testing and modeling multivariate threshold models abstract threshold autoregressive models in which the process is piecewise linear in the threshold space have received much attention in recent years in this article i use predictive residuals to construct a test statistic for detecting threshold nonlinearity in a vector time series and propose a procedure for building a multivariate threshold model the thresholds and the model are selected jointly based on the akaike information criterion the finite sample performance of the proposed test is studied by simulation the modeling procedure is then used to study arbitrage in security markets and results in a threshold cointegration between logarithms of future contracts and spot prices of a security after adjusting for the cost of carrying the contracts in this particular application thresholds are determined in part by the transaction costs i also apply the proposed procedure to u s monthly interest rates and two river flow series of iceland

on the combined effects of surface tension force calculation and interface advection on spurious currents within volume of fluid and level set frameworks this paper deals with the comparison of eulerian methods to take into account the capillary contribution in the vicinity of a fluid fluid interface eulerian methods are well known to produce additional vorticity close to the interface that leads to non physical spurious currents numerical equilibrium between pressure gradient and capillary force for the static bubble test case within a vof framework has been reached in 35 with the height function technique 14 35 however once the bubble is translated in a uniform flow spurious currents are maintained by slight errors induced by translation schemes in this work two main points are investigated the ability of volume of fluid and level set methods to accurately calculate the curvature and the magnitude of spurious currents due to errors in the calculation of the curvature after advection in both translating and rotating flows the spurious currents source term is expressed from the vorticity equation and used to discuss and compare the methods simulations of gas liquid taylor flow at low capillary number show that the flow structure and the bubble velocity can be significantly affected by spurious currents

self weighted lad based inference for heavy tailed threshold autoregressive models abstract the least squares estimator of the threshold autoregressive tar model may not be consistent when its tail is less than or equal to 2 neither theory nor methodology can be applied to model fitting in this case this paper is to develop a systematic procedure of statistical inference for the heavy tailed tar model we first investigate the self weighted least absolute deviation estimation for the model it is shown that the estimated slope parameters are n consistent and asymptotically normal and the estimated thresholds are n consistent each of which converges weakly to the smallest minimizer of a compound poisson process based on this theory the wald test statistic is considered for testing the linear restriction of slope parameters and a procedure is given for inference of threshold parameters we finally construct a sign based portmanteau test for model checking simulations are carried out to assess the performance of our procedure and a real example is given

a mesh decoupled height function method for computing interface curvature in this paper a mesh decoupled height function method is proposed and tested the method is based on computing height functions within columns that are not aligned with the underlying mesh and have variable dimensions because they are decoupled from the computational mesh the columns can be aligned with the interface normal vector which is found to improve the curvature calculation for under resolved interfaces where the standard height function method often fails a computational geometry toolbox is used to compute the heights in the complex geometry that is formed at the intersection of the computational mesh and the columns the toolbox reduces the complexity of the problem to a series of straightforward geometric operations using simplices the proposed scheme is shown to compute more accurate curvatures than the standard height function method on coarse meshes a combined method that uses the standard height function where it is well defined and the proposed scheme in under resolved regions is tested this approach achieves accurate and robust curvatures for under resolved interface features and second order converging curvatures for well resolved interfaces

a nonlinear autoregressive conditional duration model with applications to financial transaction data abstract this paper presents a new model that improves upon several inadequacies of the original autoregressive conditional duration acd model considered in engle and russell econometrica 66 5 1998 1127 1162 we propose a threshold autoregressive conditional duration tacd model to allow the expected duration to depend nonlinearly on past information variables conditions for the tacd process to be ergodic and existence of moments are established strong evidence is provided to suggest that fast transacting periods and slow transacting periods of nyse stocks have quite different dynamics based on the improved model we identify multiple structural breaks in the transaction duration data considered and those break points match nicely with real economic events

