a proposal for a residual autocorrelation test in linear models summary this note proposes a test of goodness of fit for time series models based on the sum of the squared residual partial autocorrelations the test statistic is asymptotically x2 its small sample performance is studied through a monte carlo experiment it appears sensitive to erroneous specifications especially when the fitted model understates the order of the moving average component residual analysis is a fundamental step in building empirical time series models when checking the adequacy of the model one usually tests for the absence of residual autocorrelation there is a number of tests designed for this purpose both in the time and frequency domains see for instance quenouille 1947 1949 bartlett 1954 box pierce 1970 ljung box 1978 ansley newbold 1979 godfrey 1979 in this paper a test based on residual partial autocorrelations is proposed which is particularly powerful in cases when the fitted model underestimates the order of the moving average component let x be a zero mean process generated by a arma model o b x 0 b at where b is the backshift operator b is a polynomial of order p 0 b is a polynomial of order q and a is a white noise let a atn be the residuals obtained after estimating the model a very popular goodness of fit test proposed by box pierce 1970 and improved by ljung box 1978 is based on the statistic m

adaptive surface related multiple elimination the major amount of multiple energy in seismic data is related to the large reflectivity of the surface a method is proposed for the elimination of all surface related multiples by means of a process that removes the influence of the surface reflectivity from the data an important property of the proposed multiple elimination process is that no knowledge of the subsurface is required on the other hand the source signature and the surface reflectivity do need to be provided as a consequence the proposed process has been implemented adaptively meaning that multiple elimination is designed as an inversion process where the source and surface reflectivity properties are estimated and where the multiple free data equals the inversion residue results on simulated data and field data show that the proposed multiple elimination process should be considered as one of the key inversion steps in stepwise seismic inversion

an inverse scattering series method for attenuating multiples in seismic reflection data we present a multidimensional multiple attenuation method that does not require any subsurface information for either surface or internal multiples to derive these algorithms we start with a scattering theory description of seismic data we then introduce and develop several new theoretical concepts concerning the fundamental nature of and the relationship between forward and inverse scattering these include 1 the idea that the inversion process can be viewed as a series of steps each with a specific task 2 the realization that the inverse scattering series provides an opportunity for separating out subseries with specific and useful tasks 3 the recognition that these task specific subseries can have different and more favorable data requirements convergence and stability conditions than does the original complete inverse series and most importantly 4 the development of the first method for physically interpreting the contribution that individual terms and pieces of terms in the inv

one way versions of the kirchhoff integral the conventional kirchhoff integral based on the two way wave equation states how the acoustic pressure at a point a inside a closed surface s can be calculated when the acoustic wave field is known on s in its general form the integrand consists of two terms one term contains the gradient of a green s function and the acoustic pressure the other term contains a green s function and the gradient of the acoustic pressure the integrand can be simplified by choosing reflecting boundary conditions for the two way green s functions in such a way that either the first term or the second term vanishes on s this conventional approach to deriving rayleigh type integrals has practical value only for media with small contrasts so that the two way green s functions do not contain significant multiple reflections we present a modified approach for simplifying the integrand of the kirchhoff integral by choosing absorbing boundary conditions for the one way green s functions the resulting rayleigh type integr

diagnostic checking for time series models with conditional heteroscedasticity estimated by the least absolute deviation approach the recent paper by peng yao 2003 gave an interesting extension of least absolute deviation estimation to generalised autoregressive conditional heteroscedasticity garch time series models the asymptotic distributions of absolute residual autocorrelations and squared residual autocorrelations from the garch model estimated by the least absolute deviation method are derived in this paper these results lead to two useful diagnostic tools which can be used to check whether or not a garch model fitted by using the least absolute deviation method is adequate some simulation experiments give further support to the asymptotic theory and a real data example is also reported

testing for contagion under asymmetric dynamics evidence from the stock markets between us and taiwan abstract this article is an attempt to test through the use of forward forecasting test on dynamic conditional correlation dcc for contagion between taiwan and us stocks under asymmetry the process includes three steps the first step uses the iterated cumulative sums of squares icss algorithm to detect the structural breaks of market return the second step creates dummy variables for breaks estimates egarch model of conditional generalized error distribution and computes dynamic conditional correlation coefficients of dcc multivariate garch model the third step employs one step and n step forecast test to check for contagion effect the evidences prove the asymmetric leverage effect of taiwan weighted stock index and new york nyse composite index interestingly we discovered that there are two kinds of contagion positive and negative between markets

testing the constancy of regression parameters against continuous structural change abstract a standard explicit or implicit assumption underlying many parameter constancy tests in linear models is that there is a single structural break in the sample in this paper that assumption is replaced by a more general one stating that the parameters of the model may change continuously over time the pattern of change is parameterized giving rise to a set of parameter constancy tests against a parameterized alternative the power properties of the lm type tests in small samples are compared to those of other tests like the cusum and fluctuation test by simulation and found very satisfactory an application is considered

