martingale transforms goodness of fit tests in regression models this paper discusses two goodness of fit testing problems the first problem pertains to fitting an error distribution to an assumed nonlinear parametric regression model while the second pertains to fitting a parametric regression model when the error distribution is unknown for the first problem the paper contains tests based on a certain martingale type transform of residual empirical processes the advantage of this transform is that the corresponding tests are asymptotically distribution free for the second problem the proposed asymptotically distribution free tests are based on innovation martingale transforms a monte carlo study shows that the simulated level of the proposed tests is close to the asymptotic level for moderate sample sizes

diagnostics for nonlinearity and heteroscedasticity in errors in variables regression we suggest new plotting methods for residual analysis in errors in variables regression the standard residuals analyses are based on the methods of miller and fuller and are appropriate when the errors in the regression and the measurement error are symmetrically distributed by appropriate we mean that in large samples the plots will not falsely identify a nonexistent pattern of heteroscedasticity or nonlinearity the standard methods are not appropriate in this sense for skewed error distributions our methods require replication of the error prone predictors but they are appropriate for both symmetric and skewed error distributions besides residual plots we also construct hypothesis tests for heteroscedasticity in terms of power for detecting heteroscedasticity we show that the standard plot is more efficient when the residuals are normally distributed although it does not achieve its nominal level for skewed error distributions simulations are used to illustrate the results we also conside

joint and marginal specification tests for conditional mean and variance models this article proposes a class of joint and marginal spectral diagnostic tests for parametric conditional means and variances of linear and nonlinear time series models the use of joint and marginal tests is motivated from the fact that marginal tests for the conditional variance may lead to misleading conclusions when the conditional mean is misspecified the new tests are based on a generalized spectral approach and do not need to choose a lag order depending on the sample size or to smooth the data moreover the proposed tests are robust to higher order dependence of unknown form in particular to conditional skewness and kurtosis it turns out that the asymptotic null distributions of the new tests depend on the data generating process hence we implement the tests with the assistance of a wild bootstrap procedure a simulation study compares the finite sample performance of the proposed and competing tests and shows that our tests can play a valuable role in time series modeling finally an application to the s p 500 highlights the merits of our approach

a new analytical and numerical treatment for singular two point boundary value problems via the adomian decomposition method based on the adomian decomposition method a new analytical and numerical treatment is introduced in this research to investigate linear and non linear singular two point bvps the effectiveness of the proposed approach is verified by several linear and non linear examples

weak convergence of the sequential empirical processes of residuals in arma models this paper studies the weak convergence of the sequential empirical process hat k n of the estimated residuals in arma p q models when the errors are independent and identically distributed it is shown that under some mild conditions hat k n converges weakly to a kiefer process the weak convergence is discussed for both finite and infinite variance time series models an application to a change point problem is considered

goodness of fit problem and scanning innovation martingales this paper is mainly devoted to the following statistical problem in the case of random variables of any finite dimension and both simple or parametric hypotheses how to construct convenient empirical processes which could provide the basis for goodness of fit tests more or less in the same way as the uniform empirical process does in the case of simple hypothesis and scalar random variables the solution of this problem is connected here with the theory of multiparameter martingales and the theory of function parametric processes namely for the limiting gaussian processes some kind of filtration is introduced and so called scanning innovation processes are constructed the adapted standard wiener processes in one to one correspondence with initial gaussian processes this is done for the function parametric versions of the processes

detecting shocks outliers and breaks in time series abstract a single outlier in a regression model can be detected by the effect of its deletion on the residual sum of squares an equivalent procedure is the simple intervention in which an extra parameter is added for the mean of the observation in question similarly for unobserved components or structural time series models the effect of elaborations of the model on inferences can be investigated by the use of interventions involving a single parameter such as trend or level changes because such time series models contain more than one variance the effect of the intervention is measured by the change in individual variances we examine the effect on the estimated parameters of moving various kinds of intervention along the series the horrendous computational problems involved are overcome by the use of score statistics combined with recent developments in filtering and smoothing interpretation of the resulting time series plots of diagnostics is aided by simulation envelopes our procedures illustrated with four example permit keen insights into the fragility of inferences to specific shocks such as outliers and level breaks although the emphasis is mostly on parameter estimation forecast are also considered possible extensions include seasonal adjustment and detrending of series

