a one factor multivariate time series model of metropolitan wage rates abstract the paper formulates and estimates a single factor multivariate time series model the model is a dynamic generalization of the multiple indicator or factor analysis model it is shown to be a special case of the general state space model and can be estimated by maximum likelihood methods using the kalman filter algorithm the model is used to obtain estimates of the unobserved metropolitan wage rate for los angeles based on observations of sectoral wages within the standard metropolitan statistical area hypothesis tests model diagnostics and out of sample forecasts are used to evaluate the model

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

the classical limit of the relativistic vlasov maxwell system solutions of the relativistic vlasov maxwell system of partial differential equations are considered in three space dimensions the speed of light c appears as a parameter in this system for smooth cauchy data classical solutions are shown to exist on a time interval that is independent ofc then using an integral representation for the electric and magnetic fields due to glassey and strauss 6 conditions are given under which solutions of the relativistic vlasov maxwell system converge in pointwise sense to solutions of the non relativistic vlasov poisson system at the asymptotic rate of 1 c asc tends to infinity

use of canonical analysis in time series model identification summary the second order moment structure of time series models is used to derive a canonical analysis in time series modelling consistency properties of certain canonical correlations and the corresponding eigenvectors are shown based on these properties a canonical correlation approach for tentative order determination in building autoregressivemoving average models is proposed this approach can handle directly nonstationary as well as stationary processes and it also provides consistent estimates of the autoregressive parameters involved the asymptotic distribution of the identification statistic is discussed

higher regularity of the tangential fields in the relativistic vlasov maxwell system abstract it is shown that the tangential electric and magnetic fields in the glassey strauss representation formulas are in fact bounded in l loc t l x 2 for some 0

classical solutions and the glassey strauss theorem for the 3d vlasov maxwell system r glassey and w strauss have proved in arch rational mech anal 92 1986 59 90 that c1 solutions to the relativistic vlasov maxwell system in three space dimensions do not develop singularities as long as the support of the distribution function in the momentum variable remains bounded the present paper simplifies their proof

on likelihood ratio tests for threshold autoregression summary this paper addresses the null distribution of the likelihood ratio statistic for threshold autoregression with normally distributed noise the problem is non standard because the threshold parameter is a nuisance parameter which is absent under the null hypothesis we reduce the problem to the first passage probability associated with a gaussian process which in some special cases turns out to be a brownian bridge it is also shown that in some specific cases the asymptotic null distribution of the test statistic depends only on the degrees of freedom and not on the exact null joint distribution of the time series

a new continuation criterion for the relativistic vlasov maxwell system the global existence of solutions to the relativistic vlasov maxwell system given sufficiently regular finite energy initial data is a longstanding open problem the main result of glassey and strauss arch ration mech anal 92 59 90 1986 shows that a solution f e b remains c 1 as long as the momentum support of f remains bounded alternate proofs were later given by bouchut et al arch ration mech anal 170 1 15 2003 and klainerman and staffilani commun pure appl anal 1 103 125 2002 we show that only the boundedness of the momentum support of f after projecting to any two dimensional plane is needed for f e b to remain c 1

some history of the conjugate gradient and lanczos methods this paper gives some of the history of the conjugate gradient and lanczos algorithms and an annotated bibliography for the period 1948 1976

forecasting and testing in co integrated systems abstract this paper examines the behavior of forecasts made from a co integrated system as introduced by granger 1981 granger and weiss 1983 and engle and granger 1987 it is established that a multi step forecast will satisfy the co integrating relation exactly and that this particular linear combination of forecasts will have a finite limiting forecast error variance a simulation study compares the multi step forecast accuracy of unrestricted vector autoregression with the two step estimation of the vector autoregression imposing the co integration restriction to test whether a system exhibits co integration the procedures introduced in engle and granger 1987 are extended to allow different sample sizes and numbers of variables

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

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 instability of some gradient methods for ill posed problems for the solution of linear ill posed problems some gradient methods like conjugate gradients and steepest descent have been examined previously in the literature it is shown that even though these methods converge in the case of exact data their instability makes it impossible to base a priori parameter choice regularization methods upon them

multivariate exponential smoothing and dynamic factor model applied to hourly electricity price analysis thanks to its very simple recursive computing scheme exponential smoothing has become a popular technique to forecast time series in this work we show the advantages of its multivariate version and present some properties of the model which allows us to perform a dynamic factor analysis this analysis leads to a simple methodology to reduce the number of parameters useful when the dimension of observations is large via a linear transformation that decomposes the multivariate process into independent univariate exponential smoothing processes characterized by a single smoothing parameter that goes from zero white noise process to one random walk process a computer implementation of the expectation maximization em algorithm has been built for the maximum likelihood estimation of the models the practicality of the method is demonstrated by its application to hourly electricity price predictions in some day ahead markets such as omel powernext and nord pool markets whose forecasts are given

