estimating dynamic equilibrium models using mixed frequency macro and financial data abstract we provide a framework for inference in dynamic equilibrium models including financial market data at daily frequency along with macro series at standard lower frequency our formulation of the macro finance model in continuous time conveniently accounts for the difference in observation frequency we suggest the use of martingale estimating functions mef to infer the structural parameters of the model directly through a nonlinear scheme this method is compared to regression based methods and the generalized method of moments gmm we illustrate our approaches by estimating various versions of the ak vasicek model with mean reverting interest rates we provide asymptotic theory and monte carlo evidence on the small sample behavior of the estimators and report empirical estimates using 30 years of us macro and financial data

renormalization group and asymptotics of solutions of nonlinear parabolic equations we present a general method for studying long time asymptotics of nonlinear parabolic partial differential equations the method does not rely on a priori estimates such as the maximum principle it applies to systems of coupled equations to boundary conditions at infinity creating a front and to higher possibly fractional differential linear terms we present in detail the analysis for nonlinear diffusion type equations with initial data falling off at infinity and also for data interpolating between two different stationary solutions at infinity in an accompanying paper 5 the method is applied to systems of equations where some variables are slaved such as the complex ginzburg landau equation c 1994 john wiley sons inc

existence and stability of propagating fronts for an autocatalytic reaction diffusion system we study a one dimensional reaction diffusion system which describes an isothermal autocatalytic chemical reaction involving both a quadratic a b 2b and a cubic a 2b 3b autocatalysis the parameters of this system are in the ratio d d b d a of the diffusion constants of the reactant a and the autocatalyst b and the relative activity ii of the cubic reaction first for all values of d 0 and k greater than or equal to 0 we prove the existence of a family of propagating fronts or travelling waves describing the advance of the reaction in particular in the quadratic case k 0 we recover the results of billingham and needham phil trans r sec london a 334 1991 1 24 then if d is close to 1 and k is sufficiently small we prove using energy functionals that these propagating fronts are stable against small perturbations in exponentially weighted sobolev spaces this extends part of the results that are known for the scalar equation to which our system reduces when d 1 c 1998 elsevier science b v

stability of strong travelling waves for a non local time delayed reaction diffusion equation the paper is concerned with a non local time delayed reaction diffusion equation we prove the time asymptotic stability of a travelling wavefront without a smallness assumption on its wavelength i e the so called strong wavefront by means of the technical weighted energy method when the initial perturbation around the wave is small the exponential convergent rate is also given selection of a suitable weight plays a key role in the proof

stability of moving fronts in the ginzburg landau equation we use renormalization group ideas to study stability of moving fronts in the ginzburg landau equation in one spatial dimension in particular we prove stability of the real fronts under complex perturbations this extends the results of aronson and weinberger to situations where the maximum principle is inapplicable and constitutes a step in proving the general marginal stability hypothesis for the ginzburg landau equation

discrete vakonomic mechanics discretizations of vakonomic mechanics are developed by using the methodology of variational integrators the resulting algorithms are symplectic in some sense that we will explain and preserve the momentum map associated with a lie group of symmetries a specific example illustrating the theory is tested numerically

an exact discrete analog of an open linear non stationary first order continuous time system with mixed sample abstract this article deals with the derivation of an exact discrete model that corresponds to an open linear non stationary first order continuous time system with mixed stock and flow data this exact discrete model is under appropriate additional conditions a stationary autoregressive moving average time series model and may allow one to obtain asymptotically efficient estimators of the parameters describing the continuous time system

systematic sampling temporal aggregation seasonal adjustment and cointegration theory and evidence abstract we consider in this paper the theoretical possibility that a unit root at the zero frequency can arise because of temporal aggregation of series which in fact possess a unit root possibly at some seasonal frequency thus the long run component of a time series can be misinterpreted similarly a finding of cointegration at the zero frequency could arise between a series which has a unit root at the zero frequency and another with a unit root at another frequency empirical evidence using an international macroeconomic data set is presented which suggests that the above theoretical results have some practical validity

symplectic energy momentum preserving variational integrators the purpose of this paper is to develop variational integrators for conservative mechanical systems that are symplectic and energy and momentum conserving to do this a space time view of variational integrators is employed and time step adaptation is used to impose the constraint of conservation of energy criteria for the solvability of the time steps and some numerical examples are given

invariant conservation law preserving discretizations of linear and nonlinear wave equations symmetry and conservation law preserving finite difference discretizations are obtained for linear and nonlinear one dimensional wave equations on five and nine point stencils using the theory of lie point symmetries of difference equations and the discrete direct multiplier method of conservation law construction in particular for the linear wave equation an explicit five point scheme is presented that preserves the discrete analogs of its basic geometric point symmetries and six of the corresponding conservation laws for a class of nonlinear wave equations arising in hyperelasticity a nine point implicit scheme is constructed preserving four point symmetries and three local conservation laws other discretizations of the nonlinear wave equations preserving different subsets of conservation laws are discussed