new types of exact solutions for nonlinear schrodinger equation with cubic nonlinearity although many exact solutions were obtained for the cubic schrodinger equation by many researchers we obtained in this research not only more exact solutions but also new types of exact solutions in terms of jacobi elliptic functions and weierstrass elliptic function

edge preserving and peak preserving smoothing an alternative procedure is developed to the smoothed linear fitting method of mcdonald and owen the procedure is based on the detection of discontinuities by comparing at any given position three smooth fits diagnostics are used to detect discontinuities in the regression function itself edge detection or in its first derivative peak detection an application in electron microscopy is discussed

order preserving nonparametric regression with applications to conditional distribution and quantile function estimation in some regression problems we observe a response yti to level t of a treatment applied to an individual with level xi of a given characteristic where it has been established that response is monotone increasing in the level of the treatment a related problem arises when estimating conditional distributions where the raw data are typically independent and identically distributed pairs xi zi and yti denotes the proportion of zi s that do not exceed t we expect the regression means gt x e yti xi x to enjoy the same order relation as the responses that is gt gs whenever s t this requirement is necessary to obtain bona fide conditional distribution functions for example if we estimate gt by passing a linear smoother through each dataset t xi yti 1 i n then the order preserving property is guaranteed if and only if the smoother has nonnegative weights however in such cases the estimators generally have high levels of boundary bias on the other hand the order preser

derivative estimation for longitudinal data analysis examining features of blood pressure measured repeatedly during pregnancy estimating velocity and acceleration trajectories allows novel inferences in the field of longitudinal data analysis such as estimating change regions rather than change points and testing group effects on nonlinear change in an outcome ie a nonlinear interaction in this article we develop derivative estimation for 2 standard approaches polynomial mixed models and spline mixed models we compare their performance with an established method principal component analysis through conditional expectation through a simulation study we then apply the methods to repeated blood pressure bp measurements in a uk cohort of pregnant women where the goals of analysis are to i identify and estimate regions of bp change for each individual and ii investigate the association between parity and bp change at the population level the penalized spline mixed model had the lowest bias in our simulation study and we identified evidence for bp change regions in over 75 of pregnant women using mean velocity difference revealed differences in bp change between women in their first pregnancy compared with those who had at least 1 previous pregnancy we recommend the use of penalized spline mixed models for derivative estimation in longitudinal data analysis

two integrable lattice hierarchies and their respective darboux transformations two integrable lattice hierarchies associated with two discrete matrix spectral problems are derived and the infinitely many conservation laws of the first integrable model is obtained moreover the darboux transformations based on different darboux matrixes 2 3 4 and 3 2 4 for the above mentioned integrable hierarchies are established with the help of two different gauge transformations of lax pairs in this paper as an application the explicit solutions of the two integrable hierarchies are presented

a decomposition method for solving the nonlinear klein gordon equation in this paper adomian s decomposition scheme is presented as an alternate method for solving the nonlinear klein gordon equation the method is demonstrated by several examples comparing the scheme with existing collocation finite difference and finite element techniques shows that the present approach is highly accurate and converges rapidly

estimation and model selection of semiparametric copula based multivariate dynamic models under copula misspecification we introduce a new class of semiparametric copula based multivariate dynamic scomdy models which specify the conditional mean and the conditional variance of a multivariate time series parametrically but specify the multivariate distribution of the standardized innovation semiparametrically as a parametric copula evaluated at nonparametric marginal distributions we first study large sample properties of the estimators of scomdy model parameters under a misspecified parametric copula then propose pseudo likelihood ratio plr tests for model selection between two scomdy models with possibly misspecified copulas and finally develop plr tests for model selection between more than two scomdy models the limiting null distributions of the plr tests do not depend on the estimation of conditional mean and conditional variance parameters hence are very easy to simulate empirical applications to three and higher dimensional daily exchange rate series indicate that a scomdy model with a tail dependent copula is generally preferred