flux normalized wavefield decomposition and migration of seismic data separation of wavefields into directional components can be accomplished by an eigenvalue decomposition of the accompanying system matrix in conventional pressurenormalized wavefield decomposition the resulting one way wave equations contain an interaction term which depends on the reflectivity function applying directional wavefield decomposition using flux normalized eigenvalue decomposition and disregarding interaction between up and downgoing wavefields these interaction terms were absent by also applying a correction term for transmission loss the result was an improved estimate of the up and downgoing wavefields in the wave equation angle transform a crosscorrelation function in local offset coordinates was fourier transformed to produce an estimate of reflectivity as a function of slowness or angle we normalized this wave equation angle transform with an estimate of the planewave reflection coefficient the flux normalized oneway wave propagation scheme was applied to imaging and to the normalized wave equation angle transform on synthetic and field data this proved the effectiveness of the new methods

perturbation approach to depth extrapolation the born series solution of the lippmann schwinger equation does not necessarily converge properly for depth extrapolation problems even more seriously the lippmann schwinger equation is not necessarily self consistent for depth extrapolation unless it is interpreted correctly a solution is proposed by using the generalized lippmann schwinger equation that includes boundary value contributions that normally are ignored a modified version of the lippmann schwinger equation for depth extrapolation is obtained the corrections to the born series expansion for depth extrapolation are demonstrated the new system has the desired convergence and self consistency properties explicit depth extrapolation is discussed in the context of the lippmann schwinger equation a partial explanation for why explicit depth extrapolation works reasonably well in laterally inhomogeneous media may be that the contribution from the perturbation term in the lippmann schwinger equation for that problem is small for a wide var

a boundary integral equation method for an inverse problem related to crack detection this paper discusses an application of a boundary integral equation method biem to an inverse problem of determining the shape and the location of cracks by boundary measurements suppose that a given body contains an interior crack the shape and the location of which are unknown on the exterior boundary of this body one carries out measurements which are interpreted mathematically as prescribing dirichlet data and measuring the corresponding neumann data or vice versa for a field governed by laplace s equation the inverse problem considered here attempts to determine the geometry of the crack from these experimental data we propose to solve this problem by minimizing the error of a certain boundary integral equation bie the process of this minimization however is shown to require solutions of certain are proposed several 2d and 3d numerical examples are given in order to test the performance of the present method

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

on the efficiency and accuracy of the boundary element method and the finite element method the efficiency and computational accuracy of the boundary element and finite element methods are compared in this paper this comparison is carried out by employing different degrees of mesh refinement to solve a specific illustrative problem by the two methods

a tukey nonadditivity type test for time series nonlinearity the past few years have seen a revived interest in the study of nonlinear stationary time series the most general form of a nonlinear stationary process is that referred to as a volterra expansion this is to a linear process what a higher order polynomial is to a linear function the so called bilinear model is a special case which is quite broad and is defined by a small number of parameters volterra expansions involve more than secondorder theory and require higher order cumulant spectra various tests for linearity have been proposed although none is totally satisfactory because of the similarity of volterra expansions to polynomials an analogue of tukey s 1949 one degree of freedom for nonadditivity test seems quite reasonable as a diagnostic for linearity versus a second order volterra expansion such a test would be time domain based and computationally less complex than the frequency domain based alternatives directly generalizable to higher order than second and possibly suggestive of a power transformation toward linearity

estimating regression models of finite but unknown order abstract this paper considers some problems associated with estimation and inference in the normal linear regression model y t j 1 m0 j x tj e t var e t 2 when m 0 is unknown the regressors are taken to be stochastic and assumed to satisfy v grenander s 1954 conditions almost surely it is further supposed that estimation and inference are undertaken in the usual way conditional on a value of m 0 chosen to minimize the estimation criterion function ec m t 2 m mg t with respect to m where 2m is the maximum likelihood estimate of 2 it is shown that subject to weak side conditions if g t a s 0 and tg t a s then this estimate is weakly consistent it follows that estimates conditional on the chosen value of m 0 are asymptotically efficient and inference undertaken in the usual way is justified in large samples when g t converges to a positive constant with probability one then in large samples m 0 will never be chosen too small but the probability of choosing m 0 too large remains positive the results of the paper are stronger than similar ones r shibata 1976 r j bhansali and d y downham 1977 in that a known upper bound on m 0 is not assumed the strengthening is made possible by the assumptions of strictly exogenous regressors and normally distributed disturbances the main results are used to show that if the model selection criteria of h akaike 1974 t amemiya 1980 c l mallows 1973 or e parzen 1979 are used to choose m 0 in 1 then in the limit the probability of choosing m 0 too large is at least 0 2883 the approach taken by g schwarz 1978 leads to a consistent estimator of m 0 however these results are illustrated in a small sampling experiment