interface curvature via volume fractions heights and mean values on nonuniform rectangular grids estimating the local curvature of an interface involves the local determination of normals to the interface and the rates that they turn along the interface this is challenging in volume of fluid type methods since the interface between materials is specified by the relative amount it cuts off from the computational cells that it crosses also referred to as volume fraction data rather than by a discrete set of points lying on the interface itself in this work we generalize the height function method to nonuniform rectangular grids we demonstrate analytically and numerically that using three successive adjacent integral mean values or column heights interface curvature can be estimated to second order accuracy the first derivative interface normal to third order accuracy and the curve location to fourth order accuracy each at its own special points we also show that there are special points where the curvature can be estimated to fourth order accuracy when using five successive mean values instead underlying all this is a result about the accuracy of the jth derivative of the kth degree polynomial that interpolates a function f at k 1 stencil points placed irregularly in an interval of width h namely for all smooth enough functions f and for k fixed and h getting small there are k 1 j special points in the interval at which the error in the jth derivative is of order o h k 2 j this is one order higher than the usual o h k 1 j error holding over the whole interval for that derivative the special points in the interval are the k 1 j real zeroes of certain f independent polynomials of degree k 1 j with coefficients depending on the interval s stencil points in our case let f x be an indefinite integral of the unknown interfacial curve f x then f x i at k 1 successive stencil points x i is calculated using cumulative sums of the k successive integral mean values of f weighted by the successive interval sizes the k 1 points x i f x i are now interpolated by a kth degree polynomial pf x it s first derivative pf 1 approximates the unknown curve f while pf 2 and pf 3 respectively approximate f 1 and f 2 thus the results above using three successive mean values correspond to k 3 and j 3 2 1 the curvature result using five successive mean values correspond to k 5 and j 3 for this last case since the curvature k f 2 1 f 1 2 3 2 we use the facts that f 1 f 2 pf 2 o h 4 on the whole stencil interval not just at the three special points having o h 4 accuracy for f 2

modeling multiple time series with applications abstract an approach to the modeling and analysis of multiple time series is proposed properties of a class of vector autoregressive moving average models are discussed modeling procedures consisting of tentative specification estimation and diagnostic checking are outlined and illustrated by three real examples

limiting properties of the least squares estimator of a continuous threshold autoregressive model the continuous threshold autoregressive model is a sub class of the threshold autoregressive model subject to the requirement that the piece wise linear autoregressive function be continuous everywhere in contrast with the discontinuous case it is shown that under suitable regularity conditions the conditional least squares estimator of the parameters including the threshold parameter is root n consistent and asymptotically normally distributed the theory is illustrated by a simulation study and is applied to the quarterly u s unemployment rates

on likelihood ratio tests for threshold autoregression summary this paper addresses the null distribution of the likelihood ratio statistic for threshold autoregression with normally distributed noise the problem is non standard because the threshold parameter is a nuisance parameter which is absent under the null hypothesis we reduce the problem to the first passage probability associated with a gaussian process which in some special cases turns out to be a brownian bridge it is also shown that in some specific cases the asymptotic null distribution of the test statistic depends only on the degrees of freedom and not on the exact null joint distribution of the time series

least squares estimation of large dimensional threshold factor models abstract this paper studies large dimensional factor models with threshold type regime shifts in the loadings we estimate the threshold by concentrated least squares and factors and loadings by principal components the estimator for the threshold is superconsistent with convergence rate that depends on the time and cross sectional dimensions of the panel and it does not affect the estimator for factors and loadings this has the same convergence rate as in linear factor models we propose model selection criteria and a linearity test empirical application of the model shows that connectedness in financial variables increases during periods of high economic policy uncertainty

model averaging based on leave subject out cross validation for vector autoregressions abstract the vector autoregressive var model is a useful tool for economic evaluation and prediction this paper develops a leave subject out cross validation model averaging lsoma method to average predictions from var models the approximate unbiasedness of lsoma and its asymptotic optimality in terms of obtaining the lowest possible quadratic errors are established the rate of the lsoma based weights converging to the optimal weights minimizing the expected quadratic errors is also derived simulation experiments show that our method is generally more efficient than the other frequently used model selection and averaging methods two empirical applications further illustrate that the proposed method is promising

using threshold autoregressive models to study dyadic interactions considering a dyad as a dynamic system whose current state depends on its past state has allowed researchers to investigate whether and how partners influence each other some researchers have also focused on how differences between dyads in their interaction patterns are related to other differences between them a promising approach in this area is the model that was proposed by gottman and murray which is based on nonlinear coupled difference equations in this paper it is shown that their model is a special case of the threshold autoregressive tar model as a consequence we can make use of existing knowledge about tar models with respect to parameter estimation model alternatives and model selection we propose a new estimation procedure and perform a simulation study to compare it to the estimation procedure developed by gottman and murray in addition we include an empirical example based on interaction data of three dyads