g dimension complete intersection dimension complexity and relative homological algebra abstract it is shown that the g dimension and the complete intersection dimension are relative projective dimensions relative auslander buchsbaum formulas are discussed new cohomology theories called complexity cohomology are constructed the new theories play the same role in identifying rings and modules with prescribed complexity as tate vogel cohomology does in identifying modules of finite projective dimension

testing multivariate distributions in garch models in this paper we consider testing distributional assumptions in multivariate garch models based on empirical processes using the fact that joint distribution carries the same amount of information as the marginal together with conditional distributions we first transform the multivariate data into univariate independent data based on the marginal and conditional cumulative distribution functions we then apply the khmaladze s martingale transformation k transformation to the empirical process in the presence of estimated parameters the k transformation eliminates the effect of parameter estimation allowing a distribution free test statistic to be constructed we show that the k transformation takes a very simple form for testing multivariate normal and multivariate t distributions the procedure is applied to a multivariate financial time series data set

weak convergence of the residual empirical process in explosive autoregression this paper proves the weak convergence of the residual empirical process in an explosive autoregression model to the brownian bridge as an application the kolmogorov smirnov goodness of fit test for testing that the errors have a specified distribution is shown to be asymptotically distribution free

asymptotics of some estimators and sequential residual empiricals in nonlinear time series this paper establishes the asymptotic uniform linearity of m and r scores in a family of nonlinear time series and regression models it also gives an asymptotic expansion of the standardized sequential residual empirical process in these models these results are in turn used to obtain the asymptotic normality of certain classes of m r and minimum distance estimators of the underlying parameters the classes of estimators considered include analogs of hodges lehmann huber and lad least absolute deviation estimators some applications to the change point and testing of the goodness of fit problems in threshold and amplitude dependent exponential autoregression models are also given the paper thus offers a unified functional approach to some aspects of robust inference for a large class of nonlinear time series models

distribution free specification tests of conditional models this article proposes a class of asymptotically distribution free specification tests for parametric conditional distributions these tests are based on a martingale transform of a proper sequential empirical process of conditionally transformed data standard continuous functionals of this martingale provide omnibus tests while linear combinations of the orthogonal components in its spectral representation form a basis for directional tests finally neyman type smooth tests a compromise between directional and omnibus tests are discussed as a special example we study in detail the construction of directional tests for the null hypothesis of conditional normality versus heteroskedastic contiguous alternatives a small monte carlo study shows that our tests attain the nominal level already for small sample sizes

nonhomogeneity analysis using borrowed strength abstract this article develops a borrowed strength methodology for estimating local probability densities in a random field under a piecewise stationarity condition similarities between the densities in different regions of the field can be exploited by estimating a global mixture density and imposing the parameter space support of this borrowed strength estimate on the local estimation problems the local estimates are then used in an analysis of the homogeneity of the field which is shown to benefit from the method of borrowing strength

limit theory for the sample covariance and correlation functions of moving averages abstract document describes a moving average process which have regularly varying tail probabilities with index alpha 0 the limit distribution of the sample covariance function is derived in the case that the process has a finite variance but an infinite variance but an infinite fourth moment furthermore in the infinite variance case 0 alpha 2 the sample correlation function is shown to converge in distribution to the ratio of two independent stable random variables with indices alpha and alpha 2 respectively this result immediately gives the limit distribution for the least squares estimates of the parameters in an autoregressive process author

the quantilogram with an application to evaluating directional predictability abstract we propose a new diagnostic tool for time series called the quantilogram the tool can be used formally and we provide the inference tools to do this under general conditions and it can also be used as a simple graphical device we apply our method to measure directional predictability and to test the hypothesis that a given time series has no directional predictability the test is based on comparing the correlogram of quantile hits to a pointwise confidence interval or on comparing the cumulated squared autocorrelations with the corresponding critical value we provide the distribution theory needed to conduct inference propose some model free upper bound critical values and apply our methods to s p500 stock index return data the empirical results suggest some directional predictability in returns the evidence is strongest in mid range quantiles like 5 10 and for daily data the evidence for predictability at the median is of comparable strength to the evidence around the mean and is strongest at the daily frequency