non linear stability of modulated fronts for the swift hohenberg equation we consider front solutions of the swift hohenberg equation t u 1 x 2 2 u 2 u u 3 these are traveling waves which leave in their wake a periodic pattern in the laboratory frame using renormalization techniques and a decomposition into bloch waves we show the non linear stability of these solutions it turns out that this problem is closely related to the question of stability of the trivial solution for the model problem t u x t x 2 u x t 1 tanh x ct u x t u x t p with p 3 in particular we show that the instability of the perturbation ahead of the front is entirely compensated by a diffusive stabilization which sets in once the perturbation has hit the bulk behind the front

pattern propagation in nonlinear dissipative systems abstract we discuss the problem of pattern selection in situations where a stable nonuniform state of a nonlinear dissipative system propagates into an initially unstable homogeneous region our strategy is to consider this process as a generalization of front propagation in a nonlinear diffusion problem for which rigorous results are known and we point out that these known properties are consistent with a marginal stability hypothesis that has been suggested in the theory of dendritic crystal growth we then describe a more general interpretation of the marginal stability hypothesis and finally present numerical evidence for its validity from three different pattern forming models

structural estimation of jump diffusion processes in macroeconomics this paper shows how to solve and estimate a continuous time dynamic stochastic general equilibrium dsge model with jumps it also shows that a continuous time formulation can make it simpler relative to its discrete time version to compute and estimate the deep parameters using the likelihood function when non linearities and or non normalities are considered we illustrate our approach by solving and estimating the stochastic ak and the neoclassical growth models our monte carlo experiments demonstrate that non normalities can be detected for this class of models moreover we provide strong empirical evidence for jumps in aggregate us data

stability of fronts for a kpp system ii the critical case abstract we study a system of n 1 coupled semilinear parabolic equations on the real line which depends on a small parameter and reduces to the scalar kolmogorov petrovsky piscounov kpp equation when 0 under appropriate scaling the system has a family of traveling fronts parametrized by their speed when 2 as in the scalar kpp case the case of critical speed 2 say is investigated and it is shown that the system inherits some crucial properties of the kpp equation when is small in particular the asymptotic stability of the front in a local and semiglobal sense first we describe the properties of the front and then apply functional arguments to prove its local stability in an adequate weighted sobolev space moreover the decay rate of the perturbations is shown to be polynomial in time finally we show a semiglobal stability property of the front which also is inherited from the scalar kpp equation

discrete time lagrangian mechanics on lie groups with an application to the lagrange top we develop the theory of discrete time lagrangian mechanics on lie groups originated in the work of veselov and moser and the theory of lagrangian reduction in the discrete time setting the results thus obtained are applied to the investigation of an integrable time discretization of a famous integrable system of classical mechanics the lagrange top we recall the derivation of the euler poinsot equations of motion both in the frame moving with the body and in the rest frame the latter ones being less widely known we find a discrete time lagrange function turning into the known continuous time lagrangian in the continuous limit and elaborate both descriptions of the resulting discrete time system namely in the body frame and in the rest frame this system naturally inherits poisson properties of the continuous time system the integrals of motion being deformed the discrete time lax representations are also found kirchhoff s kinetic analogy between elastic curves and motions of the lagrange top is also generalised to the discrete context

mechanical systems subject to holonomic constraints differential algebraic formulations and conservative integration abstract the numerical integration in time of the equations of motion for mechanical systems subject to holonomic constraints is considered schemes are introduced for the direct treatment of a differential algebraic form of the equations that preserve the constraints the total energy and other integrals such as linear and angular momentum arising from affine symmetries moreover the schemes can be shown to preserve the property of time reversibility in an appropriate sense an example is given to illustrate various aspects of the proposed methods

intrinsic random functions and the paradox of l f noise by means of a generalized fejer theorem certain stationary increment random functions and random fields are shown to possess nonintegrable time invariant spectra the periodogram computed from a stationary increment process is shown to have the same sort of asymptotic statistical properties e g central limit theorem as the periodogram of a stationary process does these results throw light on the paradoxical nature of flicker noise and related phenomena that occur with random fields

multisymplectic geometry variational integrators and nonlinear pdes this paper presents a geometric variational approach to continuous and discrete mechanics and field theories using multisymplectic geometry we show that the existence of the fundamental geometric structures as well as their preservation along solutions can be obtained directly from the variational principle in particular we prove that a unique multisymplectic structure is obtained by taking the derivative of an action function and use this structure to prove covariant generalizations of conservation of symplecticity and noether s theorem natural discretization schemes for pdes which have these important preservation properties then follow by choosing a discrete action functional in the case of mechanics we recover the variational symplectic integrators of veselov type while for pdes we obtain covariant spacetime integrators which conserve the corresponding discrete multisymplectic form as well as the discrete momentum mappings corresponding to symmetries we show that the usual notion of symplecticity along an infinite dimensional space of fields can be naturally obtained by making a spacetime split all of the aspects of our method are demonstrated with a nonlinear sine gordon equation including computational results and a comparison with other discretization schemes

