estimation for partially nonstationary multivariate autoregressive models abstract for an m variate partially nonstationary vector autoregressive process y t we consider the autoregressive model l y t e t where l i 1 l p l p and det z 0 has d m roots equal to unity and all other roots are outside the unit circle it is also assumed that rank 1 r r m d so that each component of the first differences w t y t y t 1 is stationary the relation of the model to error correction models and co integration engle and granger 1987 is discussed the process y t has the error correction representation l 1 l y t p 2 i r r q 2 1 y t 1 e t where q i m 1 p j diag i d r is in jordan canonical form and q q 1 q 2 it follows that the transformation z t qy t zt 1t z2 2t t is such that the d 1 process z 1t is nonstationary with z 1t z 1t 1 stationary while z 2t is stationary asymptotic distribution theory for least squares parameter estimators of the model is first considered a gaussia

testing for cointegration using partially linear models abstract a partially linear model of cointegration is developed where stationary covariates enter nonparametrically we propose tests for cointegration using singular values of the estimated autoregressive matrix the tests are based on eigenvalues of standardized matrices and are relatively simple to compute asymptotic theory of the proposed test is developed it is shown that the limiting distribution of the proposed test is similar to that of several tests in the recent literature a gamma approximation of the distribution is discussed to facilitate inference finite sample properties of the proposed procedure are illustrated in some limited monte carlo experiments an empirical application to us macroeconomic time series is conducted to highlight the approach

note on fuzzy regression abstract regression analysis has been widely used in several areas for many years fuzzy linear regression was introduced in 1980 by h tanaka s uejima and k asai in this paper the general form of regression equations is developed for fuzzy numbers it is showed that the problem of fuzzy regression can be formulated as a mathematical programming problem the special case of linear regression yields a linear programming problem different measures of vagueness are introduced to define the best estimate two simple numerical examples illustrate the methodology and allow a partial comparison among the different measures of vagueness

on the rationality of knorr s virtually irreducible lattices abstract it was established by reinhard knorr that the half of brauer s height zero conjecture which assumes an abelian defect group would follow from the nonexistence of certain integral representations of abelian p groups we establish nonexistence of such representations of rank less than 14 for the elementary abelian group of order 8 and believe these to be the first results of this kind the result is made possible by imposing a simple rationality condition

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

vertex method for computing functions of fuzzy variables abstract this paper is to introduce a new approach the vertex method for computing functions of fuzzy variables the method is based on the cut concept and interval analysis the vertex method can avoid abnormality due to the discretization technique on the variables domain and the widening of the resulting function value set due to multi occurrence of variables in the functional expression by conventional interval analysis methods the algorithm is very easy to implement and can be applied to many practical problems some examples are given to illustrate the applications

testing for an unstable root in conditional and structural error correction models abstract this paper proposes a class of wald tests for the hypothesis of an unstable root in conditional error correction models both single equation models and simultaneous equations models in structural form are considered the asymptotic distribution of the test statistics under the null hypothesis is derived in terms of a vector brownian motion process and critical values are obtained via monte carlo simulation in an empirical model of the demand for money and the rate of inflation in the uk the tests reject the instability hypothesis

a bootstrap algorithm for testing cointegration rank in var models in the presence of stationary variables abstract in this paper a bootstrap algorithm for a reduced rank vector autoregressive var model which also includes stationary regressors is analyzed it is shown that the bootstrap distribution for estimating the rank converges to the distribution derived from the usual asymptotic framework because the asymptotic distribution will typically depend on unknown parameters bootstrap distributions are of considerable interest in this context the result of an application and some monte carlo experiments are also presented

knorr lattices their characters and some subsets of fpd examples of positive height cyclic knorr lattices for elementary abelian p groups are constructed and bounds relating the height of such lattices to the size of the group are given the problem is formulated in terms of finite geometry when p 2 certain examples are shown to arise from difference sets

schur indices and abelian defect groups abstract we show that the irreducible characters lying in 2 blocks of finite solvable groups with abelian defect groups have trivial 2 local schur indices

duality in g algebras keywords finite group complete discrete valuation ring symmetric g algebra symmetric bilinear form projective ideal symmetric algebra rg lattice unimodular symmetric g algebra almost projective ideal almost split sequences block defect groups virtually irreducible lattices splitting trace lattices reference ctg article 1988 005doi 10 1007 bf01161746 record created on 2008 12 16 modified on 2017 05 12