testing constancy of the error covariance matrix in vector models in this paper a lagrange multiplier test of the hypothesis that the covariance matrix of a multivariate time series model is constant over time is considered it is assumed that under the alternative the error variances are time varying whereas the correlations remain constant over time under the parameterized alternative hypothesis the variances may change continuously as a function of time or some observable stochastic variables small sample properties of the test statistic are investigated by simulation the assumption of constant correlations does not appear overly restrictive

application of the complex variable boundary element method to solving potential problems in doubly connected domains the complex variable boundary element method cvbem developed by hromadka for the solution of potential problems in simply connected domains is extended to the solution of heat conduction problems in doubly connected domains a cut is made in the doubly connected domain and it was found that the complex potentials along the cut do not cancel out but result in a complex stream function that plays the role of perturbation in the nodal equations cauchy riemann conditions are used to derive additional equations which relate the stream functions and the boundary heat fluxes and potentials when neumann and robin conditions are imposed on the boundaries the resulting nodal equations are expressed in matrix form and coding rules and methods for checking the matrix elements are developed three solution methods implicit explicit and hybrid are described and by means of examples the efficacy of these methods is discussed and compared

boundary element method analysis of thermoelastic deformation in nonhomogeneous media abstract this paper presents a boundary element method bem formulation and numerical implementation of thermoelasticity problems in nonhomogeneous media the formulation uses the known kernels of the displacement equations for elasticity problems in homogeneous media this formulation leads to a domain integral containing the unknown displacement field in addition to the usual boundary integrals with displacements and tractions an iterative scheme is used to determine the displacement fields numerical results are presented for some illustrative plane strain problems the iterative scheme is shown to converge rapidly for these problems with moderate temperature gradients the bem results are compared with results from the finite element method fem for these problems and also with exact solutions whenever possible

nonlinearity tests for time series summary this paper considers two nonlinearity tests for stationary time series the idea of tukey s one degree of freedom for nonadditivity test is generalized to the time series setting the case of concurrent nonlinearity is discussed in detail simulation results show that the proposed tests are more powerful than that of keenan 1985

a powerful portmanteau test of lack of fit for time series a new portmanteau test for time series more powerful than the tests of ljung and box and monti is proposed the test is based on the mth root of the determinant of the mth autocorrelation matrix it is shown that the proposed statistic is a function of all of the squared multiple correlation coefficients of the regressions of the residuals on their lags when the number of lags goes from 1 to m it can also be written as a function of the first m partial autocorrelation coefficients the asymptotic distribution of the test statistic is a linear combination of chi squared distributions and can be approximated by a gamma distribution it is shown depending on the model and sample size that this test can be up to 50 more powerful than the ljung and box and monti tests the test is applied to the detection of several types of nonlinearity by using the autocorrelation matrix of the squared residuals and it is shown that in general the new test is more powerful than the test of mcleod and li an example

on the efficient computation of the stress components near a closed boundary in plane elasticity by using classical complex boundary integral equations complex boundary integral equations fredholm type regular or cauchy type singular or even hadamard mangler type hypersingular have been used for the numerical solution of general plane isotropic elasticity problems the related muskhelishvili and particularly lauricella sherman equations are famous in the literature but several more extensions of the lauricella sherman equations have also been proposed in this paper it is just mentioned that the stress and displacement components can be very accurately computed near either external or internal simple closed boundaries for anyone of the above equations regular or singular or hypersingular but with a prerequisite their actual numerical solution through the appropriate use of the even more classical elementary cauchy theorem in complex analysis this approach has been already used for the accurate numerical computation of analytic functions and their derivatives by ioakimidis papadakis and perdios bit 1991 31 276 285 without applications to elasticity problems but here the much more complicated case of the elastic complex potentials is studied even when just an appropriate non analytic complex density function such as an edge dislocation loading distribution density is numerically available on the boundary the present results are also directly applicable to inclusion problems anisotropic elasticity antiplane elasticity and classical two dimensional fluid dynamics but unfortunately not to crack problems in fracture mechanics brief numerical results for the complex potentials showing the dramatic increase of the computational accuracy are also displayed and few generalizations proposed copyright 2000 john wiley sons ltd