d alembert lagrange analytical dynamics for nonholonomic systems the d alembert lagrange principle dlp is designed primarily for dynamical systems under ideal geometric constraints although it can also cover linear velocity constraints its application to nonlinear kinematic constraints has so far remained elusive mainly because there is no clear method whereby the set of linear conditions that restrict the virtual displacements can be easily extracted from the equations of constraint on recognition that the commutation rule traditionally accepted for velocity displacements in lagrangian dynamics implies displaced states that do not satisfy the kinematic constraints we show how the property of possible displaced states can be utilized ab initio so as to provide an appropriate set of linear auxiliary conditions on the displacements which can be adjoined via lagrange s multipliers to the d alembert lagrange equation to yield the equations of state and also new transpositional relations for nonholonomic systems the equations of state so obtained for systems under general nonlinear velocity and acceleration constraints are shown to be identical with those derived in appendix a from the quite different gauss principle the present advance therefore solves a long outstanding problem on the application of dlp to ideal nonholonomic systems and as an aside provides validity to axioms as the chetaev rule previously left theoretically unjustified a more general transpositional form of the boltzmann hamel equation is also obtained

limit cycles in the presence of convection a traveling wave analysis we consider a diffusion model with limit cycle reaction functions in an unbounded domain diffusion spreads the pattern outwards from the source convection adds instability to the reaction diffusion system the result of this instability is a readiness to create a pattern we choose the lambda omega reaction functions for their simple limit cycle we carry out a transformation of the dependent variables into polar form from this we consider the initiation of the pattern to approximate a traveling wave we carry out numerical experiments to test our analysis these confirm the premise of the analysis that the initiation can be modeled by a traveling wave furthermore the analysis produces a good estimate of the numerical results most significantly we confirm that the pattern consists of two different types

discrete versions of some classical integrable systems and factorization of matrix polynomials discrete versions of several classical integrable systems are investigated such as a discrete analogue of the higher dimensional force free spinning top euler arnold equations the heisenberg chain with classical spins and a new discrete system on the stiefel manifold the integrability is shown with the help of a lax pair representation which is found via a factorization of certain matrix polynomials the complete description of the dynamics is given in terms of abelian functions the flow becomes linear on a prym variety corresponding to a spectral curve the approach is also applied to the billiard problem in the interior of ann dimensional ellipsoid

bias in estimating multivariate and univariate diffusions a b s t r a c t multivariate continuous time models are now widely used in economics and finance empirical applications typically rely on some process of discretization so that the system may be estimated with discrete data this paper introduces a framework for discretizing linear multivariate continuous time systems that includes the commonly used euler and trapezoidal approximations as special cases and leads to a general class of estimators for the mean reversion matrix asymptotic distributions and bias formulae are obtained for estimates of the mean reversion parameter explicit expressions are given for the discretization bias and its relationship to estimation bias in both multivariate and in univariate settings in the univariate context we compare the performance of the two approximation methods relative to exact maximum likelihood ml in terms of bias and variance for the vasicek process the bias and the variance of the euler method are found to be smaller than the trapezoidal method which are in turn smaller than those of exact ml simulations suggest that when the mean reversion is slow the approximation methods work better than ml the bias formulae are accurate and for scalar models the estimates obtained from the two approximate methods have smaller bias and variance than exact ml for the square root process the euler method outperforms the nowman method in terms of both bias and variance simulation evidence indicates that the euler method has smaller bias and variance than exact ml nowman s method and the milstein method

frequency domain estimation of temporally aggregated gaussian cointegrated systems this paper considers joint estimation of long run equilibrium coefficients and parameters governing the short run dynamics of a fully parametric gaussian cointegrated system formulated in continuous time the model allows the stationary disturbances to be generated by a stochastic differential equation system and for the variables to be a mixture of stocks and flows we derive a precise form for the exact discrete analogue of the continuous time model in triangular error correction form which acts as the basis for frequency domain estimation of the unknown parameters using discrete time data we formally establish the order of consistency and the asymptotic sampling properties of such an estimator the estimator of the cointegrating parameters is shown to converge at the rate of the sample size to a mixed normal distribution while that of the short run parameters converges at the rate of the square root of the sample size to a limiting normal distribution

