time series model specification in the presence of outliers abstract outliers are commonplace in data analysis time series analysis is no exception noting that the effect of outliers on model identification statistics could be serious this article is concerned with the problem of time series model specification in the presence of outliers an iterative procedure is proposed to identify the outliers to remove their effects and to specify a tentative model for the underlying process the procedure is essentially based on the iterative estimation procedure of chang and tiao 1983 and the extended sample autocorrelation function esacf model identification method of tsay and tiao 1984 an example is given properties of the proposed procedure are discussed

aggregation vs global diffusive behavior in the higher dimensional keller segel model abstract we consider the classical parabolic parabolic keller segel system u t u u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a smooth bounded domain r n it is proved that in space dimension n 3 for each q n 2 and p n one can find e 0 0 such that if the initial data u 0 v 0 satisfy u 0 l q e and v 0 l p e then the solution is global in time and bounded and asymptotically behaves like the solution of a discoupled system of linear parabolic equations in particular u v approaches the steady state m m as t where m is the total mass m u 0 of the population moreover we shall show that if is a ball then for arbitrary prescribed m 0 there exist unbounded solutions emanating from initial data u 0 v 0 having total mass u 0 m

testing for the cointegrating rank of a var process with level shift at unknown time a systems cointegration rank test is proposed that is applicable for vector autoregressive var processes with a structural shift at unknown time the structural shift is modeled as a simple shift in the level of the process it is proposed to estimate the break date first on the basis of a full unrestricted var model two alternative estimators are considered and their asymptotic properties are derived in the next step the deterministic part of the process including the shift size is estimated and the series are adjusted by subtracting the estimated deterministic part a johansen type test for the cointegrating rank is applied to the adjusted series the test statistic is shown to have a well known asymptotic null distribution that does not depend on the break date the performance of the procedure in small samples is investigated by simulations

outlier detection in multivariate time series by projection pursuit in this article we use projection pursuit methods to develop a procedure for detecting outliers in a multivariate time series we show that testing for outliers in some projection directions can be more powerful than testing the multivariate series directly the optimal directions for detecting outliers are found by numerical optimization of the kurtosis coefficient of the projected series we propose an iterative procedure to detect and handle multiple outliers based on a univariate search in these optimal directions in contrast with the existing methods the proposed procedure can identify outliers without prespecifying a vector arma model for the data the good performance of the proposed method is illustrated in a monte carlo study and in a real data analysis

global existence and asymptotic behavior in a two species chemotaxis system with logistic source abstract in this work we consider the two species chemotaxis system with logistic source we present the global existence of generalized solutions under appropriate regularity assumptions on the initial data in addition the asymptotic behavior of the solutions is studied and our results generalize and improve some well known results in the literature

evaluation of maximum likelihood parameter estimation techniques for conceptual rainfall runoff models influence of calibration data variability and length on model credibility the success of an automatic calibration procedure is highly dependent on the choice of the objective function and the nature quantity and quality of the data used the objective function should be selected on the basis of the stochastic properties of the errors present in the data and in the model also the data should be chosen so as to contain as much valuable information about the process as possible in this paper we compare the performance of two maximum likelihood estimators the amle which assumes the presence of first lag autocorrelated homogeneous variance errors and the hmle which assumes the presence of uncorrelated inhomogeneous variance errors to the commonly used simple least squares criterion sls the model calibrated was the soil moisture accounting model of the u s national weather service s river forecast system sma nwsrfs the results indicate that a properly chosen objective function can enhance the possibility of obtaining unique and conceptually realistic parameter estimates furthermore the sensitivity of the estimation results to various characteristics of the calibration data such as hydrologic variability and length are substantially reduced

cluster identification using projections this article describes a procedure to identify clusters in multivariate data using information obtained from the univariate projections of the sample data onto certain directions the directions are chosen as those that minimize and maximize the kurtosis coefficient of the projected data it is shown that under certain conditions these directions provide the largest separation for the different clusters the projected univariate data are used to group the observations according to the values of the gaps or spacings between consecutive ordered observations these groupings are then combined over all projection directions the behavior of the method is tested on several examples and compared to k means mclust and the procedure proposed by jones and sibson in 1987 the proposed algorithm is iterative affine equivariant flexible robust to outliers fast to implement and seems to work well in practice

global existence and asymptotic stability of the fractional chemotaxis fluid system in r3 abstract in this paper we consider a model arising from biology consisting of fractional chemotaxis equations coupled to viscous incompressible fluid equations throughout transport and external force in r 3 we establish the existence and uniqueness of global solution with small initial data by combining the local existence and a priori estimates as well as continuation argument moreover the decay rates of the solutions and their higher order spatial derivatives are established towards the equilibrium by introducing the negative sobolev space h s 0 s 3 2

