global regularity for a birkhoff rott α approximation of the dynamics of vortex sheets of the 2d euler equations abstract we present an regularization of the birkhoff rott equation induced by the two dimensional euler equations for the vortex sheet dynamics we show that an initially smooth self avoiding vortex sheet remains smooth for all times under the regularized dynamics provided the initial density of vorticity is an integrable function over the curve with respect to the arc length measure

testing linearity against smooth transition autoregressive models summary we study a general univariate smooth transition autoregressive star model it contains as a special case the self exciting threshold autoregressive setar model we present three tests for testing linearity against star models and discuss their properties the power of the tests in small samples is investigated by simulation when the alternative is the logistic star model one of the tests is identical to tsay s 1986 test statistic and is recommended only in a special case of the two remaining tests with wider applicability one seems superior to the other in small samples it is also more powerful than the cusum test recently proposed for testing linearity against setar models

a nonlinear long memory model with an application to us unemployment two important empirical features of us unemployment are that shocks to the series seem rather persistent and that it seems to rise faster during recessions than that it falls during expansions to jointly capture these features of long memory and nonlinearity we put forward a new time series model and evaluate its empirical performance we find that the model describes the data rather well and that it outperforms related competitive models on various measures of fit

optimal entanglement criterion for mixed quantum states we develop a strong and computationally simple entanglement criterion the criterion is based on an elementary positive map phi which operates on state spaces with even dimension n or 4 it is shown that phi detects many entangled states with a positive partial transposition ppt and that it leads to a class of optimal entanglement witnesses this implies that there are no other witnesses which can detect more entangled ppt states the map phi yields a systematic method for the explicit construction of high dimensional manifolds of bound entangled states

a new criterion for indecomposability of positive maps we give a criterion for a positive mapping on the space of operators on a hilbert space to be indecomposable we show that this criterion can be applied to two families of positive maps these families of maps can then be used to form separability criteria for bipartite quantum states that can detect the entanglement of bound entangled quantum states

extended reduction criterion and lattice states we study a particular class of states of a bipartite system consisting of two four level parties by means of an adapted extended reduction criterion we associate their entanglement properties to the geometric patterns of a planar lattice consisting of 16 points

tests for parameter instability and structural change with unknown change point this paper considers tests for parameter instability and structural change with unknown change point the results apply to a wide class of parametric models that are suitable for estimation by generalized method of moments procedures the asymptotic distributions of the test statistics considered here are nonstandard because the change point parameter only appears under the alternative hypothesis and not under the null the tests considered here are shown to have nontrivial asymptotic local power against all alternatives for which the parameters are nonconstant the tests are found to perform quite well in a monte carlo experiment reported elsewhere copyright 1993 by the econometric society

maximum likelihood estimation of the differencing parameter for invertible short and long memory autoregressive integrated moving average models in practical applications of box jenkins autoregressive integrated moving average arima models the number of times that the observed time series must be differenced to achieve approximate stationarity is usually determined by careful but mostly informal analysis of the differenced series for many time series some differencing seems appropriate but taking the first or the second difference may be too strong as an alternative hosking and granger and joyeux proposed the use of fractional differences for 1 2 1 2 can be estimated by an approximate maximum likelihood method we thus obtain a unified approach to fitting traditional box jenkins arima processes as well as stationary and non stationary fractional arima processes a confidence interval for d can be given tests such as for unit roots in the autoregressive parameter or for stationarity follow immediately the resulting confidence intervals for the arma parameters take into account the additional uncertainty due to estimation of d a simple algorithm for calculating the estimate of d and the arma parameters is given simulations and two data examples illustrate the results

information criteria for selecting possibly misspecified parametric models abstract we consider penalized likelihood criteria for selecting models of dependent processes the models may be strictly nested overlapping or nonnested linear or nonlinear and correctly specified or misspecified we provide sufficient conditions on the penalty to guarantee the selection with probability one or with probability approaching one of the model attaining the lower average kullback leibler information criterion klic or when both have the same klic the more parsimonious model as special cases our results describe the akaike schwarz and hannan quinn information criteria as examples we consider selection of armax garch and star models

testing the adequacy of smooth transition autoregressive models abstract smooth transition autoregressive models are a flexible family of nonlinear time series models that have also been used for modelling economic data this paper contributes to the evaluation stage of a proposed specification estimation and evaluation cycle of these models by introducing a lagrange multiplier lm test for the hypothesis of no error autocorrelation and lm type tests for the hypothesis of no remaining nonlinearity and that of parameter constancy small sample properties of the f versions of these tests and some alternative test statistics are investigated by simulation the results indicate that the proposed tests can be applied in small samples already

inference when a nuisance parameter is not identified under the null hypothesis many econometric testing problems involve nuisance parameters which are not identified under the null hypotheses this paper studies the asymptotic distribution theory for such tests the asymptotic distributions of standard test statistics are described as functionals of chi square processes in general the distributions depend upon a large number of unknown parameters we show that a transformation based upon a conditional probability measure yields an asymptotic distribution free of nuisance parameters and we show that this transformation can be easily approximated via simulation the theory is applied to threshold models with special attention given to the so called self exciting threshold autoregressive model monte carlo methods are used to assess the finite sample distributions the tests are applied to u s gnp growth rates and we find that potter s 1995 threshold effect in this series can be possibly explained by sampling variation

a criterion for the equivalence of the birkhoff rott and euler descriptions of vortex sheet evolution in this article we consider the evolution of vortex sheets in the plane both as a weak solution of the two dimensional incompressible euler equations and as a weak solution of the birkhoff rott equations we begin by discussing the classical birkhoff rott equations with respect to arbitrary parametrizations of the sheet we introduce a notion of weak solution to the birkhoff rott system and we prove consistency of this notion with the classical formulation of the equations our main purpose in this paper is to present a sharp criterion for the equivalence of the weak euler and weak birkhoff rott descriptions of vortex sheet dynamics

