statistical inference on cointegration rank in error correction models with stationary covariates this paper aims to extend the cointegration rank test to error correction models with exogenous stationary covariates the distribution of the likelihood ratio statistic is a function of the canonical correlations between the equation errors with and without the covariates the distribution approaches the chi squared distribution as the stationary covariates lower the canonical correlations this enables more powerful inference concerning the determination of the cointegration rank

exact solution of the six vertex model with domain wall boundary conditions disordered phase the six vertex model or the square ice model with domain wall boundary conditions dwbc has been introduced and solved for finite n by korepin and izergin the solution is based on the yang baxter equations and it represents the free energy in terms of an n n hankel determinant paul zinn justin observed that the izergin korepin formula can be re expressed in terms of the partition function of a random matrix model with a nonpolynomial interaction we use this observation to obtain the large n asymptotics of the six vertex model with dwbc in the disordered phase the solution is based on the riemann hilbert approach and the deift zhou nonlinear steepest descent method as was noticed by kuperberg the problem of enumeration of alternating sign matrices the asm problem is a special case of the six vertex model we compare the obtained exact solution of the six vertex model with known exact results for the 1 2 and 3 enumerations of asms and also with the exact solution on the so called free fermion line we prove the conjecture of zinn justin that the partition function of the six vertex model with dwbc has the asymptotics z n sim cn kappa e n 2 f as n and we find the exact value of the exponent

resolution of the nested hierarchy for rational sl n models we construct drinfel d twists for the rational sl n xxx model giving rise to a completely symmetric representation of the monodromy matrix we obtain a polarization free representation of the pseudoparticle creation operators figuring in the construction of the bethe vectors within the framework of the quantum inverse scattering method this representation enables us to resolve the hierarchy of the nested bethe ansatz for the sl n invariant rational heisenberg model our results generalize the findings of maillet and sanchez de santos for sl 2 models

a note on the calculation of paths of hopf bifurcations this paper is concerned with the analysis of a two parameter nonlinear problem whose linearisation has a double zero eigenvalue with only one eigenvector the aim of the paper is to present a new approach to the theoretical and computational analysis of the bifurcating branches at this singular point using a symmetry in the system used to calculate hopf bifurcations it is shown that standard branch switching can be used to jump on to the path of hopf bifurcations emanating from the singular point

supersymmetric vertex models with domain wall boundary conditions by means of the drinfeld twists we derive the determinant representations of the partition functions for the gl 1 1 and gl 2 1 supersymmetric vertex models with domain wall boundary conditions in the homogeneous limit these determinants degenerate to simple functions

drinfeld twists and algebraic bethe ansatz of the supersymmetric model associated with uq gl m n we construct the drinfeld twists or factorizing f matrices of the supersymmetric model associated with quantum superalgebra u q gl m vertical bar n and obtain the completely symmetric representations of the creation operators of the model in the f basis provided by the f matrix as an application of our general results we present the explicit expressions of the bethe vectors in the f basis for the u q gl 2 vertical bar 1 model the quantum t j model

determinant representations of correlation functions for the supersymmetric t j model working in the f basis provided by the factorizing f matrix the scalar products of bethe states for the supersymmetric t j model are represented by determinants by means of these results we obtain determinant representations of correlation functions for the model

partition function of the eight vertex model with domain wall boundary condition we derive the recursive relations of the partition function for the eight vertex model on an n n square lattice with domain wall boundary condition solving the recursive relations we obtain the explicit expression of the domain wall partition function of the model in the trigonometric rational limit our results recover the corresponding ones for the six vertex model

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

symmetric functions and wavefunctions of xxz type six vertex models and elliptic felderhof models by izergin korepin analysis we present a method to analyze the wavefunctions of six vertex models by extending the izergin korepin analysis originally developed for domain wall boundary partition functions first we apply the method to the case of the basic wavefunctions of the xxz type six vertex model by giving the izergin korepin characterization of the wavefunctions we show that these wavefunctions can be expressed as multiparameter deformations of the quantum group deformed grothendieck polynomials as a second example we show that the izergin korepin analysis is effective for analysis of the wavefunctions for a triangular boundary and present the explicit forms of the symmetric functions representing these wavefunctions as a third example we apply the method to the elliptic felderhof model which is a face type version and an elliptic extension of the trigonometric felderhof model we show that the wavefunctions can be expressed as one parameter deformations of an elliptic analog of the vandermonde determinant and elliptic symmetric functions we present a method to analyze the wavefunctions of six vertex models by extending the izergin korepin analysis originally developed for domain wall boundary partition functions first we apply the method to the case of the basic wavefunctions of the xxz type six vertex model by giving the izergin korepin characterization of the wavefunctions we show that these wavefunctions can be expressed as multiparameter deformations of the quantum group deformed grothendieck polynomials as a second example we show that the izergin korepin analysis is effective for analysis of the wavefunctions for a triangular boundary and present the explicit forms of the symmetric functions representing these wavefunctions as a third example we apply the method to the elliptic felderhof model which is a face type version and an