some cyclic virtually irreducible lattices abstract virtually irreducible lattices which satisfy a simple rationality condition and have positive height are constructed for elementary abelian 2 groups the non existence of such lattices would have implied part of brauer s height zero conjecture a characterization of rank 6 lattices for the elementary abelian group of size 16 is given

tackling an mcdm problem with the help of some results from fuzzy set theory abstract the problem to be addressed and tackled in this paper arose as a byproduct from some efforts at solving problems involving multiple goals by linking linear and goal programming models the critical issue was that some forms for interdependence among the goals could not be handled in the programming models here we will deal with a set of goals with realistic counterparts in a finnish plywood industry in which a subset of the goals are i conflicting another subset ii unilaterally supporting and a third subset iii mutually supporting it is furthermore observed that the elements of a studied set of goals may be partly independent and partly interdependent which makes the context a fullfledged mcdm problem it is tackled with a technique which is based on the theory of fuzzy sets the conceptual framework for fuzzy decisions and the algorithms developed for fuzzy mathematical programming the resulting fuzzy multiobjective programming model is simplified and tested with the help of a fairly complex numerical example

fuzzy set and probabilistic techniques for health risk analysis a brief review of three non fuzzy set techniques available for performing risk analysis under uncertainty probabilistic error propagation bayesian analysis and the shannon entropy is given using health risk assessment to illustrate the approach the advantages and difficulties in applying each of these techniques are pointed out next a fourth technique is developed in some detail namely the fuzzy set analysis of risk here a given risk analysis problem evaluated under different sets of hypotheses may yield different fuzzy numbers which can then be combined and compared the elements of the methodology which may be considered as an extension of interval analysis are fuzzy numbers and operations including their ranking fuzzy regression to model a dose response relationship locating two dimensional fuzzy numbers for risk management and combining and ranking fuzzy risk estimates

fuzzy sets and statistical data abstract specific features of probability and possibility theories are discussed with emphasis on semantical aspects instead of putting forward the acknowledged usefulness of possibility theory for the non statistical modelling of subjective categories we try to figure out how statistical data and possibility theory could be matched as a result procedures for constructing weak possibilistic substitutes of probability measures and for processing imprecise statistical data are outlined they provide new insights on relationship between fuzzy sets and probability theories

potential applications of fuzzy sets in industrial safety engineering abstract this paper discusses potential applications of fuzzy set theory to risk analysis in the area of industrial safety engineering vagueness and imprecision in mathematical quantification of risk are equated with fuzziness rather than randomness the concept of risk evaluation using linguistic representation of the likelihood of the occurrence of a hazardous event exposure and possible consequences of that event is proposed the approximate reasoning technique based on fuzzy logic is used to derive fuzzy values of risk

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

some comments on fuzzy variables abstract nahmias introduced the concept of a fuzzy variable as a possible axiomatic framework from which a rigorous theory of fuzziness may be constructed in this paper we attempt to shed more light on fuzzy variables in analogy with random variables in particular we study the problem if x1 x2 xn are mutually unrelated fuzzy variables with common membership function and 1 2 n are real numbers satisfying i o for every i and i 1n i 1 when does does z i 1n ixi have the same membership function

a way to deal with fuzzy preferences in multi criteria decision problems this paper presents a special multiple criteria decision making approach for solving problems in context with fuzzy individual preferences at first we briefly expose the proposed methodology the individual preferences are explicitly given by a complete transitive relation r on a set of reference actions the modelling of the decision maker s preferences is obtained by means of fuzzy outranking relations these fuzzy relations are based on a system of additive utility functions which are estimated by means of ordinal regression methods analysing the preference relation r this is followed by a presentation of two real multicriteria problems which the proposed methodology has been applied to i e a highway plan choice problem and a problem in marketing research dealing with the launching of a new product in each application we tried to specify this method according to the specific structure of the problem considered

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

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

blocks of defect zero and products of elements of orderp abstract suppose thatgis a finite group and thatfis a field of characteristicp 0 which is a splitting field for all subgroups ofg lete0be the sum of the block idempotents of defect zero infg and let be the set of solutions togp 1 ing we show thate0 2 whenpis odd ande0 3 whenp 2 in the latter case 2 r whereris the set of real elements of 2 defect zero soe0 r r 2 we also show thate0 4 4 2 whenp 2 where 4is the set of solutions tog4 1 these results give us various criteria for the existence ofp blocks of defect zero