asymptotic stability of a two species chemotaxis system with non diffusive chemoattractant abstract we study the behavior of two biological populations u and v attracted by the same chemical substance whose behavior is described in terms of second order parabolic equations the model considers a logistic growth of the species and the interactions between them are relegated to the chemoattractant production the system is completed with a third equation modeling the evolution of chemical we assume that the chemical w is a non diffusive substance and satisfies an ode more precisely u t u u 1 w w 1 u 1 u x t 0 v t v v 2 w w 2 v 1 v x t 0 w t h u v w x t 0 under appropriate boundary and initial conditions in an n dimensional open and bounded domain we consider the cases of positive chemo sensitivities not necessarily constant elements the chemical production function h increases as the concentration of the species u and v increases we first study the global existence and uniform boundedness of the solutions by using an iterative approach the asymptotic stability of the homogeneous steady state is a consequence of the growth of h i and the size of i finally some examples of the theoretical results are presented for particular functions h and i

bayesian inference and prediction for mean and variance shifts in autoregressive time series abstract this article is concerned with statistical inference and prediction of mean and variance changes in an autoregressive time series we first extend the analysis of random mean shift models to random variance shift models we then consider a method for predicting when a shift is about to occur this involves appending to the autoregressive model a probit model for the probability that a shift occurs given a chosen set of explanatory variables the basic computational tool we use in the proposed analysis is the gibbs sampler for illustration we apply the analysis to several examples

boundedness and asymptotic stability of solutions to a two species chemotaxis system with consumption of chemoattractant this paper deals with a two competing species chemotaxis system with consumption of chemoattractant ut d1 u u 1 w w 1u 1 u a1v x t 0 vt d2 v v 2 w w 2v 1 a2u v x t 0 wt d3 w u v w x t 0 under homogeneous neumann boundary conditions in a bounded domain rn rn n 1n 1 with smooth boundary where the initial data u0 v0 c0 2 and w0 w1 w0 w1 are non negative and the parameters d1 d2 d3 0d1 d2 d3 0 1 2 0 1 2 0 a1 a2 0a1 a2 0 and 0 0 the chemotactic function i w i w i 1 2i 1 2 is smooth and satisfying some conditions it is proved that the corresponding initial boundary value problem possesses a unique global bounded classical solution if one of the following cases hold for i 1 2i 1 2 i i w 0 i 0 i w 0 i 0 and w0 l did3n 1 0 i 2did3n 1 0 iarctan di d32n 1did3 ii 0 w0 l d33 n 1 i l 0 w0 l min 2didi d3 1 moreover we prove asymptotic stabilization of solutions in the sense that if a1 a2 0 1 a1 a2 0 1 and u0 0 v0u0 0 v0 then any global bounded solution exponentially converge to 1 a11 a1a2 1 a21 a1a2 0 as t t if a1 1 a2 0a1 1 a2 0 and v0 0v0 0 then any global bounded solution exponentially converge to 0 1 0 0 1 0 as t t if a1 1 a2 0a1 1 a2 0 and v0 0v0 0 then any global bounded solution algebraically converge to 0 1 0 0 1 0 as t t

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

global solutions in a high dimensional two species chemotaxis model with lotka volterra competitive kinetics abstract this paper deals with the two species chemotaxis system with logistic source u t u 1 u w 1 u 1 u a 1 v x t 0 v t v 2 v w 2 v 1 a 2 u v x t 0 w t w w u v x t 0 under homogeneous neumann boundary condition in a smooth bounded domain r n n 1 it is proved that in convex domains the problem possesses a unique global bounded solution if 1 and 2 are large enough moreover we establish the existence of global weak solution for any 1 0 and 2 0

a maximum likelihood criterion for use with data collected at unequal time intervals a new maximum likelihood nmle criterion suitable for model calibration using data which are recorded at unequal time intervals and contain autocorrelated errors is derived validation of the nmle criterion has been carried out both on a simple two parameter reservoir model using synthetically generated data and on a more complicated hillslope model using real data from the pukeiti catchment in new zealand comparison between the nmle criterion and the simple least squares criterion reveals the superiority of the former over the latter comparison between the nmle criterion and the maximum likelihood criterion for the autocorrelated case proposed by sorooshian 1978 has shown that both criteria would yield results with no practical difference if equal time interval data were used however the nmle criterion can work on variable time interval data which provide more information than equal time interval data and therefore produce better visual results in hydrologic simulations