gaussian mixture vector autoregression this paper proposes a new nonlinear vector autoregressive var model referred to as the gaussian mixture vector autoregressive gmvar model the gmvar model belongs to the family of mixture vector autoregressive models and is designed for analyzing time series that exhibit regime switching behavior the main difference between the gmvar model and previous mixture var models lies in the definition of the mixing weights that govern the regime probabilities in the gmvar model the mixing weights depend on past values of the series in a specific way that has very advantageous properties from both theoretical and practical point of view a practical advantage is that there is a wide diversity of ways in which a researcher can associate different regimes with specific economically meaningful characteristics of the phenomenon modeled a theoretical advantage is that stationarity and ergodicity of the underlying stochastic process are straightforward to establish and contrary to most other nonlinear autoregressive models explicit expressions of low order stationary marginal distributions are known these theoretical properties are used to develop an asymptotic theory of maximum likelihood estimation for the gmvar model whose practical usefulness is illustrated in a bivariate setting by examining the relationship between the eur usd exchange rate and a related interest rate data

spatial quantile estimation of multivariate threshold time series models abstract in this paper we study spatial quantile regression estimation of multivariate threshold time series models bahadur s representations for our estimators are established which naturally lead to asymptotic normality of the estimators simulations and a real example are used to evaluate the performance of the proposed estimators

on the least squares estimation of multiple regime threshold autoregressive models abstract this paper studies the least squares estimator lse of the multiple regime threshold autoregressive tar model and establishes its asymptotic theory it is shown that the lse is strongly consistent when the autoregressive function is discontinuous over each threshold the estimated thresholds are n consistent and asymptotically independent each of which converges weakly to the smallest minimizer of a one dimensional two sided compound poisson process the remaining parameters are n consistent and asymptotically normal the theory of chan 1993 is revisited and a numerical approach is proposed to simulate the limiting distribution of the estimated threshold via simulating a related compound poisson process based on the numerical result one can construct a confidence interval for the unknown threshold this issue is not straightforward and has remained as an open problem since the publication of chan 1993 this paper provides not only a solution to this long standing open problem but also provides methodological contributions to threshold models simulation studies are conducted to assess the performance of the lse in finite samples the results are illustrated with an application to the quarterly u s real gnp data over the period 1947 2009

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

a portmanteau test for self exciting threshold autoregressive type nonlinearity in time series summary a portmanteau test to detect self exciting threshold autoregressive type nonlinearity in time series data is proposed the test is based on cumulative sums of standardized residuals from autoregressive fits to the data significance levels for the test under the hypothesis of linearity are obtain from the asymptotic distribution of the cumulative sums as brownian motion the performance of the test is evaluated for simulated data from linear bilinear and self exciting threshold autoregressive models it is also compared with another test which has been suggested for detecting general nonlinearity features of the proposed test which make it useful in identifying the autoregressive order and the lag in threshold models are discussed

reconstructing volume tracking a new algorithm for the volume tracking of interfaces in two dimensions is presented the algorithm is based upon a well defined second order geometric solution of a volume evolution equation the method utilizes local discrete material volume and velocity data to track interfaces of arbitrarily complex topology a linearity preserving piecewise linear interface geometry approximation ensures that solutions generated retain second order spatial accuracy second order temporal accuracy is achieved by virtue of a multidimensional unsplit time integration scheme we detail our geometrically based solution method in which material volume fluxes are computed systematically with a set of simple geometric tasks we then interrogate the method by testing its ability to track interfaces through large controlled topology changes whereby an initially simple interface configuration is subjected to vortical flows numerical results for these strenuous test problems provide evidence for the algorithm s improved solution quality and accuracy

an interface reconstruction method based on analytical formulae for 2d planar and axisymmetric arbitrary convex cells in this paper we propose a non iterative interface reconstruction method for 2d planar and axisymmetric geometries that is valid for arbitrary convex cells and intended to be used in multi material simulation codes with sharp interface treatment for instance assuming that the normal vector to the interface is known we focus on the computation of the line constant so that the polygon resulting from the cell interface intersection has the requested volume to this end we first decompose the cell in trapezoidal elements and then propose a new approach to derive an exact formula for the trapezoids volumes this formula derived for both the planar and axisymmetric cases is used to first bracket and then find the line constant that exactly matches the prescribed volume the computational efficiency of the proposed method is demonstrated over a large number of reproducible conditions and against two existing methods