new weighted portmanteau statistics for time series goodness of fit testing we exploit ideas from high dimensional data analysis to derive new portmanteau tests that are based on the trace of the square of the mth order autocorrelation matrix the resulting statistics are weighted sums of the squares of the sample autocorrelation coefficients that unlike many other tests appearing in the literature are numerically stable even when the number of lags considered is relatively close to the sample size the statistics behave asymptotically as a linear combination of chi squared random variables and their asymptotic distribution can be approximated by a gamma distribution the proposed tests are modified to check for nonlinearity and to check the adequacy of a fitted nonlinear model simulation evidence indicates that the proposed goodness of fit tests tend to have higher power than other tests appearing in the literature particularly in detecting long memory nonlinear models the efficacy of the proposed methods is demonstrated by investigating nonlinear effects in apple inc an

dislocation and point force based approach to the special green s function bem for elliptic hole and crack problems in two dimensions in this paper we give the theoretical foundation for a dislocation and point force based approach to the special green s function boundary element method and formulate as an example the special green s function boundary element method for elliptic hole and crack problems the crack is treated as a particular case of the elliptic hole we adopt a physical interpretation of somigliana s identity and formulate the boundary element method in terms of distributions of point forces and dislocation dipoles in the infinite domain with an elliptic hole there is no need to model the hole by the boundary elements since the traction free boundary condition there for the point force and the dislocation dipole is automatically satisfied the green s functions are derived following the muskhelishvili complex variable formalism and the boundary element method is formulated using complex variables all the boundary integrals including the formula for the stress intensity factor for the crack are evaluated analytically to give a simple yet accurate special green s function boundary element method the numerical results obtained for the stress concentration and intensity factors are extremely accurate 1997 john wiley sons ltd

diagnostic testing of univariate time series models summary the portmanteau statistic for testing the adequacy of an autoregressive moving average model is based on the first m autocorrelations of the residuals from the fitted model this paper examines the properties of this test for various choices of m a modification which allows the use of small values of m is shown to result in a more powerful test the lagrange multiplier statistic godfrey 1979 and a test statistic examined by newbold 1980 are also discussed

extended local born fourier migration method a migration approach based on a local application of the born approximation within each extrapolation interval contains a singularity that can make direct application unstable previous authors have suggested adding an imaginary part to the vertical wavenumber to eliminate the singularity however their method requires that the reference slowness must be the maximum slowness of a given layer consequently the slowness perturbations are larger than those when the average slowness is selected as a reference slowness therefore its applicability is limited we develop an extended local born fourier migration method that circumvents the singularity problem of the local born solution and makes it possible to choose the average slowness as a reference slowness it is computationally efficient because of the use of a fast fourier transform algorithm it can handle wider angles or steeper interfaces and scattering effects of heterogeneities more accurately than the split step fourier ssf method which acco

regularized estimation of large covariance matrices this paper considers estimating a covariance matrix of p variables from n observations by either banding the sample covariance matrix or estimating a banded version of the inverse of the covariance we show that these estimates are consistent in the operator norm as long as logp 2 n 0 and obtain explicit rates the results are uniform over some fairly natural well conditioned families of covariance matrices we also introduce an analogue of the gaussian white noise model and show that if the population covariance is embeddable in that model and well conditioned then the banded approximations produce consistent estimates of the eigenvalues and associated eigenvectors of the covariance matrix the results can be extended to smooth versions of banding and to non gaussian distributions with su ciently short tails a resampling approach is proposed for choosing the banding parameter in practice this approach is illustrated numerically on both simulated and real data

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

wave field extrapolation techniques in seismic migration a tutorial the objective of this paper is to provide a general view on methods of wave field extrapolation as used in seismic modeling and seismic migration i e the kirchhoff summation approach the plane wave method k f method and the finite difference technique particular emphasis is given to the relationship between the different methods by formulating the problem in the space frequency domain x y omega domain a systems approach can be adopted which results in simple and concise expressions these expressions clearly show that forward extrapolation is described by a spatial convolution procedure and inverse extrapolation is described by a spatial deconvolution procedure in the situation of lateral velocity variations the de convolution procedure becomes space variant the space frequency domain is most suitable for recursive depth migration in addition frequency dependent properties such as absorption dispersion and spatial bandwidth can be handled easily it is shown that all extrapolation methods are based on two equations taylor series and wave equation in the kirchhoff summation approach all terms of the taylor series are summed to an exact analytical expression the kirchhoff integral for plane surfaces it formulates the extrapolation procedure in terms of a spatial convolution integral which must be discretized in practical applications the fourier transformed version of the kirchhoff integral is used in the plane wave method k f method this actually means that spatial de convolution in the x y omega domain is translated into multiplication in the k x k y omega domain of course this is not allowed if the extrapolation operators are space variant in explicit finite difference techniques a truncated version of the taylor series is used with some optimum adjustments of the coefficients for only one or two terms in the taylor series a spatial low pass filter must be applied to compensate for the amplitude errors at high tilt angles explicit methods are simple and most suitable for three dimensional 3 d applications in implicit finite difference schemes the wave field extrapolator is written in terms of an explicit forward extrapolator and an explicit inverse extrapolator properly designed implicit schemes do not show amplitude errors and therefore amplitude correction filters need not be applied in comparison with explicit schemes implicit schemes are more sensitive to improper boundary conditions at both ends of the data file it is shown that the forward seismic model can be elegantly described by a matrix equation using separate operators for downward and upward traveling waves using this model inverse extrapolation involves one matrix inversion procedure to compensate for the downward propagation effects and one matrix inversion procedure to compensate for the upward propagation effects