error correction and long run equilibrium in continuous time this paper deals with error correction models ecm s and cointegrated systems that are formulated in continuous time long run equilibrium coefficients in the continuous system are always identified in the discrete time reduced form so that there is no aliasing problem for these parameters the long run relationships are also preserved under quite general data filtering frequency domain procedures are outlined for estimation and inference these methods are asymptotically optimal under gaussian assumptions and they have the advantages of simplicity of computation and generality of specification thereby avoiding some methodological problems of dynamic specification in addition they facilitate the treatment of data irregularities such as mixed stock and flow data and temporally aggregated partial equilibrium formulations models with restricted cointegrating matrices are also considered

on the geometry of non holonomic lagrangian systems we present a geometric framework for non holonomic lagrangian systems in terms of distributions on the configuration manifold if the constrained system is regular an almost product structure on the phase space of velocities is constructed such that the constrained dynamics is obtained by projecting the free dynamics if the constrained system is singular we develop a constraint algorithm which is very similar to that developed by dirac and bergmann and later globalized by gotay and nester special attention to the case of constrained systems given by connections is paid in particular we extend the results of koiller for caplygin systems an application to the so called non holonomic geometry is given

variational integrators and the newmark algorithm for conservative and dissipative mechanical systems the purpose of this work is twofold first we demonstrate analytically that the classical newmark family as well as related integration algorithms are variational in the sense of the veselov formulation of discrete mechanics such variational algorithms are well known to be symplectic and momentum preserving and to often have excellent global energy behavior this analytical result is veried through numerical examples and is believed to be one of the primary reasons that this class of algorithms performs so well second we develop algorithms for mechanical systems with forcing and in particular for dissipative systems in this case we develop integrators that are based on a discretization of the lagrange d alembert principle as well as on a variational formulation of dissipation it is demonstrated that these types of structured integrators have good numerical behavior in terms of obtaining the correct amounts by which the energy changes over the integration run

forecasting discrete stock and flow data generated by a second order continuous time system abstract this paper extends recent results on forecasting discrete stock and flow data generated by a continuous time model formulated as a system of second order stochastic differential equations an algorithm is presented for the computation of the forecasts and an expression for the asymptotic mean square error matrix of the forecasts is also derived these results when combined with the estimation algorithm in 1 provide a computationally efficient method of estimation forecasting and inference in continuous time systems

time discretized variational formulation of non smooth frictional contact the present work extends the non smooth contact class of algorithms introduced by kane et al to the case of friction the formulation specifically addresses contact geometries e g involving multiple collisions between tightly packed non smooth bodies for which neither normals nor gap functions can be properly defined a key aspect of the approach is that the incremental displacements follow from a minimum principle the objective function comprises terms which account for inertia strain energy contact friction and external forcing the euler lagrange equations corresponding to this extended variational principle are shown to be consistent with the equations of motion of solids in frictional contact in addition to its value as a basis for formulating numerical algorithms the variational framework offers theoretical advantages as regards the selection of trajectories in cases of non uniqueness we present numerical and analytical examples which demonstrate the good momentum and energy conservation characteristics of the numerical algorithms as well as the ability of the approach to account for stick and slip conditions

the estimation of systems of joint differential difference equations this paper considers estimation of the parameters of systems of joint differential difference equations the existence and uniqueness of the solution to the model are demonstrated and the properties of the continuous time and discretely sampled processes are derived the focus is on frequency domain methods throughout one of the main technical achievements being the derivation of a computable expression for the spectral density function of the discretely observed data which are allowed to be mixtures of stock and flow variables a frequency domain gaussian estimator is proposed and its consistency and asymptotic normality are established without requiring the assumption that the data are gaussian the finite sample properties of the estimator are assessed in a small simulation exercise

travelling kinks in schlogl s second model for non equilibrium phase transitions using the separation technique developed by osborne and stuart 1980 travelling wave solutions are written down for the nonlinear reaction diffusion equation of schlogl s second model assuming that the necessary conditions for the static phase coexistence are satisfied

explicit form of approximate transition probability density functions of diffusion processes abstract a continuous time diffusion process is very popular in modeling and provides useful tools to analyze particularly but not restricted to a variety of economic and financial variables the transition probability density function tpdf of a diffusion process plays an important role in understanding and explaining the dynamics of the process a new way to find closed form approximate tpdfs for multivariate diffusions is proposed in this paper this method can be applied to general multivariate time inhomogeneous diffusion processes as long as roughly speaking they have smooth drift and volatility functions a diffusion process is said to be reducible if it can be converted into a unit diffusion process where the volatility is the identity matrix we have established how to obtain the approximate tpdf of a reducible diffusion explicitly when a diffusion process is not reducible an explicit form of approximate tpdf can be obtained by using the results in ait sahalia 2008 and choi 2013 the tpdf expansion suggested here enables us to obtain a recursive formula for the coefficient of the approximate tpdf for a multivariate jump diffusion monte carlo simulation studies of conducting maximum likelihood estimation mle using our approximations provide convincing evidence that our tpdf expansion can be used for the mle when the true tpdf is unavailable we also applied our approximate tpdfs to option pricing the differences between our option prices and those from the extended black scholes formula are shown to be quite small this implies that our methods can be employed to price assets whose underlying state variables follow general diffusion models