boundedness vs blow up in a chemotaxis system abstract we determine the critical blow up exponent for a keller segel type chemotaxis model where the chemotactic sensitivity equals some nonlinear function of the particle density assuming some growth conditions for the chemotactic sensitivity function we establish an a priori estimate for the solution of the problem considered and conclude the global existence and boundedness of the solution furthermore we prove the existence of solutions that become unbounded in finite or infinite time in that situation where this a priori estimate fails

boundedness and stabilization in a two species chemotaxis system with signal absorption abstract this paper is concerned with the neumann initial boundary value problem for the two species chemotaxis system with consumption of chemoattractant u t u 1 u w x t 0 v t v 2 v w x t 0 w t w u v w x t 0 in a smooth bounded domain r n n 2 where the parameters 1 2 and are positive it is proved that if max 1 2 w x 0 l 2 n the problem possesses a unique global classical solution that is uniformly bounded moreover we prove that u x t 1 u x 0 v x t 1 v x 0 and w x t 0 as t uniformly with respect x

holder estimates for local solutions of some doubly nonlinear degenerate parabolic equations abstract we prove interior and boundary holder continuity for bounded weak soluttions of a class of quasilinear parabolic equations whose prototype is u t div u m 1 du p 2 du

modeling flat stretches bursts and outliers in time series using mixture transition distribution models abstract the class of mixture transition distribution mtd time series models is extended to general non gaussian time series in these models the conditional distribution of the current observation given the past is a mixture of conditional distributions given each one of the last p observations they can capture non gaussian and nonlinear features such as flat stretches bursts of activity outliers changepoints in a single unified model class they can also represent time series defined on arbitrary state spaces univariate or multivariate continuous discrete or mixed which need not even be euclidean they perform well in the usual case of gaussian time series without obvious nonstandard behaviors the models are simple analytically tractable easy to simulate readily estimated the stationarity and autocorrelation properties of the models are derived a simple em algorithm is given and shown to work well for estimation the models are applied to several real and simulated datasets with satisfacto

outliers in multivariate time series summary this paper generalises four types of disturbance commonly used in univariate time series analysis to the multivariate case highlights the differences between univariate and multivariate outliers and investigates dynamic effects of a multivariate outlier on individual components the effect of a multivariate outlier depends not only on its size and the underlying model but also on the interaction between the size and the dynamic structure of the model the latter factor does not appear in the univariate case a multivariate outlier can introduce various types of outlier for the marginal component models by comparing and contrasting results of univariate and multivariate outlier detections one can gain insights into the characteristics of an outlier we use real examples to demonstrate the proposed analysis

eventual smoothness and asymptotics in a three dimensional chemotaxis system with logistic source abstract we prove existence of global weak solutions to the chemotaxis system u t u u v u u 2 v t v v u under homogeneous neumann boundary conditions in a smooth bounded convex domain r n for arbitrarily small values of 0 additionally we show that in the three dimensional setting after some time these solutions become classical solutions provided that is not too large in this case we also consider their large time behaviour we prove decay if 0 and the existence of an absorbing set if 0 is sufficiently small

boundedness and stabilization in a two dimensional two species chemotaxis navier stokes system with competitive kinetics abstract this paper deals with the two species chemotaxis navier stokes system with lotka volterra competitive kinetics n 1 t u n 1 n 1 1 n 1 c 1 n 1 1 n 1 a 1 n 2 in 0 n 2 t u n 2 n 2 2 n 2 c 2 n 2 1 a 2 n 1 n 2 in 0 c t u c c n 1 n 2 c in 0 u t u u u p n 1 n 2 u 0 in 0 under homogeneous neumann boundary conditions in a bounded domain r 2 with smooth boundary this system consists of two models which were attracting mathematical interests one is a chemotaxis navier stokes system which is known as a challenging model the other is a two species chemotaxis system with lotka volterra competitive kinetics which has a complicated form both systems were recently well investigated however the above mixed system seems to be not studied yet this paper gives results for global existence boundedness and stabilization of solutions to the above system

global existence and asymptotic stability of solutions to a two species chemotaxis system with any chemical diffusion abstract this paper deals with the two species chemotaxis system u t u u 1 w w 1 u 1 u in 0 v t v v 2 w w 2 v 1 v in 0 w t d w h u v w in 0 where is a bounded domain in r n with smooth boundary n n h i are functions satisfying some conditions negreanu tello 2014 2015 12 13 proved global existence and asymptotic behavior of solutions to the above system when 0 d 1 the main purpose of the present paper is to remove the restriction of 0 d 1