testing a linear time series model against its threshold extension this paper derives the asymptotic null distribution of a quasilikelihood ratio test statistic for an autoregressive moving average model against its threshold extension the null hypothesis is that of no threshold and the error term could be dependent the asymptotic distribution is rather complicated and all existing methods for approximating a distribution in the related literature fail to work hence a novel bootstrap approximation based on stochastic permutation is proposed in this paper besides being robust to the assumptions on the error term our method enjoys more flexibility and needs less computation when compared with methods currently used in the literature monte carlo experiments give further support to the new approach and an illustration is reported

consistency and limiting distribution of the least squares estimator of a threshold autoregressive model it is shown that under some regularity conditions the least squares estimator of a stationary ergodic threshold autoregressive model is strongly consistent the limiting distribution of the least squares estimator is derived it is shown that the estimator of the threshold parameter is n consistent and its limiting distribution is related to a compound poisson process

a higher order accurate surface tension modelling volume of fluid scheme for 2d curvilinear meshes abstract this paper proposes a higher order accurate curvature calculation method for volume of fluid vof based surface tension modelling on 2d curvilinear meshes the scheme extends the interface reconstruction component of the height function hf method to curvilinear meshes in 2d linear reconstructions are computed in each column overlapping the interface which results in a piecewise linear plic representation of the free surface this is done in a volume conservative manner by employing a novel sweep line algorithm the interface curvature is then computed analytically by fitting either second or fourth order polynomials to local stencils of plic facets formal second and fourth order accuracy of interface curvature is demonstrated by comparing numerical results with a variety of analytical interface definitions the curvature algorithm is implemented into a balanced force continuum surface force surface tension scheme for variable density flows second and fourth order accuracy are again demonstrated for the laplace pressure jump in the simulation of a stationary bubble with a high liquid gas density ratio lastly second order accuracy is demonstrated in computing the frequency of an inviscid oscillating droplet in zero gravity

forecasting and testing in co integrated systems abstract this paper examines the behavior of forecasts made from a co integrated system as introduced by granger 1981 granger and weiss 1983 and engle and granger 1987 it is established that a multi step forecast will satisfy the co integrating relation exactly and that this particular linear combination of forecasts will have a finite limiting forecast error variance a simulation study compares the multi step forecast accuracy of unrestricted vector autoregression with the two step estimation of the vector autoregression imposing the co integration restriction to test whether a system exhibits co integration the procedures introduced in engle and granger 1987 are extended to allow different sample sizes and numbers of variables

diagnosis with dependent symptoms bayes theorem and the analytic hierarchy process judgments are needed in medical diagnosis to determine what tests to perform given certain symptoms for many diseases what information to gather on symptoms and what combination of symptoms lead to a given disease are not well known even when the number of symptoms is small the required number of experiments to generate adequate statistical data can be unmanageably large there is need in diagnosis for an integrative model that incorporates both statistical data and expert judgment when statistical data are present but no expert judgment is available one property of this model should be to reproduce results obtained through time honored procedures such as bayes theorem when expert judgment is also present it should be possible to combine judgment with statistical data to identify the disease that best describes the observed symptoms here we are interested in the analytic hierarchy process ahp framework that deals with dependence among the elements or clusters of a decision structure to combine statistical and judgmental information it is shown that the posterior probabilities derived from bayes theorem are part of this framework and hence that bayes theorem is a sufficient condition of a solution in the sense of the ahp an illustration is given as to how a purely judgment based model in the ahp can be used in medical diagnosis the application of the model to a case study demonstrates that both statistics and judgment can be combined to provide diagnostic support to medical practitioner colleagues with whom we have interacted in doing this work

testing and modeling threshold autoregressive processes abstract the threshold autoregressive model is one of the nonlinear time series models available in the literature it was first proposed by tong 1978 and discussed in detail by tong and lim 1980 and tong 1983 the major features of this class of models are limit cycles amplitude dependent frequencies and jump phenomena much of the original motivation of the model is concerned with limit cycles of a cyclical time series and indeed the model is capable of producing asymmetric limit cycles the threshold autoregressive model however has not received much attention in application this is due to a the lack of a suitable modeling procedure and b the inability to identify the threshold variable and estimate the threshold values the primary goal of this article therefore is to suggest a simple yet widely applicable model building procedure for threshold autoregressive models based on some predictive residuals a simple statistic is proposed to test for threshold nonlinearity and specify the