representation of seismic sources in the one way wave equations one way extrapolation of downgoing and upgoing acoustic waves plays an essential role in the current practice of seismic migration berkhout 1985 stolt and benson 1986 claerbout 1985 gardner 1985 generally one way wave equations are derived for the source free situation sources are then represented as boundary conditions for the one way extrapolation problem this approach is valid provided the source representation is done with utmost care for instance it is not correct to represent a monopole source by a spatial delta function and to use this as input data for a standard one way extrapolation scheme this yields an erroneous directivity pattern as illustrated below

a simple design procedure for depth extrapolation operators that compensate for absorption and dispersion i compensate for the effects of absorption and dispersion in deriving the space frequency domain depth extrapolation operators by starting from the ones without such compensation the procedure is simple and requires only trivial cosine transforms applied to the original noncompensating operators i show that compensating operators enhance resolution as a function of depth when applied in prestack depth migration

axisymmetric viscoplastic deformation by the boundary element method abstract this paper presents a boundary element formulation and numerical implementation of the problem of small axisymmetric deformation of viscoplastic bodies while the extension from planar to axisymmetric problems can be carried out fairly simply for the finite element method fem this is far from true for the boundary element method bem the primary reason for this fact is that the axisymmetric kernels in the integral equations of the bem contain elliptic functions which cannot be integrated analytically even over boundary elements and internal cells of simple shape thus special methods have to be developed for the efficient and accurate numerical integration of these singular and sensitive kernels over discrete elements the accurate determination of stress rates by differentiation of the displacement rates presents another formidable challenge a successful numerical implementation of the boundary element method with elementwise called the mixed approach or pointwise called the pure bem or bem approach determination of stress rates has been carried out a computer program has been developed for the solution of general axisymmetric viscoplasticity problems comparisons of numerical results from the bem and fem for several illustrative problems are presented and discussed in the paper it is possible to get direct solutions for the simpler class of problems for cylinders of uniform cross section and these solutions are also compared with the bem and fem results for such cases

removal of surface related wave phenomena the marine case removal of the effects of the free surface from seismic reflection data is an essential preprocessing step before prestack migration the problem can be formulated by means of rayleigh s reciprocity theorem which leads to an integral equation of the second kind for the desired pressure field that does not include these free surface effects this integral equation can be solved numerically both in the spatial domain and in the double radon domain solving the integral equation in the double radon domain has the advantage of reducing the computation time significantly since the kernel of the integral equation becomes dominant diagonally two methods are proposed to solve the integral equation direct matrix inversion and a recursive subtraction of the free surface multiples using a neumann series both methods have been developed and tested on a synthetic data set which was computed with the help of an independent forward modeling scheme

constrained nonlinear programming for volatility estimation with garch models this paper proposes a constrained nonlinear programming view of generalized autoregressive conditional heteroskedasticity garch volatility estimation models in financial econometrics these models are usually presented to the reader as unconstrained optimization models with recursive terms in the literature whereas they actually fall into the domain of nonconvex nonlinear programming our results demonstrate that constrained nonlinear programming is a worthwhile exercise for garch models especially for the bivariate and trivariate cases as they offer a significant improvement in the quality of the solution of the optimization problem over the diagonal vech and the bekk representations of the multivariate garch model

the complex variable boundary element method applications the complex variable boundary element method cvbem is used to approximate several potential problems where analytical solutions are known a modelling result produced from the cvbem is a measure of relative error in matching the known boundary condition values of the problem a cvbem error reduction algorithm is used to reduce the relative error of the approximation by adding nodal points in boundary regions where error is large from the test problems overall error is reduced significantly by utilizing the adaptive integration algorithm

determination of poles of sectionally meromorphic functions abstract the numerical methods of abd ellal delves and reid for locating poles of meromorphic functions inside smooth closed contours c in the complex plane are generalized to apply to sectionally meromorphic functions satisfying a homogeneous or nonhomogeneous riemann hilbert boundary value problem on the simple closed contours of their discontinuity which may intersect c in the first case the zeros of the meromorphic functions can be determined as well two simple illustrations of the present generalization are also presented