the dimensionality of the aliasing problem in models with rational spectral densities this paper reconsiders the aliasing problem of identifying the parameters of a continuous time stochastic process from discrete time data it analyzes the extent to which restricting attention to processes with rational spectral density matrices reduces the number of observationally equivalent models it focuses on rational specifications of spectral density matrices since rational parameterizations are commonly employed in the analysis of the time series data this abstract was borrowed from another version of this item

continuous time state space modeling of panel data by means of sem maximum likelihood parameter estimation of the continuous time linear stochastic state space model is considered on the basis of largen discrete time data using a structural equation modeling sem program random subject effects are allowed to be part of the model the exact discrete model edm is employed which links the discrete time model parameters to the underlying continuous time model parameters by means of nonlinear restrictions the edm is generalized to cover not only time invariant parameters but also the cases of stepwise time varying piecewise time invariant parameters and parameters varying continuously over time according to a general polynomial scheme the identification of the continuous time parameters is discussed and an educational example is presented

existence of traveling waves of invasion for ginzburg landau type problems in infinite cylinders we study a class of systems of reaction diffusion equations in infinite cylinders which arise within the context of ginzburg landau theories and describe the kinetics of phase transformation in second order or weakly first order phase transitions with non conserved order parameters we use a variational characterization to study the existence of a special class of traveling wave solutions which are characterized by a fast exponential decay in the direction of propagation our main result is a simple verifiable criterion for existence of these traveling waves under the very general assumptions of non linearities we also prove boundedness regularity and some other properties of the obtained solutions as well as several sufficient conditions for existence or non existence of such traveling waves and give rigorous upper and lower bounds for their speed in addition we prove that the speed of the obtained solutions gives a sharp upper bound for the propagation speed of a class of disturbances which are initially sufficiently localized we give a sample application of our results using a computer assisted approach

geometric integrators and nonholonomic mechanics a geometric derivation of nonholonomic integrators is developed it is based in the classical technique of generating functions adapted to the special features of nonholonomic systems the theoretical methodology and the integrators obtained are different from those obtained in cortes and martinez nonholonomic integrators nonlinearity 14 1365 1392 2001 in the case of mechanical systems with linear constraints a family of geometric integrators preserving the nonholonomic constraints is given

renormalization group and the ginzburg landau equation we use renormalization group methods to prove detailed long time asymptotics for the solutions of the ginzburg landau equations with initial data approaching asx different spiraling stationary solutions a universal pattern is formed depending only on this asymptotics at spatial infinity

closed form likelihood expansions for multivariate time inhomogeneous diffusions the aim of this paper is to find approximate log transition density functions for multivariate timeinhomogeneous diffusions in closed form there are many empirical evidences that the underlying data generating processes for many economic variables might change over time one possible way to explain the time dependent behavior of state variables is to model the drift or volatility terms as functions of time as well as state variables closed form likelihood expansions for multivariate time homogeneous diffusions have been obtained by ait sahalia 2008 this research is built on his work and extends his results to time inhomogeneous cases simulation study reveals that our method yields a very accurate approximate likelihood function that can be a good candidate when the true likelihood function is unavailable

discrete and continuous time cointegration we give a definition of integration and cointegration in continuous time and study characterizations of those definitions in particular for carma continuous time arma processes we check also that such singularities in carma processes may imply unit roots problems in the discretized corresponding process then error correction representations in continuous time are exhibited and discussed and a general theorem of representation giving a precise description of the singularities is proved lastly we look at other singularities emphasizing the importance of estimating the continuous time model if it is the true one a one dimensional noise can generate a two dimensional regular ar process

frequency domain estimation of cointegrating vectors with mixed frequency and mixed sample data this paper proposes a simple method for exploiting the information contained in mixed frequency and mixed sample data in the estimation of cointegrating vectors the asymptotic properties of easy to compute spectral regression estimators of the cointegrating vectors are derived and these estimators are shown to belong to the class of optimal cointegration estimators furthermore wald statistics based on these estimators have asymptotic chi square distributions which enable inferences to be made straightforwardly simulation experiments suggest that the spectral regression estimators considered perform well in finite samples and are at least as good as time domain fully modified estimators the finite sample size and power properties of the spectral regression based wald statistic are also found to be good