dependence and independence from linear hierarchies to nonlinear networks abstract most decisions need to be free from assumptions of independence to be faithful to the complex problems in which they arise this paper illustrates how to generate priorities for decisions involving general types of dependence of criteria on alternatives criteria on criteria and alternatives on alternatives it is based on the feedback system framework of the analytic hierarchy process of which a hierarchy is a special case

testing for two regime threshold cointegration in vector error correction models this paper examines a two regime vector error correction model with a single cointegrating vector and a threshold effect in the error correction term we propose a relatively simple algorithm to obtain maximum likelihood estimation of the complete threshold cointegration model for the bivariate case we propose a suplm test for the presence of a threshold we derive the null asymptotic distribution show how to simulate asymptotic critical values and present a bootstrap approximation we investigate the performance of the test using monte carlo simulation and find that the test works quite well applying our methods to the term structure model of interest rates we find strong evidence for a threshold effect

estimation and model selection based inference in single and multiple threshold models this paper evaluates the properties of a joint and sequential estimation procedure for estimating the parameters of single and multiple threshold models we initially proceed under the assumption that the number of regimes is known a priori but subsequently relax this assumption via the introduction of a model selection based procedure that allows the estimation of both the unknown parameters and their number to be performed jointly theoretical properties of the resulting estimators are derived and their finite sample properties investigated

testing for a linear ma model against threshold ma models this paper investigates the conditional quasi likelihood ratio test for the threshold in ma models under the hypothesis of no threshold it is shown that the test statistic converges weakly to a function of the centred gaussian process under local alternatives it is shown that this test has nontrivial asymptotic power the results are based on a new weak convergence of a linear marked empirical process which is independently of interest this paper also gives an invertible expansion of the threshold ma models

a soft computing method for multi criteria decision making with dependence and feedback in this paper the decision making problems with the dependence and the feedback effects are considered although the analytic network hierarchy process anp ahp has been proposed to deal with the problems above several problems make the method impractical in this paper we proposed the fuzzy decision maps fdm which incorporates the eigenvalue method the fuzzy cognitive maps fcm and the weighting equation to overcome the problem of preferential independent and the shortcomings of the anp in addition two numerical examples are used to demonstrate the proposed method on the basis of the numerical results we can conclude that the proposed method can soundly deal with the decision making problems with the dependence and the feedback effects

introduction to m m processes abstract in this paper we introduce a new type of nonlinear model called the min max model and analyze its properties for a pair of series the stability conditions of this system are given for a nonlinearly integrated bivariate series under these stability conditions the difference between the two series exhibits threshold type nonlinearity it is possible to construct a threshold error correction model from the min max processes neglected nonlinearity tests are applied both to the univariate series and to the bivariate system in order to detect nonlinearity and it turns out that the tests using the bivariate series have better power we apply the min max model to u s treasury bills and commercial paper interest rates the spread of these interest rates shows threshold type nonlinearity and this model outperforms a linear model in terms of its predictability for out of sample data

a universal voting system based on the potential method abstract pairwise comparison of various objects alternatives is common in many procedures related to decision making potential method pm uses a weighted preference graph as the basic structure generated by such comparisons to obtain a value function potential on the set of alternatives the potential is calculated as a solution of a system of equations involving the laplacian matrix of the preference graph in multiple criteria decision analysis or group decision making each criterion or decision maker is represented by its preference graph a multigraph obtained by joining these graphs aggregates the individual preferences and generates the group potential moreover the influence weight of each criterion or decision maker on the group potential may be adjusted in this article the aggregation of preference graphs is applied to voting systems many different forms of voting ballots can generate preference graphs which gives us a universal ballot independent voting system as an illustration of the pm in the voting context we have chosen the eurovision song contest and the analysis of the cookie type ballots where the voters allocate a certain number of points cookies to the candidates

axiomatic foundation of the analytic hierarchy process this paper contains an axiomatic treatment of the analytic hierarchy process ahp the set of axioms corresponding to hierarchic structures are a special case of axioms for priority setting in systems with feedback which allow for a wide class of dependencies the axioms highlight 1 the reciprocal property that is basic in making paired comparisons 2 homogeneity that is characteristic of people s ability for making comparisons among things that are not too dissimilar with respect to a common property and hence the need for arranging them within an order preserving hierarchy 3 dependence of a lower level on the adjacent higher level 4 the idea that an outcome can only reflect expectations when the latter are well represented in the hierarchy the ahp neither assumes transitivity or the stronger condition of consistency nor does it include strong assumptions of the usual notions of rationality a number of facts are derived from these axioms providing an operational basis for the ahp

