we provide general conditions guaranteeing the weak ergodic convergence of each trajectory x cdot to a zero of a limit maximal monotone operator a infty as the time variable t tends to infty the crucial point is to use the brezis haraux function or equivalently the fitzpatrick function to express at which rate the excess of mathrm gph a infty over mathrm gph a t tends to zero this approach gives a sharp and unifying view of this subject in the case of operators a t partial phi t which are subdifferentials of proper closed convex functions phi t we show convergence results for the trajectories then we specialize our results to multiscale evolution equations and obtain asymptotic properties of hierarchical minimization and selection of viscosity solutions illustrations are given in the field of coupled systems and partial differential equations

well posedness of initial boundary value problem of degenerate parabolic equations abstract we study a nonlinear degenerate parabolic equation associated with an arbitrary maximal monotone graph we impose initial and dirichlet boundary conditions and prove that the problem is well posed

identifying a simplifying structure in time series abstract this article studies how to identify hidden factors in multivariate time series process this problem is important because when the series are driven by a set of common factors a a large number of parameters may be needed to obtain an adequate representation of the system and b the estimated parameters will be highly correlated therefore a complex and badly defined relationship can appear when in fact a simpler and parsimonious model in terms of a few common factors can be operating this article develops a methodology to identify the number of factors and to build a simplifying transformation to represent the series it is proved that the number of factors is equal to the rank of the covariance matrices and the parameter matrices of the infinite moving average representation of the process the eigenvectors of these matrices will provide the canonical transformation the method is illustrated with one example using series of the price of wheat in five provinces of spain in the 19th ce

asymptotic behaviour of solutions to parabolic elliptic variational inequalities in a real hilbert space h where j is a given interval in r 0 co j is the subdifferential of a convex function 4 on h and b is a maximal monotone operator in h the abstract setting reflects the form of a class of parabolic elliptic boundary value problems with time dependent obstacles such problems arise in particular as mathematical models of various processes in electrochemical technology and some flows with saturations in porous media time dependent obstacles may represent geometric controls moving control actions in these problems in particular such controls may be comprehended in variable boundary conditions prescribed over time dependent parts of the boundary of domain or in source terms distributed over time dependent subdomains the former refers to control of flows via variable water table in reservoirs the latter characterizes control of electrochemical process via mechanically driven motion of a toolpiece cathode the most typical control objective consists there in stabilizing the state of the process at a given spatial distribution for example constant water head and desired shape of anode this motivates our interest in the asymptotic behavior of solutions to the corresponding boundary value problems as t a to the knowledge of the authors this question has so far not been studied in literature as it has been shown in kenmochi pawlow 16 171 the class of considered time dependent problems admits a representation in the form of evolution equation e b in 16 171 the corresponding results on existence uniqueness and stability of solutions have been established in the present paper we study the asymptotic properties of solutions to e c b as t 00 provided some hypotheses are imposed on the family t e r and the limit 4 of as t a for the solution u u of e d b on r we prove that

forecasting with nonstationary dynamic factor models abstract in this paper we analyze the structure and the forecasting performance of the dynamic factor model it is shown that the forecasts obtained by the factor model imply shrinkage pooling terms similar to the ones obtained from hierarchical bayesian models that have been applied successfully in the econometric literature thus the results obtained in this paper provide an additional justification for these and other types of pooling procedures the expected decrease in mse for using a factor model versus univariate arima and shrinkage models are studied for the one factor model monte carlo simulations are presented to illustrate this result a factor model is also built to forecast gnp of european countries and it is shown that the factor model can provide a substantial improvement in forecasts with respect to both univariate and shrinkage univariate forecasts

the aliasing problem in discrete time wigner distributions there is no straightforward way to proceed from the continuous time wigner distribution to a discrete time version of this time frequency signal representation a previously given definition of such a function turned out to yield a distribution that was periodic with period instead of 2 and this caused aliasing to occur various alternative definitions are considered and compared with respect to aliasing and computational complexity from this comparison it appears that no definition leads to a function that is optimum in all respects this is illustrated by an example

time varying filtering and signal estimation using wigner distribution synthesis techniques the short time fourier transform stft the ambiguity function af and the wigner distribution wd are mixed time frequency signal representations that use fourier transform techniques to map a one dimensional function of time into a two dimensional function of time and frequency these mixed time frequency mappings have been used to analyze the local frequency characteristics of a variety of signals and systems although much work has also been done to develop stft and af synthesis algorithms that can be used to implement a variety of time varying signal processing operations no such synthesis techniques have thus far been developed for the wd in this paper a signal synthesis algorithm that works directly with the real valued high resolution wd will be derived examples of how this wd synthesis procedure can be used to perform time varying filtering operations or signal separation will be given

a class of nonlinear elliptic parabolic equations with time dependent constraints on etudie les equations d evolutions non lineaires de la forme f t du t dt t v t v t bu t 0 t t dans un espace de hilbert h ou t est la sous differentielle d une fonction convexe t definie sur h b est un operateur monotone maximal dans h on considere l existence et l unicite des solutions ainsi que des estimations a priori