inversion versus migration a new perspective to an old discussion seismic imaging techniques can be subdivided into inversion and migration the object functions for inversion and migration are respectively the medium contrast parameters and reflectivity in this paper the relationship between inversion and migration is approached by analyzing the underlying representations the forward models it appears that the two way representation which underlies inversion as well as the one way representation which underlies migration can both be expressed in terms of a volume integral over the appropriate object function in their linearized form these representations account for primaries only in this case the one way representation in terms of reflectivity is the most accurate of the two which implies that proper migration is more accurate than linearized inversion internal multiples can be taken into account by the nonlinear representations as an alternative however the generalized primary representation is introduced in its explicit form this one way

on the application of robust regression based diagnostics to models of conditional means and conditional variances abstract a strategy is proposed for applying a class of robust regression based diagnostics to nonlinear models of conditional means and conditional variances for cross section or time series data the distinguishing feature of the current approach which builds on already popular residual based procedures is that no auxiliary assumptions are imposed at any testing stage consequently the statistics are guaranteed to have the correct asymptotic size under the relevant null hypothesis several new regression based conditional mean and conditional variance diagnostics are proposed the case of incompletely specified dynamics in time series models is explicitly covered

application of the cvbem to non uniform st venant torsion abstract the complex variable boundary element method or cvbem is used to approximate the stress distribution associated with non uniform st venant torsion problems by specifying either the normal or tangential force equilibrium equation in terms of the warping function or its conjugate a laplace equation results which is immediately tractable by using the cvbem a comparison of modeling results to known solutions indicates that the modeling technique is a useful approach for the estimation of interior stresses as well as for the evaluation of modeling error by means of an approximate boundary determined by the cvbem approximation function

comparison of boundary element and finite element methods in the inelastic torsion of prismatic shafts the accuracy and computational efficiency of the boundary element and the finite element methods are compared in this paper for problems of time dependent inelastic torsion of prismatic shafts several cross sections and two types of twisting history are considered in the numerical examples the shaft material is assumed to obey an elastic time hardening creep constitutive model

grid optimization for the boundary element method the quality of solution obtained using the boundary element method bem is dependent on how the boundary is discretized this is particularly true in domains of complex geometry a rule for grid optimization for the bem is derived on the bases of an asymptotic measure of the boundary element error that preserves the number of elements degrees of freedom three example problems are provided to show the advantages of grid optimization in terms of accuracy and cost

use of cumulative sums of squares for retrospective detection of changes of variance abstract this article studies the problem of multiple change points in the variance of a sequence of independent observations we propose a procedure to detect variance changes based on an iterated cumulative sums of squares icss algorithm we study the properties of the centered cumulative sum of squares function and give an intuitive basis for the icss algorithm for series of moderate size i e 200 observations and beyond the icss algorithm offers results comparable to those obtained by a bayesian approach or by likelihood ratio tests without the heavy computational burden required by these approaches simulation results comparing the icss algorithm to other approaches are presented

a complex variable boundary element method development a generalized boundary integral equation method for the solution of the laplace equation is developed based on the cauchy integral theorem for analytical complex variable functions although the approach is complicated by the utilization of complex variable theory the resulting model involves direct integration along straight line boundary segments elements rather than using quadrature formulae that are required in current real variable boundary element formulations previously published boundary integral equation methods based on the cauchy integral theorem are shown to be a subset of the generalized model theory developed in this paper

kirchhoff scattering series insight into the multiple attenuation method there are two basic integral equations used to represent wavefields in theoretical seismology the lippmann schwinger integral equation and the representation theorem the born scattering series currently used for attenuating free surface multiples has been derived from the lippmann schwinger integral equation similarly we have used the representation theorem here to derive a kirchhoff scattering series for attenuating free surface multiples in towed streamer data the kirchhoff series for attenuating free surface multiples is in theory equivalent to the born series most important like the born series it does not require any knowledge of the subsurface however it still provides useful insight into the multiple attenuation methods because the form of some quantities involved in the kirchhoff series is different from the form in the born series for example in towed streamer seismic data the kirchhoff series requires measurements of the vertical derivative of the pressure field in addition to the