optimal tests when a nuisance parameter is present only under the alternative this paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null for example the results apply to tests of structural change with unknown changepoint the testing problem considered is nonstandard and the classical asymptotic optimality results for the lagrange multiplier wald and likelihood ratio do not apply a weighted average power criterion is used here to generate optimal tests this criterion is similar to that used by a wald 1943 to obtain the classical asymptotic optimality properties of wald tests in regular testing problems copyright 1994 by the econometric society

wigner functions and separability for finite systems a discussion of discrete wigner functions in phase space related to mutually unbiased bases is presented this approach requires mathematical assumptions which limits it to systems with density matrices defined on complex hilbert spaces of dimension pn where p is a prime number with this limitation it is possible to define a phase space and wigner functions in close analogy to the continuous case that is we use a phase space that is a direct sum of n two dimensional vector spaces each containing p2 points this is in contrast to the more usual choice of a two dimensional phase space containing p2n points a useful aspect of this approach is that we can relate complete separability of density matrices and their wigner functions in a natural way we discuss this in detail for bipartite systems and present the generalization to arbitrary numbers of subsystems when p is odd special attention is required for two qubits p 2 and our technique fails to establish the separability property for more than two qubits finally we give a brief discussion of hamiltonian dynamics in the language developed in the paper

finite time analyticity for the two and three dimensional kelvin helmholtz instability the well posed property for the finite time vortex sheet problem with analytic initial data was first conjectured by birkhoff in two dimensions and is shown here to hold both in two and three dimensions incompressible inviscid and irrotational flow with a velocity jump across an interface is assumed in two dimensions global existence of a weak solution to the euler equation with such initial conditions is established in three dimensions a lagrangian representation of the vortex sheet analogous to the birkhoff equation in two dimensions is presented

asymptotic theory for time series with changing mean and variance abstract the paper develops point estimation and asymptotic theory with respect to a semiparametric model for time series with moving mean and unconditional heteroscedasticity these two features are modelled nonparametrically whereas autocorrelations are described by a short memory stationary parametric time series model we first study the usual least squares estimate of the coefficient of the first order autoregressive model based on constant but unknown mean and variance allowing for both the latter to vary over time in a general way we establish its probability limit and a central limit theorem for a suitably normed and centred statistic giving explicit bias and variance formulae as expected mean variation is the main source of inconsistency and heteroscedasticity the main source of inefficiency though we discuss circumstances in which the estimate is consistent for and asymptotically normal about the autoregressive coefficient albeit inefficient we then consider standard implicitly defined whittle estimates of a more general class of short memory parametric time series model under otherwise more restrictive conditions when the mean is correctly assumed to be constant estimates that ignore the heteroscedasticity are again found to be asymptotically normal but inefficient allowing a slowly time varying mean we resort to trimming out of low frequencies to achieve the same outcome returning to finite order autoregression nonparametric estimates of the varying mean and variance are given asymptotic justification and forecasting formulae developed finite sample properties are studied by a small monte carlo simulation and an empirical example is also included

specification estimation and evaluation of smooth transition autoregressive models abstract this article considers the application of two families of nonlinear autoregressive models the logistic lstar and exponential estar autoregressive models this includes the specification of the model based on simple statistical tests linearity testing against smooth transition autoregression determining the delay parameter and choosing between lstar and estar models are discussed estimation by nonlinear least squares is considered as well as evaluating the properties of the estimated model the proposed techniques are illustrated by examples using both simulated and real time series

a multiple regime smooth transition heterogeneous autoregressive model for long memory and asymmetries in this paper we propose a flexible model to describe nonlinearities and long range dependence in time series dynamics the new model is a multiple regime smooth transition extension of the heterogeneous autoregressive har model which is specifically designed to model the behavior of the volatility inherent in financial time series the model is able to simultaneously approximate long memory behavior as well as describe sign and size asymmetries a sequence of tests is developed to determine the number of regimes and an estimation and testing procedure is presented monte carlo simulations evaluate the finite sample properties of the proposed tests and estimation procedures we apply the model to several dow jones industrial average index stocks using transaction level data from the trades and quotes database that covers ten years of data we find strong support for long memory and both sign and size asymmetries furthermore the new model when combined with the linear har model is viable and flexible for purposes of forecasting volatility

mutually unbiased bases generalized spin matrices and separability abstract a collection of orthonormal bases for a complex d dimensional hilbert space is called mutually unbiased mub if for any two vectors v and w from different bases the square of the inner product equals 1 d v w 2 1 d the mub problem is to prove or disprove the existence of a maximal set of d 1 bases it has been shown in ann phys 191 1989 363 that such a collection exists if d is a power of a prime number p we revisit this problem and use d d generalizations of the pauli spin matrices to give a constructive proof of this result specifically we give explicit representations of commuting families of unitary matrices whose eigenvectors solve the mub problem additionally we give formulas from which the orthogonal bases can be readily computed we show how the techniques developed here provide a natural way to analyze the separability of the bases the techniques used require properties of algebraic field extensions and the relevant part of that theory is included in the appendix

impulse response analysis in nonlinear multivariate models abstract this paper presents a unified approach to impulse response analysis which can be used for both linear and nonlinear multivariate models after discussing the advantages and disadvantages of traditional impulse response functions for nonlinear models we introduce the concept of a generalized impulse response function which we argue is applicable to both linear and nonlinear models we develop measures of shock persistence and asymmetric effects of shocks derived from the generalized impulse response function we illustrate the use of these measures for a nonlinear bivariate model of us output and the unemployment rate