estimation for partially nonstationary multivariate autoregressive models with conditional heteroscedasticity this paper investigates a partially nonstationary multivariate autoregressive model which allows its innovations to be generated by a multivariate arch autoregressive conditional heteroscedastic process three estimators including the least squares estimator a full rank maximum likelihood estimator and a reduced rank maximum likelihood estimator are considered and their asymptotic distributions are derived when the multivariate arch process reduces to the innovation with a constant covariance matrix these asymptotic distributions are the same as those given by ahn reinsel 1990 however in the presence of multivariate arch innovations the asymptotic distributions of the full rank maximum likelihood estimator and the reduced rank maximum likelihood estimator involve two correlated multivariate brownian motions which are different from those given by ahn reinsel 1990 simulation results show that the full rank and reduced rank maximum likelihood estimator are more efficient than the least squares estimator an empirical example shows that the two features of multivariate conditional heteroscedasticity and partial nonstationarity may be present simultaneously in a multivariate time series

calculation of norms of bethe wave functions a class of two dimensional completely integrable models of statistical mechanics and quantum field theory is considered eigenfunctions of the hamiltonians are known for these models norms of these eigenfunctions in the finite box are calculated in the present paper these models include in particular the quantum nonlinear schrodinger equation and the heisenbergxxz model

folds in solutions of two parameter systems and their calculation part i this paper is concerned with paths of turning points in solutions of nonlinear systems having two parameters it is well known that these paths are solutions of a particular extended system of nonlinear equations in this paper both regular points and simple turning points in the extended system are related to the local geometry of the solution surface of the original nonlinear system a description is given of numerical methods both for solving the extended system and for calculating certain quantities which determine the local geometry of the solution surface applications to perturbed bifurcation to the formation of isolas and to the calculation of the multiplicity of solutions are also discussed numerical examples are given

distribution theory for unit root tests with conditional heteroskedasticity abstract this paper explores the asymptotic distribution theory of autoregressive ar unit root tests where the error follows a generalized autoregressive conditional heteroskedastic garch process the proposed unit root test is based on maximum likelihood estimation which estimates the ar unit root and the garch parameters jointly the asymptotic distribution of the t statistic for the ar unit root is a mixture of the dickey fuller t distribution and the standard normal with the relative weight depending on the magnitude of the garch effect and the fourth moment of the standardized errors as the garch effect increases the power of the tests improves significantly these results show that significant power gains emerge from the joint estimation rather than relying on the conventional adf test which ignores the heteroskedasticity in the data

six vertex model with domain wall boundary conditions and one matrix model the partition function of the six vertex model on a square lattice with domain wall boundary conditions dwbc is rewritten as a hermitian one matrix model or a discretized version of it similar to sums over young diagrams depending on the phase the expression is exact for finite lattice size which is equal to the size of the corresponding matrix in the thermodynamic limit the matrix integral is computed using traditional matrix model techniques thus providing a complete treatment of the bulk free energy of the six vertex model with dwbc in the different phases in particular in the antiferroelectric phase the bulk free energy and a subdominant correction are given exactly in terms of elliptic theta functions

thermodynamic limit of the six vertex model with domain wall boundary conditions we address the question of the dependence of the bulk free energy on boundary conditions for the six vertex model here we compare the bulk free energy for periodic and domain wall boundary conditions using a determinant representation for the partition function with domain wall boundary conditions we derive toda differential equations and solve them asymptotically in order to extract the bulk free energy we find that it is different and bears no simple relation to the free energy for periodic boundary conditions the six vertex model with domain wall boundary conditions is closely related to algebraic combinatorics alternating sign matrices this implies new results for the weighted counting for large size alternating sign matrices finally we comment on the interpretation of our results in particular in connection with domino tilings dimers on a square lattice

scalar products of bethe vectors in models with gl 2 1 symmetry 2 determinant representation we study integrable models with mathfrak gl 2 1 symmetry and solvable by nested algebraic bethe ansatz we obtain a determinant representation for scalar products of bethe vectors when the bethe parameters obey some relations weaker than the bethe equations this representation allows us to find the norms of on shell bethe vectors and obtain determinant formulas for form factors of the diagonal entries of the monodromy matrix

asymptotic and bootstrap tests for linearity in a tar garch 1 1 model with a unit root this paper derives the limiting distribution of the lagrange multiplier lm test for threshold nonlinearity in a tar model with garch errors when one of the regimes contains a unit root it is shown that the asymptotic distribution is nonstandard and depends on nuisance parameters that capture the degree of conditional heteroskedasticity and non gaussian nature of the process we propose a bootstrap procedure for approximating the exact finite sample distribution of the test for linearity and establish its asymptotic validity

determinant formula for the six vertex model the partition function of a six vertex model with domain wall boundary conditions is considered on the finite lattice the authors show that the partition function satisfies a recursive relation they solve the recursion relation by a determinant formula this gives a determinant representation for the partition function they use the quantum inverse scattering method qism