solutions without phase slip for the ginsburg landau equation we consider the ginsburg landau equation for a complex scalar field in one dimension and consider initial data which have two different stationary solutions as their limits in space asx if these solutions are not very different then we show that the initial data will evolve to a stationary solution by a phase melting process which avoids phase slips i e which does not go through zero amplitude

an analogue model of phase averaging procedures abstract this paper analyses the statistical and econometric effects that fixed n period phase averaging has on time series generated by some simple dynamic processes we focus on the variance and autocorrelation of the data series and of the disturbance term for levels and difference equations involving the phase average data further we consider the effect of phase averaging on the exogeneity of variables in those equations and the implications phase averaging has for conducting statistical inference to illustrate these analytical results we examine features of the observed annual and phase average series on money income prices and interest rates from friedman and schwartz 1982 while the analogue model developed above is a simplified characterisation of the nber phase averaging techniques employed by friedman and schwartz it does offer several insights into the likely consequences of this approach

the non linear stability of front solutions for parabolic partial differential equations for the ginzburg landau equation and similar reaction diffusion equations on the line we show convergence of complex perturbations of front solutions towards the front solutions by exhibiting a coercive functional

gaussian estimation of structural parameters in higher order continuous time dynamic models this paper is concerned with the efficient estimation of structural parameters in closed linear systems of higher order stochastic differential equations when the data are in discrete form and the model generally includes both stock and flow variables a general existence and uniqueness theorem for the solution of such a system is proved and used in the rigorous derivation of exact discrete models satisfied by the various types of data it is shown how these models can be used in the computation of various asymptotically efficient estimates obtained by the maximization of the gaussian likelihood or approximations to it

almost global existence and transient self similar decay for poiseuille flow at criticality for exponentially long times abstract we consider nonlinear diffusion equations with critical exponent as tu x2u u3 with x r for small initial data in l1 l it is well known that almost all solutions of this system explode in finite time however we make the observation that in terms of the norm of the initial conditions it takes an exponentially long time moreover before explosion the l norm of such solutions becomes exponentially small which makes it almost impossible to observe the instability in experiments as an application we consider the long time transient self similar decay to unstable poiseuille flow at criticality for exponentially long times this together with a subcritical bifurcation and short time transient amplification is a principal obstruction in all attempts to measure the critical reynolds number for this experiment more and more precisely

systematic sampling and temporal aggregation in time series models abstract within the class of armax models we consider the effects systematic sampling or temporal aggregation may have on the dynamic relationships between variables these include changes in lag lengths and causal ordering and may occur even in simple models some implications for the modelling of time series are noted for the subclass of arima models we also analyse the consequences of sampling or aggregating seasonal models

towards a hamilton jacobi theory for nonholonomic mechanical systems in this paper we obtain a hamilton jacobi theory for nonholonomic mechanical systems the results are applied to a large class of nonholonomic mechanical systems the so called caplygin systems

self similar decay of localized perturbations in the integral boundary layer equation abstract the integral boundary layer equation ible arises as a long wave approximation for the flow of a viscous incompressible fluid down an inclined plane the trivial solution of the ible is linearly at best marginally stable i e it has essential spectrum at least up to the imaginary axis here we show that in the stable case this trivial solution is in fact nonlinearly stable with a burgers like self similar decay of localized perturbations the proof uses renormalization theory and the fact that in the stable case burgers equation is the amplitude equation for long small amplitude waves in the ible

impulse response functions based on a causal approach to residual orthogonalization in vector autoregressions abstract a data determined method for testing structural models of the errors in vector autoregressions is discussed the method can easily be combined with prior economic knowledge and a subjective analysis of data characteristics to yield valuable information concerning model selection and specification in one dimension it turns out that standard t statistics can be used to test the various overidentifying restrictions that are implied by a model in another dimension the method compares a priori knowledge of a structural model for the errors with the properties exhibited by the data thus this method may help to ensure that orderings of the errors for impulse response and forecast error variance decomposition analyses are sensible given the data two economic examples are used to illustrate the method

a multiscale asymptotic analysis of time evolution equations on the complex plane using an appropriate norm on the space of entire functions we extend to the complex plane the renormalization group method as developed by bricmont et al the method is based upon a multiscale approach that allows for a detailed description of the long time asymptotics of solutions to initial value problems the time evolution equation considered here arises in the study of iterations of the block spin renormalization group transformation for the hierarchical n vector model we show that for initial conditions belonging to a certain frechet space of entire functions of exponential type the asymptotics is universal in the sense that it is dictated by the fixed point of a certain operator acting on the space of initial conditions

travelling waves in radially symmetric parabolic systems on montre que toutes les solutions ondes planes de propagation ou stationnaire de certains systemes paraboliques a symetrie radiale peuvent etre trouvees en resolvant une equation differentielle scalaire associee