nonparametric maximum likelihood approach to multiple change point problems in multiple change point problems different data segments often follow different distributions for which the changes may occur in the mean scale or the entire distribution from one segment to another without the need to know the number of change points in advance we propose a nonparametric maximum likelihood approach to detecting multiple change points our method does not impose any parametric assumption on the underlying distributions of the data sequence which is thus suitable for detection of any changes in the distributions the number of change points is determined by the bayesian information criterion and the locations of the change points can be estimated via the dynamic programming algorithm and the use of the intrinsic order structure of the likelihood function under some mild conditions we show that the new method provides consistent estimation with an optimal rate we also suggest a prescreening procedure to exclude most of the irrelevant points prior to the implementation of the nonparametric likelihood method simulation studies show that the proposed method has satisfactory performance of identifying multiple change points in terms of estimation accuracy and computation time

exact solutions for the generalized klein gordon equation via a transformation and exp function method and comparison with adomian s method in this paper a suitable transformation and a so called exp function method are used to obtain different types of exact solutions for the generalized klein gordon equation these exact solutions are in full agreement with the previous results obtained in refs sirendaoreji auxiliary equation method and new solutions of klein gordon equations chaos solitons fractals 31 4 2007 943 950 huiqun zhang extended jacobi elliptic function expansion method and its applications communications in nonlinear science and numerical simulation 12 5 2007 627 635 one of these exact solutions is compared with the approximate solutions obtained by the modified decomposition method accurate numerical results for a wider range of time are obtained after using different types of adm pade approximation our results show that the exp function method is very effective in finding exact solutions for the problem considered while the modified decomposition method is very powerful in finding numerical solutions with good accuracy for nonlinear pde without any need for a transformation or perturbation

a numerical solution of the klein gordon equation and convergence of the decomposition method the decomposition method for solving the klein gordon equation has been implemented the explicit and numerical solutions of the equation are calculated in the form of convergent power series with easily computable components the present method performs extremely well in terms of accuracy efficiency simplicity stability and reliability we also proved the convergence of adomian s decomposition method for the nonlinear klein gordon equation

detecting relevant changes in time series models summary most of the literature on change point analysis by means of hypothesis testing considers hypotheses of the form h0 1 2versush1 1 2 where 1 and 2 denote parameters of the process before and after a change point the paper takes a different perspective and investigates the null hypotheses of no relevant changes i e h0 1 2 where is an appropriate norm this formulation of the testing problem is motivated by the fact that in many applications a modification of the statistical analysis might not be necessary if the difference between the parameters before and after the change point is small a general approach to problems of this type is developed which is based on the cumulative sum principle for the asymptotic analysis weak convergence of the sequential empirical process must be established under the alternative of non stationarity and it is shown that the resulting test statistic is asymptotically normally distributed the results can also be used to establish similarity of the parameters i e h1 1 2 at a controlled type 1 error and to estimate the magnitude 1 2 of the change with a corresponding confidence interval several applications of the methodology are given including tests for relevant changes in the mean variance parameter in a linear regression model and distribution function among others the finite sample properties of the new tests are investigated by means of a simulation study and illustrated by analysing a data example from portfolio management

nonparametric semiparametric estimation and testing of econometric models with data dependent smoothing parameters we consider nonparametric semiparametric estimation and testing of econometric models with data dependent smoothing parameters most of the existing works on asymptotic distributions of a nonparametric semiparametric estimator or a test statistic are based on some deterministic smoothing parameters while in practice it is important to use data driven methods to select the smoothing parameters in this paper we give a simple sufficient condition that can be used to establish the first order asymptotic equivalence of a nonparametric estimator or a test statistic with stochastic smoothing parameters to those using deterministic smoothing parameters we also allow for general weakly dependent data