multivariate contemporaneous threshold autoregressive models this paper proposes a contemporaneous threshold multivariate smooth transition autoregressive c mstar model in which the regime weights depend on the ex ante probabilities that latent regime specific variables exceed certain threshold values a key feature of the model is that the transition function depends on all the parameters of the model as well as on the data since the mixing weights are also a function of the regime specific noise covariance matrix the model can account for contemporaneous regime specific co movements of the variables the stability and distributional properties of the proposed model are discussed as well as issues of estimation testing and forecasting the practical usefulness of the c mstar model is illustrated by examining the relationship between us stock prices and interest rates

an accelerated fully coupled parallel 3d hybrid finite volume fluid structure interaction scheme abstract in this paper we propose a fast parallel 3d fully coupled partitioned hybrid unstructured finite volume fluid structure interaction fsi scheme spatial discretisation is effected via a vertex centred finite volume method where a hybrid nodal elemental strain procedure is employed for the solid in the interest of accuracy for the incompressible fluid a split step algorithm is presented which allows the entire fluid solid system to be solved in a fully implicit yet matrix free manner the algorithm combines a preconditioned gmres solver for implicit integration of pressures with dual timestepping on the momentum equations thereby allowing strong coupling of the system to occur through the inner solver iterations further acceleration is provided at little additional cost by applying lu sgs relaxation to the viscous and advective terms the solver is parallelised for distributed memory systems using mpi and its scaling efficiency evaluated the developed modelling technology is evaluated by application to two 3d fsi problems the advanced matrix free solvers achieve reductions in overall cpu time of up to 50 times while preserving close to linear parallel computing scaling using up to 128 cpus for the problems considered

miscellanea a note on tests for nonlinearity in a vector time series a multivariate extension of the univariate nonlinearity test of tsay 1986 is presented simulation results show that the multivariate test is more powerful than its univariate counterpart especially for series having nonlinear structure involving several components of the vector process and weakly or moderately cross correlated process error terms for illustration the test is applied to a set of seasonally adjusted quarterly capital expenditures and appropriations in u s manufacturing and a vector nonlinear model for the data is constructed

threshold models in time series analysis some reflections abstract in this paper i reflect on the developments of the threshold model in time series analysis since its birth in 1978 with particular reference to econometrics

multivariate functional coefficient regression models for nonlinear vector time series data summary vector time series data are widely found in practice in this paper we propose a multivariate functional coefficient regression model with heteroscedasticity for modeling such data the local linear smoother is employed to estimate the unknown coefficient matrices asymptotic normality 10 of the proposed estimators is established and bandwidth selection is considered to deal with cointegration widely observed in financial markets we propose an error corrected multivariate functional coefficient model simulations show that the proposed estimation procedures capture nonlinear structures of coefficients well analysis of united states interest rates illustrates the proposed methodology 15

accurate interface normal and curvature estimates on three dimensional unstructured non convex polyhedral meshes this paper presents a framework for extending the height function technique for the calculation of interface normals and curvatures to unstructured non convex polyhedral meshes with application to the piecewise linear interface calculation volume of fluid method the methodology is developed with reference to a collocated node based finite volume two phase flow solver that utilizes the median dual mesh requiring a set of data structures and algorithms for non convex polyhedral operations truncation of a polyhedron by a plane intersection of two polyhedra joining of two convex polyhedra volume enforcement of a polyhedron by a plane and volume fraction initialization by a signed distance function by leveraging these geometric tools a geometric interpolation strategy for embedding structured height function stencils in unstructured meshes is developed the embedded height function technique is tested on surfaces with known interface normals and curvatures namely cylinder sphere and ellipsoid tests are performed on the median duals of a uniform cartesian mesh a wedge mesh and a tetrahedral mesh and comparisons are made with conventional methods across the tests the embedded height function technique outperforms contemporary methods and its accuracy approaches the accuracy that the traditional height function technique exemplifies on uniform cartesian meshes

hysteretic autoregressive time series models this paper extends the classical two regime threshold autoregressive model by introducing hysteresis to its regime switching structure which leads to a new model the hysteretic autoregressive model the proposed model enjoys the piecewise linear structure of a threshold model but has a more flexible regime switching mechanism a sufficient condition is given for geometric ergodicity conditional least squares estimation is discussed and the asymptotic distributions of its estimators and information criteria for model selection are derived simulation results and an example support the model