a new delta expansion for multivariate diffusions via the ito taylor expansion abstract in this paper we develop a new delta expansion approach to deriving analytical approximation to the transition densities of multivariate diffusions using the ito taylor expansion of the conditional expectation of the dirac delta function our approach yields an explicit recursive formulas for the expansion coefficients and is universally applicable for a wide spectrum of models particularly the time inhomogeneous non affine irreducible multivariate diffusions we show that this new approach can be viewed as an extension of ait sahalia 2002 and lee et al 2014 to the case of multivariate models the derived expansions are proved to converge to the true probability density as the observational time interval shrinks the obtained approximations can thereby be used to carry out the maximum likelihood estimation for the diffusions with discretely observed data extensive numerical experiments demonstrate the accuracy and effectiveness of our approach

fully nonparametric estimation of scalar diffusion models we propose a functional estimation procedure for homogeneous stochastic differential equations based on a discrete sample of observations and with minimal requirements on the data generating process we show how to identify the drift and diffusion function in situations where one or the other function is considered a nuisance parameter the asymptotic behavior of the estimators is examined as the observation frequency increases and as the time span lengthens we prove almost sure consistency and weak convergence to mixtures of normal laws where the mixing variates depend on the chronological local time of the underlying diffusion process that is the random time spent by the process in the vicinity of a generic spatial point the estimation method and asymptotic results apply to both stationary and nonstationary recurrent processes

frequency domain gaussian estimation of temporally aggregated cointegrated systems this paper discusses the joint estimation of the long run equilibrium coe cients and the parameters governing the short run dynamics of a fully parametric cointegrated system formulated in continuous time the model allows the stationary disturbances to be generated by a stochastic di erential equation system and for the variables to be a mixture of stocks and flows we derive a precise form for the exact discrete analogue of the continuous time model in triangular error correction form which acts as the basis for frequency domain gaussian estimation of the unknown parameters using discrete time data we formally establish the order of consistency and the asymptotic sampling properties of such an estimator the function of the data that estimates the cointegrating parameters is shown to converge at the rate of the sample size to a mixed normal distribution while that estimating the short run parameters converges at the rate of the square root of the sample size to a limiting normal distribution

extended yule walker identification of varma models with single or mixed frequency data chen and zadrozny 1998 developed the linear extended yule walker xyw method for determining the parameters of a vector autoregressive var model with available covariances of mixed frequency observations on the variables of the model if the parameters are determined uniquely for available population covariances then the var model is identified the present paper extends the original xyw method to an extended xyw method for determining all arma parameters of a vector autoregressive moving average varma model with available covariances of single or mixed frequency observations on the variables of the model the paper proves that under conditions of stationarity regularity miniphaseness controllability observability and diagonalizability on the parameters of the model the parameters are determined uniquely with available population covariances of single or mixed frequency observations on the variables of the model so that the varma model is identified with the single or mixed frequency covariances

invariant painleve analysis and coherent structures of two families of reaction diffusion equations exact closed form coherent structures pulses fronts domain walls having the form of complicated traveling waves are constructed for two families of reaction diffusion equations by the use of invariant painleve analysis these analytical solutions which are derived directly from the underlying pde s are investigated in the light of restrictions imposed by the ode that any traveling wave reduction of the corresponding pde must satisfy in particular it is shown that the coherent structures a asymptotically satisfy the ode governing traveling wave reductions and b are accessible to the pde from compact support initial conditions the solutions are compared with each other and with previously known solutions of the equations

reduction of constrained mechanical systems and stability of relative equilibria a mechanical system with perfect constraints can be described under some mild assumptions as a constrained hamiltonian system m h d w m thephase space is a symplectic manifold h thehamiltonian a smooth function onm d theconstraint submanifold a submanifold ofm andw theprojection bundle a vector sub bundle oft d m the reduced tangent bundle alongd we prove that when these data satisfy some suitable conditions the time evolution of the system is governed by a well defined differential equation ond we define constrained hamiltonian systems with symmetry and prove a reduction theorem application of that theorem is illustrated on the example of a convex heavy body rolling without slipping on a horizontal plane two other simple examples show that constrained mechanical systems with symmetry may have an attractive or repulsive set of relative equilibria

reduction of some classical non holonomic systems with symmetry two types of nonholonomic systems with symmetry are treated i the configuration space is a total space of a g principal bundle and the constraints are given by a connection ii the configuration space is g itself and the constraints are given by left invariant forms the proofs are based on the method of quasicoordinates in passing a derivation of the maurer cartan equations for lie groups is obtained simple examples are given to illustrate the algorithmical character of the main results