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

testing for complete independence in high dimensions a simple statistic is proposed for testing the complete independence of random variables having a multivariate normal distribution the asymptotic null distribution of this statistic as both the sample size and the number of variables go to infinity is shown to be normal consequently this test can be used when the number of variables is not small relative to the sample size and in particular even when the number of variables exceeds the sample size the finite sample size performance of the normal approximation is evaluated in a simulation study and the results are compared to those of the likelihood ratio test

bootstrapping the portmanteau tests in weak auto regressive moving average models this paper uses a random weighting rw method to bootstrap the critical values for the ljung box monti portmanteau tests and weighted ljung box monti portmanteau tests in weak arma models unlike the existing methods no user chosen parameter is needed to implement the rw method as an application these four tests are used to check the model adequacy in power garch models simulation evidence indicates that the weighted portmanteau tests have the power advantage over other existing tests a real example on s p 500 index illustrates the merits of our testing procedure as one extension work the block wise rw method is also studied

removal of water layer multiples from multicomponent sea bottom data a method for suppressing water layer multiples in multicomponent sea floor measurements is presented the multiple suppression technique utilizes the concept of wavefield separation into upgoing and downgoing modes just below the sea floor for eliminating the sea floor ghost the sea surface ghost and the accompanying water layer reverberations the theory applies to each of the recorded components pressure vertical velocity and horizontal velocities the fundamental physical principle for the multiple suppression technique rests on identifying these multiples as downgoing waves just below the sea floor while the primaries of interest arriving from the subsurface are upgoing waves white presented this realization for the pressure component three decades ago hence the theory for the velocity field is an extension of the theory in this paper the theory is derived for an experiment with a marine source in the water layer above a locally flat elastic sea floor with known elastic parameters the method is otherwise multidimensional and operates on a shot to shot basis hence it is computationally fast aside from this we show that this demultiple method removes the strongest multiples in sea floor data without knowledge of the source wavelet synthetic and real data examples are provided to illustrate the application of the algorithms to the pressure in line velocity and vertical velocity components the numerical tests show that strong multiples have been attenuated on the pressure and the velocity recordings producing promising results

a born wkbj inversion method for acoustic reflection data density and bulk modulus variations in an acoustic earth are separately recoverable from standard reflection surveys by utilizing the amplitude versus offset information present in the observed wave fields both earth structure and a variable background velocity can be accounted for by combining the born and wkbj approximations in a before stack migration with two output sections one for density variations and the other for bulk modulus variations for the inversion the medium is considered to be composed of a known low spatial frequency variation the background plus an unknown high spatial frequency variation in bulk modulus and density the reflectivity the division between the background and the reflectivity depends upon the frequency content of the source for constant background parameters computations are done in the fourier domain where the first part of the algorithm includes a frequency shift identical to that in an f k migration the modulus and density variations are then determined by observing in a least squares sense amplitude versus offset wavenumber for a spatially variable background wkbj green s operators that model the direct wave in a medium with a smoothly varying background are used a downward continuation with these operators removes the effects of variable velocity from the problem and consequently the remainder of the inversion essentially proceeds as if the background were constant if the background is strictly depth dependent the inversion can be expressed in closed form the method neglects multiples and surface waves and it is restricted to precritical reflections density is distinguishable from bulk modulus only if a sufficient range of precritical incident angles is present in the data

a test for constant correlations in a multivariate garch model we introduce a lagrange multiplier lm test for the constant correlation hypothesis in a multivariate garch model the test examines the restrictions imposed on a model which encompasses the constant correlation multivariate garch model it requires the estimates of the constant correlation model only and is computationally convenient we report some monte carlo results on the finite sample properties of the lm statistic the lm test is compared against the information matrix im test due to bera and kim 1996 the lm test appears to have good power against the alternatives considered and is more robust to nonnormality we apply the test to three data sets namely spot futures prices foreign exchange rates and stock market returns the results show that the spot futures and foreign exchange data have constant correlations while the correlations across national stock market returns are time varying

inverse extrapolation of primary seismic waves forward wave field extrapolation operators simulate propagation effects from one depth level to another inverse wave field extrapolation operators eliminate those propagation effects since forward wave field extrapolation can be described in terms of spatial convolution inverse wave field extrapolation can be described in terms of spatial deconvolution a simple approximation to a stable spatially band limited deconvolution operator is obtained by taking the complex conjugate of the convolution operator a one way version of the kirchhoff integral that contains the conjugate complex green s function is derived unlike the situation with respect to the forward problem the modification of the closed surface integral into an open boundary integral involves an approximation that is identical to the approximation in the conjugate complex deconvolution approach this approximation neglects the evanescent field and causes a second order amplitude error for a plane acquisition surface the one way kirchhoff