a convergence result for nonautonomous subgradient evolution equations and its application to the steepest descent exponential penalty trajectory in linear programming abstract we present a new result on the asymptotic behavior of nonautonomous subgradient evolution equations of the form u t t u t where t t 0 is a family of closed proper convex functions the result is used to study the flow generated by the family t x f x r t where f x r ctx r exp aix bi r is the exponential penalty approximation of the linear program min ctx ax b and r t is a positive function tending to 0 when t we prove that the trajectory u t converges to an optimal solution u of the linear program and we give conditions for the convergence of an associated dual trajectory t toward an optimal solution of the dual program

generalized dynamic principal components abstractbrillinger defined dynamic principal components dpc for time series based on a reconstruction criterion he gave a very elegant theoretical solution and proposed an estimator which is consistent under stationarity here we propose a new enterally empirical approach to dpc the main differences with the existing methods mainly brillinger procedure are 1 the dpc we propose need not be a linear combination of the observations and 2 it can be based on a variety of loss functions including robust ones unlike brillinger we do not establish any consistency results however contrary to brillinger s which has a very strong stationarity flavor our concept aims at a better adaptation to possible nonstationary features of the series we also present a robust version of our procedure that allows to estimate the dpc when the series have outlier contamination we give iterative algorithms to compute the proposed procedures that can be used with a large number of variables our nonrobust and robust pr

asymptotic behavior of gradient like dynamical systems involving inertia and multiscale aspects abstract in a hilbert space h we study the asymptotic behavior as time variable t goes to of nonautonomous gradient like dynamical systems involving inertia and multiscale features given h r and h r two convex differentiable functions a positive damping parameter and t a function of t which tends to zero as t goes to we consider the second order differential equation x t x t x t t x t 0 this system models the emergence of various collective behaviors in game theory as well as the asymptotic control of coupled nonlinear oscillators assuming that t tends to zero moderately slowly as t goes to infinity we show that the trajectories converge weakly in h the limiting equilibria are solutions of the hierarchical minimization problem which consists in minimizing over the set c of minimizers of as key assumptions we suppose that 0 t d t and that for every p belonging to a convex cone c depending on the data and 0 t p c t p d t where is the fenchel conjugate of and c is the support function of c an application is given to coupled oscillators

coupling general penalty schemes for convex programming with the steepest descent and the proximal point algorithm we study the asymptotic behavior of the continuous flow generated by coupling the steepest descent method with a general class of penalty schemes for convex programming we establish convergence of the trajectories towards primal optimal solutions as well as convergence of some naturally associated dual paths the results are extended to the sequences generated by an implicit discretization scheme which corresponds to the coupling of an inexact proximal point iteration with the penalty schemes

viscosity solutions of minimization problems viscosity methods for minimization problems are revisited from some modern perspectives in variational analysis variational convergences for sequences of functions epi convergence gamma convergence mosco convergence and for sequences of operators graph convergence provide a flexible tool for such questions it is proved in a rather large setting that the solutions of the approximate problems converge to a viscosity solution of the original problem that is a solution that is minimal among all the solutions with respect to some viscosity criteria various examples coming from mathematical programming calculus of variations semicoercive elliptic equations phase transition theory hamilton jacobi equations singular perturbations and optimal control theory are considered

asymptotic properties of solutions of time dependent volterra integral equations abstract the asymptotic properties of the bounded solutions of a time dependent nonlinear volterra equation are studied in a hilbert space an application of physical interest is also given

wigner space synthesis of discrete time periodic signals a procedure that facilitates at least squares synthesis of periodic discrete time signals from wigner quasi distributions is proposed the scheme is based on expanding the desired time sequence on a generally nonorthogonal gabor type basis whose associated biorthogonal function presumably exists the specific basis selection may crucially affect the efficiency and quality of the ensuing synthesis procedure the cited basis type constitutes a considerable generalization over the standardly used orthogonal variety thus creating previously unavailable degrees of freedom of primary significance is the acquired capability of generating time frequency basis functions that are well localized localization is a highly desirable property that can advantageously serve in various applications it is shown and numerically demonstrated that benefits of localization as well as the fact that achieving effective time frequency basis localization renders a certain degree of oversampling unavoidable

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

asymptotic expansion of penalty gradient flows in linear programming we establish asymptotic expansions for nonautonomous gradient flows of the form dot u t nabla f u t r t where f x r is a penalty approximation of a linear program and the penalty parameter r t tends to 0 as t to infty under appropriate conditions we show that every integral curve satisfies u t u infty r t d 0 dot r t r t w 0 o dot r t r t for suitable vectors u infty d 0 and w 0 we deduce an asymptotic expansion for a related dual trajectory and we show that the primal dual limit point is a pair of strictly complementary optimal solutions for the linear program