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

dependence of eigenvalues on the boundary conditions of sturm liouville problems with one singular endpoint abstract this paper is concerned with continuous and differentiable dependence of isolated eigenvalues on the boundary conditions of self adjoint sturm liouville problems with one singular endpoint locally continuous dependence of eigenvalues on the boundary conditions is proved especially in the limit point case the continuous dependence of isolated eigenvalues is shown by the relationships between weyl titchmarsh m function and the spectrum of the singular problems then continuous eigenvalue branches through each isolated eigenvalue over the space of boundary conditions are formed it is rigorously shown that the eigenfunctions for the eigenvalues along a continuous simple eigenvalue branch can be continuously chosen with uniform bound in l w 2 norm its proof is different from that in the regular sturm liouville problems the derivative formulas of the continuous simple eigenvalue branch with respect to all the parameters in the boundary conditions are given and thus its monotonicity with respect to some parameters is derived

the gauss map for surfaces part 2 the euclidean case we study smooth maps t m ci of a riemann surface m into the grassmannian gi of oriented 2 planes in e2 and determine necessary and sufficient conditons on t in order that it be the gauss map of a conformai immersion x m e2 we sometimes view as an oriented riemannian vector bundle it is a subbundle of ej the trivial bundle over m with fibre e2 l the necessary and sufficient conditions obtained for simply connected m involve the curvatures of t and tx the orthogonal complement of t in e f as well as certain components of the tension of viewed as a map t m sc 1 where sc l is a unit sphere of dimension c that contains ci as a submanifold in a natural fashion if t satisfies a particular necessary condition then the results take two different forms depending on whether or not t is the gauss map of a conformai minimal immersion the case t m gl is also studied in some additional detail

spectral concentration and rapidly decaying potentials abstract we consider the spectral function 0 for the sturm liouville equation y q y 0 on 0 with a boundary condition y 0 cos y 0 sin 0 and where q l 0 a point 0 is called a point of spectral concentration if has a local maximum there we give a new formula for in terms of the prufer transformation angle and we identify a rapid transitional property of in the neighbourhood of points of spectral concentration this property provides a sensitive test of the existence of such points and lends itself to a detailed computational investigation which reveals such points in greater profusion than shown by for example sledge our approach also leads to the possibility of a theoretical investigation

on the existence of an eigenvalue below the essential spectrum this paper is concerned with a computer assisted proof of eigenvalues below the essential spectrum of the sturm liouville problem on the half line it uses methods of functional analysis and interval analysis to derive algorithms that may be used to prove the existence of such eigenvalues

eigenvalues of limit point sturm liouville problems abstract the dependence of the eigenvalues of self adjoint sturm liouville problems on the boundary conditions when each endpoint is regular or in the limit circle case is now due to some surprisingly recent results well understood here we study this dependence for singular problems with one endpoint in the limit point case

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

on a computer assisted proof of the existence of eigenvalues below the essential spectrum of the sturm liouville problem abstract there is considerable interest in determining the existence of eigenvalues of the sturm liouville problem py qy wy where the independent variable x 0 and p q and w are real valued functions and is the spectral parameter in general an analytic attack on this problem is quite difficult and usually requires the use of the variational principal together with choice of suitable test functions we show how results from functional analysis together with interval analysis and interval arithmetic can be used not only to determine the existence of such eigenvalues but also to compute provably correct bounds on their values

correction to harmonically immersed surfaces in ⁿ trans amer math soc 307 1988 no 1 363 372 mr0936822 89g 53006

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

harmonically immersed surfaces of r n some generalizations of classical results in the theory of minimal surfaces f m rn are shown to hold in the more general case of harmonically immersed surfaces introduction let m g be a connected riemann surface with a prescribed metric g in its conformal class and let f m rn be an immersion it is well known that f realizes m with the induced metric from rn as a minimal surface if and only if f is a conformal with respect to g harmonic map cf for example 3 or 8 that is the theory of minimal surfaces is substantially the theory of conformally immersed harmonic surfaces our purpose is to analyze the case when f is simply a harmonic immersion to introduce an appropriate gauss map and as the main achievement to establish in this new setting the analogue of three fundamental results cf theorems 1 1 and 2 1 and 3 in the theory of minimal surfaces the harmonicity of the gauss map ruh and vilms 13 equidistribution properties of the gauss map in cpn chern and osserman 1 and 11 and the enneper weierstrass representation formulas recently due for arbitrary codimension to hoffman and osserman 7 the last two topics the third for n 3 have alrealy been treated by t k milnor see for instance her survey article 9 but as we remark in 2 our results complement hers in an interesting way the method of the moving frame as well as the einstein summation convention are used throughout this paper 1 the gauss map and first properties let m g be as in the introduction we fix the index ranges 1 rn be an immersion a darboux frame al g f is a map e u c m e n u ope in m such that received by the editors april 6 1987 selected results of this paper were presented by the first named author november 1 1987 at the 837th meeting of the american mathematical society held at lincoln nebraska 1980 mathematics subject classification 1985 revision primary 53a07 53a10

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

harmonic maps and classical surface theory in minkowski 3 space harmonic maps from a surface s with nondegenerate prescribed and induced metrics are characterized showing that holomorphic quadratic differentials play the same role for harmonic maps from a surface with indefinite prescribed metric as they do in the riemannian case moreover holomorphic quadratic differentials are shown to arise as naturallv on surfaces of constant h or k in m3 as on their counterparts in e3 the connection between the sine gordon sinh gordon and cosh gordon equations and harmonic maps is explained various local and global results are established for surfaces in m3 with constant h or constant k 0 in particular the gauss map of a spacelike or timelike surface in m3 is shown to be harmonic if and only if h is constant also k is shown to assume values arbitrarilv close to h2 on any entire spacelike surface in m3 with constant h except on a hyperbolic cylinder

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

the gauss map for kahlerian submanifolds of ⁿ we introduce a gauss map for kahler submanifolds of euclidean space and study its geometry in relation to that of the given immersion in particular we generalize a number of results of the classical theory of minimal surfaces in euclidean space

resonances and analytic continuation for exponentially decaying sturm liouville potentials abstract the sturm liouville equation on the half line 0 is considered with a potential which decays exponentially at infinity it is known that green s function has an analytic continuation into part of the unphysical sheet im here it is shown that analytic continuation into the whole of this sheet is possible for certain types of decay the methods are constructive and they also provide a new and rigorous way of locating resonances