strichartz estimates and moment bounds for the relativistic vlasov maxwell system we consider the relativistic vlasov maxwell system with data of unrestricted size and without compact support in momentum space in the two dimensional and the two and a half dimensional cases glassey schaeffer proved commun math phys 185 257 284 1997 arch ration mech anal 141 331 354 1998 arch ration mech anal 141 355 374 1998 that for regular initial data with compact momentum support this system has unique global in time classical solutions in this work we do not assume compact momentum support for the initial data and instead require only that the data have polynomial decay in momentum space in the two dimensional and the two and a half dimensional cases we prove the global existence uniqueness and regularity for solutions arising from this class of initial data to this end we use strichartz estimates and prove that suitable moments of the solution remain bounded moreover we obtain a slight improvement of the temporal growth of the l infty x norms of the electromagnetic fields compared to glassey and schaeffer commun math phys 185 257 284 1997 arch ration mech anal 141 355 374 1998 in the three dimensional case we apply strichartz estimates and moment bounds to show that a regular solution can be extended as long as p 0 theta f l q x l 1 p remains bounded for theta frac 2 q 2 q leqq infty this improves previous results of pallard indiana univ math j 54 5 1395 1409 2005 commun math sci 13 2 347 354 2015

reduced rank models for multiple time series summary this paper is concerned with the investigation of reduced rank coefficient models for multiple time series in particular autoregressive processes which have a structure to their coefficient matrices similar to that of classical multivariate reduced rank regression are studied in detail the estimation of parameters and associated asymptotic theory are derived the exact correspondence between the reduced rank regression procedure for multiple autoregressive processes and the canonical analysis of box tiao 1977 is briefly indicated to illustrate the methods u s hog data are considered

convergence rate results for steepest descent type method for nonlinear ill posed equations convergence rate result for a modified steepest descent method and a modified minimal error method for the solution of nonlinear ill posed operator equation have been proved with noisy data to our knowledge convergence rate result for the steepest descent method and minimal error method with noisy data are not known we provide a convergence rate results for these methods with noisy data the result in this paper are obtained under less computational cost when compared to the steepest descent method and minimal error method we present an academic example which satisfies the assumptions of this paper

three new results on continuation criteria for the 3d relativistic vlasov maxwell system abstract we consider continuation criteria for the three dimensional relativistic vlasov maxwell system when the particle density f t x p is compactly supported at t 0 we prove p 0 18 5 r 1 f l t l x r l p 1 1 where 1 r 2 and 0 is arbitrarily small is a continuation criteria our continuation criteria is an improvement in the 1 r 2 range to the previously best known criteria p 0 4 r 1 f l t l x r l 1 p 1 due to kunze 7 we also consider continuation criteria when f 0 x p has noncompact support in this regime luk strain 9 proved that p 0 f l x 1 l p 1 1 is a continuation criteria for 5 we improve this result to 3 finally we build on another result by luk strain 8 the authors proved boundedness of momentum support on a fixed two dimensional plane is a sufficient continuation criteria we prove the same result even if the plane varies continuously in time

nested reduced rank autoregressive models for multiple time series abstract the nested reduced rank autoregressive ar model is considered in order to simplify and provide a more detailed description of the structure of the multivariate time series and to reduce the number of parameters in the time series modeling the multivariate ar model is yt p j 1 j y t j et where yt is m 1 and the structure of the model considered is such that the rj rank j are nonincreasing as the lag j increases so the j have the factorization j ajbj and range aj range a j 1 specification of the coefficient rank structures for such models through the use of canonical correlation analysis between yk t y t y t k and y k t 1 is discussed a canonical variable transformation that produces simpler structure in the model and explicitly illustrates how different components of the vector series depend on past lagged values to differing degrees is also examined a gaussian parameter estimation procedure is described and asymptotic properties of the gaussian estim

forecasting turning points in international output growth rates using bayesian exponentially weighted autoregression time varying parameter and pooling techniques abstract in this paper two variants of an autoregressive leading indicator arli model are employed to forecast turning points in the growth rates of 18 countries annual real output for the years 1974 1986 bayesian predictive densities have been employed to compute probabilities of downturns and upturns and they have been employed in a bayesian decision theoretic framework to obtain optimal turning point forecasts various versions of the arli model with and without pooling of data across countries produced about 70 to 80 percent correct forecasts for 158 turning points time varying parameter models performed slightly better than others the performance of the arli models in forecasting turning points is shown to be considerably better than that of four naive methods of forecasting turning points

yet another criterion for global existence in the 3d relativistic vlasov maxwell system abstract we prove that solutions of the 3d relativistic vlasov maxwell system can be extended as long as the quantity 1 t x max 1 r 3 d p 1 p 2 1 1 v f t x p is bounded in l x 2