nonparametric change point estimation consider a sequence of independent random variables x i 1 leq i leq n having cdf f for i leq theta n and cdf g otherwise a class of strongly consistent estimators for the change point theta in 0 1 is proposed the estimators require no knowledge of the functional forms or parametric families of f and g furthermore f and g need not differ in their means or other measure of location the only requirement is that f and g differ on a set of positive probability the proof of consistency provides rates of convergence and bounds on the error probability for the estimators the estimators are applied to two well known data sets in both cases yielding results in close agreement with previous parametric analyses a simulation study is conducted showing that the estimators perform well even when f and g share the same mean variance and skewness

new approach for exact solutions of time fractional cahn allen equation and time fractional phi 4 equation abstract in this article new exact analytical solutions of some nonlinear evolution equations nlees arising in science engineering and mathematical physics namely time fractional cahn allen equation and time fractional phi 4 equation are developed using tanh method by means of fractional complex transform the obtained results are demonstrated by graphs for the new solutions

estimating the innovation distribution in nonparametric autoregression we prove a bahadur representation for a residual based estimator of the innovation distribution function in a nonparametric autoregressive model the residuals are based on a local linear smoother for the autoregression function our result implies a functional central limit theorem for the residual based estimator

the homological theory of quasi resolving subcategories abstract as a generalization of a resolving subcategory which was introduced by auslander and bridger in 2 the notion of a quasi resolving subcategory of an abelian category is introduced the homological theory on quasi resolving subcategories is studied it is shown that many results in 1 2 4 5 6 8 13 14 17 18 22 25 26 27 are unified and naturally generated

nonparametric model checks for time series this paper studies a class of tests useful for testing the goodness of fit of an autoregressive model these tests are based on a class of empirical processes marked by certain residuals the paper first gives their large sample behavior under null hypotheses then a martingale transformation of the underlying process is given that makes tests based on it asymptotically distribution free consistency of these tests is also discussed briefly

influence diagnostics for linear measurement error models summary influence functions are used to show that extreme observations affect linear measurement error model estimators in directions orthogonal to and along the fitted plane rather than vertically and horizontally as with least squares estimators influence diagnostics patterned after those for least squares and derived for generalized linear models by pregibon 1981 are adapted to assess the influence of extreme observations on linear measurement error model estimators perturbation arguments and asymptotic theory are used to support the use of these diagnostics it is well known that least squares estimators are influenced by extreme observations in the response and predictor variables geometrically these influences are in directions defined by the axis of the response variable and the plane defined by the predictors as shown in 3 measurement error model estimators are affected in directions that are perpendicular to and along the fitted plane thus least squares influence diagnostics that measure the effects of observations in the vertical and the horizontal directions may fail to accurately indicate the true effects of extreme observations on measurement error model estimators kelly 1984 derives an influence function for a structural measurement error model in which the error distribution has finite fourth moments and the error covariance matrix is known up to a multiple with the aid of this influence function diagnostics such as cook s d are defined by analogy to the corresponding least squares equivalents fuller 1987 defines a measurement error model estimator of the hat matrix using estimated predictor variable values he also proposes using diagnostics and plotting techniques analogous to those of least squares with estimated model errors and estimated leverage values from the hat matrix miller 1989 provides partial theoretical justification for the use of these least squares based techniques by showing that the estimated model errors asymptotically are a gaussian process apart from these efforts little research has been conducted on influence diagnostics for measurement error models the derivation of influence diagnostics for measurement error models in this paper proceeds as follows measurement error model estimators are briefly described in 2 a more comprehensive discussion of these estimators is given by fuller 1987 ch 2 in 3 influence function arguments are used to establish the need for measurement error model diagnostics measurement error model estimators are expressed as iteratively reweighted least squares estimators in 4 leading to the adaptation of diagnostics for

fitting an error distribution in some heteroscedastic time series models this paper addresses the problem of fltting a known distribution to the innovation distribution in a class of stationary and ergodic time series models the asymptotic null distribution of the usual kolmogorov smirnov test based on the residuals generally depends on the underlying model parameters and the error distribution to overcome the dependence on the underlying model parameters we propose that tests be based on a vector of certain weighted residual empirical processes under the null hypothesis and under minimal moment conditions this vector of processes is shown to converge weakly to a vector of independent copies of a gaussian process whose covariance function depends only on the fltted distribution and not on the model under certain local alternatives the proposed test is shown to have nontrivial asymptotic power the monte carlo critical values of this test are tabulated when fltting standard normal and double exponential distributions the results obtained are shown to be applicable to garch and arma garch models the often used models in econometrics and flnance a simulation study shows that the test has satisfactory size and power for flnite samples at these models the paper also contains an asymptotic uniform expansion result for a general weighted residual empirical process useful in heteroscedastic models under minimal moment conditions a result of independent interest