diffusive stability of spatial periodic solutions of the swift hohenberg equation we are interested in the nonlinear stability of the eckhaus stable equilibria of the swift hohenberg equation on the infinite line with respect to small integrable perturbations the difficulty in showing stability for these stationary solutions comes from the fact that their linearizations possess continuous spectrum up to zero the nonlinear stability problem is treated with renormalization theory which allows us to show that the nonlinear terms are irrelevant i e that the fully nonlinear problem behaves asymptotically as the linearized one which is under a diffusive regime

nonholonomic mechanical systems with symmetry this work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of lagrangian mechanics and with a view to control theoretical applications the basic methodology is that of geometric mechanics applied to the formulation of lagrange d alembert generalizing the use of connections and momentum maps associated with a given symmetry group to this case we begin by formulating the mechanics of nonholonomic systems using an ehresmann connection to model the constraints and show how the curvature of this connection enters into lagrange s equations unlike the situation with standard configuration space constraints the presence of symmetries in the nonholonomic case may or may not lead to conservation laws however the momentum map determined by the symmetry group still satisfies a useful differential equation that decouples from the group variables this momentum equation which plays an important role in control problems involves parallel transport operators and is computed explicitly in coordinates an alternative description using a body reference frame relates part of the momentum equation to the components of the euler poincar e equations along those symmetry directions consistent with the constraints one of the purposes of this paper is to derive this evolution equation for the momentum and to distinguish geometrically and mechanically the cases where it is conserved and those where it is not an example of the former is a ball or vertical disk rolling on a flat plane and an example of the latter is the snakeboard a modified version of the skateboard which uses momentum coupling for locomotion generation we construct a synthesis of the mechanical connection and the ehresmann connection defining the constraints obtaining an important new object we call the nonholonomic connection when the nonholonomic connection is a principal connection for the given symmetry group we show how to perform lagrangian reduction in the presence of nonholonomic constraints generalizing previous results which only held in special cases several detailed examples are given to illustrate the theory september 1994 revised march 1995 revised june 1995

seasonal bvar models abstract many authors have stressed the importance of using seasonally unadjusted data in modelling time series however few seasonal multivariate methodologies are currently available in this paper we extend the bayesian vector autoregressive bvar methodology of litterman 1979 1984 1986 doan litterman and sims 1984 and sims 1989 to the context of seasonal time series we examine some possible modifications to the regular litterman s priors along three time domain specifications often encountered in seasonal time series modelling we assess the forecasting performance of the seasonal bvar models in the context of a monthly model of the u s economy 1967 1 1989 9 comprising both seasonal and nonseasonal variables

mechanical integrators derived from a discrete variational principle many numerical integrators for mechanical system simulation are created by using discrete algorithms to approximate the continuous equations of motion in this paper we present a procedure to construct time stepping algorithms that approximate the flow of continuous odes for mechanical systems by discretizing hamilton s principle rather than the equations of motion the discrete equations share similarities to the continuous equations by preserving invariants including the symplectic form and the momentum map we first present a formulation of discrete mechanics along with a discrete variational principle we then show that the resulting equations of motion preserve the symplectic form and that this formulation of mechanics leads to conservation laws from a discrete version of noether s theorem we then use the discrete mechanics formulation to develop a procedure for constructing symplectic momentum mechanical integrators for lagrangian systems with holonomic constraints we apply the construction procedure to the rigid body and the double spherical pendulum to demonstrate numerical properties of the integrators

existence and stability of traveling fronts in the extended fisher kolmogorov equation abstract we study traveling wave solutions to a general fourth order differential equation that is a singular perturbation of the fisher kolmogorov equation we apply the geometric method for singularly perturbed systems to show that for every positive wavespeed there exists a traveling wave also we find that there exists a critical wavespeed c which divides these solutions into monotonic c c and oscillatory c c solutions we show that the monotonic fronts are locally stable under perturbations in appropriate weighted sobolev spaces by using various energy functionals

the estimation of continuous time models with mixed frequency data this paper derives exact representations for discrete time mixed frequency data generated by an underlying multivariate continuous time model allowance is made for different combinations of stock and flow variables as well as deterministic trends and the variables themselves may be stationary or nonstationary and possibly cointegrated the resulting discrete time representations allow for the information contained in high frequency data to be utilised alongside the low frequency data in the estimation of the parameters of the continuous time model monte carlo simulations explore the finite sample performance of the maximum likelihood estimator of the continuous time system parameters based on mixed frequency data and a comparison with extant methods of using data only at the lowest frequency is provided an empirical application demonstrates the methods developed in the paper and it concludes with a discussion of further ways in which the present analysis can be extended and refined

a nonnested approach to testing continuous time models against discrete alternatives abstract this paper considers a test of two competing models when one is formulated in continuous time as a system of stochastic differential equations and the other is formulated in discrete time as a system of nonlinear equations since the competing hypotheses are nonnested the appropriate formulae are derived for the implementation of the cox test this approach is illustrated with an application to the demand for food and related products in the united kingdom