3 d depth migration via mcclellan transformations three dimensional seismic wavefields may be extrapolated in depth one frequency at a time by two dimensional convolution with a circularly symmetric frequency and velocity dependent filter this depth extrapolation performed for each frequency independently lies at the heart of 3 d finite difference depth migration the computational efficiency of 3 d depth migration depends directly on the efficiency of this depth extrapolation mcclellan transformations provide an efficient method for both designing and implementing two dimensional digital filters that have a particular form of symmetry such as the circularly symmetric depth extrapolation filters used in 3 d depth migration given the coefficients of one dimensional frequency and velocity dependent filters used to accomplish 2 d depth migration mcclellan transformations lead to a simple and efficient algorithm for 3 d depth migration 3 d depth migration via mcclellan transformations is simple because the coefficients of two dimensional depth

explicit 3d depth migration with a constrained operator numerical anisotropy is one of the main problems in the design of explicit 3d depth extrapolation operators this paper introduces a new method based on constraining the number of independent coefficients for the full 3d extrapolation operator the extrapolation operator is divided into two regions the coefficients for the inner part of the extrapolation operator are treated the same as the full 3d extrapolation operator the coefficients for the outer part of the extrapolation operator are constrained to be constant as a function of azimuth for a given radius this strategy reduces the number of floating point operations because for each extrapolation step the number of complex multiplications are reduced and replaced by complex additions the numerical workload of this alternative scheme is comparable to the hale mcclellan scheme impulse responses are compared with finite difference solutions for the two way acoustic wave equation it is demonstrated that the numerical anisotropy for the proposed sc

global hemispheric temperatures and co shifting a vector shifting mean autoregressive analysis abstract this paper examines local changes in annual temperature data for the northern and southern hemispheres 1850 2017 by using a multivariate generalization of the shifting meanautoregressive model of gonzalez and terasvirta 2008 univariate models are first fitted to each series by using the quickshift methodology full information maximum likelihood estimates of a bivariate system of temperature equations are then obtained and asymptotic properties of the corresponding estimators considered the system is then used to perform formal tests of co movements called co shifting in the series the results show evidence of co shifting in the two series

locating a crack of arbitrary but known shape by the method of path independent integrals abstract the solution of a crack problem of an arbitrary but known shape inside an infinite plane isotropic elastic medium can be achieved in general by the method of complex singular integral equations and their numerical solution by using the gauss or the lobatto chebyshev methods in a few special cases like straight or circular arc shaped cracks this solution is available in closed form in this paper we will not contribute to the above methods of solution of crack problems but we will propose a method for the determination of the exact position of such a crack inside a closed contour in the elastic medium by gathering and using information along this contour only by experimental techniques and applying the method of complex path independent integrals for the location of the crack this paper constitutes a nontrivial generalization of relevant previous results by the author and it is of quite general applicability in fracture mechanics for nondestructive testing numerical results for the particular case of a straight crack are displayed for the illustration of the efficiency of the method the generalization of the present results to the determination of additional geometric and loading parameters of the crack is also suggested very briefly and related numerical results concerning the length of the crack and the pressure distribution on it in the aforementioned numerical application are also presented

an iterative inversion of back scattered acoustic waves the application of the born approximation to the scattered wave field followed by a wkbj and far field approximation on the propagation green s function for a slowly varying background medium leads to a simple integral relation between the density and bulk modulus anomalies superimposed on the background medium and the scattered wave field an iterative inversion scheme based on successive back projections of the wave field is used to reconstruct the two acoustic parameters the scheme when applied to data generated using the direct integral relation shows that the variations of the parameters can be reconstructed the procedure is readily applicable to actual data since every iterative step is essentially a prestack kirchhoff migration followed by the application of the direct born approximation and far field operator

multidimensional signature deconvolution and free surface multiple elimination of marine multicomponent ocean bottom seismic data this paper presents a wave equation method for multidimensional signature deconvolution designature and elimination of free surface related multiples demultiple in four component 4c ocean bottom seismic data the designature demultiple method has the following characteristics it preserves primary amplitudes while attenuating free surface related multiples it requires no knowledge of the sea floor parameters and the subsurface it requires information only of the local density and acoustic wave propagation velocity just above the sea floor it accommodates source arrays and no information except location of the physical source array its volume and its radiation characteristics wavelet is required designature is an implicit part of the demultiple process hence the method is capable of transforming recorded reflection data excited by any source array below the sea surface into free surface demultipled data that would be recorded from a point source with any desired signature in addition the incident wavefield is not subtracted from the data prior to free surface demultiple hence separation of incident and scattered fields is not an issue as it is for most other free surface demultiple schemes the designature demultiple algorithm can be divided into two major computational steps first a multidimensional deconvolution operator inversely proportional to the time derivative of the downgoing part of the normal component of the particle velocity just above the sea floor is computed second an integral equation is solved to find any component of the designatured free surface demultipled multicomponent field when the geology is horizontally layered the designature and free surface demultiple scheme greatly simplifies and lends itself toward implementation in the p domain or frequency wavenumber domain as deterministic deconvolution of common shot gathers or common receiver gathers when source array variations are negligible