asymptotically distribution free tests for the volatility function of a diffusion abstract this paper develops two tests for parametric volatility function of a diffusion model based on khmaladze 1981 s martingale transformation the tests impose no restrictions on the functional form of the drift function and are shown to be asymptotically distribution free the tests are consistent against a large class of fixed alternatives and have nontrivial power against a class of root n local alternatives the paper also extends the tests of volatility to testing for joint specifications of drift and volatility monte carlo simulations show that the tests perform well in finite samples the proposed tests are then applied to testing models of short term interest using data of treasury bill rate and eurodollar deposit rate the empirical results show that the commonly used ckls volatility function of chan et al 1992 fits volatility function poorly and none of the parametric interest rate models considered in the paper fit data well

the half half plot the half half hh plot is a new graphical method to investigate qualitatively the shape of a regression curve the empirical hh plot counts observations in the lower and upper quarter of a strip that moves horizontally over the scatterplot the plot displays jumps clearly and reveals further features of the regression curve we prove a functional central limit theorem for the empirical hh plot with rate of convergence in a simulation study the good performance of the plot is demonstrated the method is also applied to two case studies the proofs and one more case study are deferred to a supplement which is available online

a martingale approach to the changepoint problem abstract the changepoint problem for a binary sequence is considered a test statistic based on recursive residuals is compared to the test statistic suggested by pettitt the new test statistic has more interesting properties for use in sequential testing however neither of the two test statistics dominates the other sequential versions of the martingale based test forward and reverse are given and compared to other tests by means of a simulation study the reverse martingale tests detect a shift earlier if it is detected the price to be paid is a slightly higher probability of not detecting a shift

testing for parameter constancy in linear regressions an empirical distribution function approach this paper proposes some tests for parameter constancy in linear regressions the tests use weighted empirical distribution functions of estimated residuals and are asymptotically distribution free the local power analysis reveals that the proposed tests have nontrivial local power against a wide range of alternatives in particular the tests are capable of detecting error heterogeneity that is not necessarily manifested in the form of changing variances the model allows for both dynamic and trending regressors the residuals may be obtained based on any root n consistent estimator under the null of regression parameters as an intermediate result some weak convergence for stochastically weighted sequential empirical processes is established

parameter estimation for arma models with infinite variance innovations abstract we consider a standard arma process of the form phi b xt theta b zt where the innovations zt belong to the domain of attraction of a stable law so that neither the zt nor the xt have a finite variance our aim is to estimate the coefficients of phi and theta since maximum likelihood estimation is not a viable possibility due to the unknown form of the marginal density of the innovation sequence we adopt the so called whittle estimator based on the sample periodogram of the x sequence despite the fact that the periodogram does not a priori seem like a logical object to study in this non l situation we show that our estimators are consistent obtain their asymptotic distributions and show that they converge to the true values faster than in the usual l2 case

consistent order determination for processes with infinite variance summary order determination for autoregressive processes when the residuals have a distribution belonging to the domain of attraction of an infinite variance stable law is examined the use of the fpe criterion of bhansali and downham 1977 is shown to provide a consistent estimator of the order with any a 0 order determination for moving average processes is considered a procedure based on autoregressive estimates of the inverse correlations see bhansali 1983 is shown to provide a consistent estimator of the order consistency of the estimated autoregressive and moving average parameters of an arbitrary order is established the question of consistent discrimination between autoregressive and moving average models is also considered the finite sample behaviour of the discrimination procedure is investigated by means of a simulation study

nonparametric tests for nonstandard change point problems we consider independent random elements x 1 x n n n with values in a measurable space h b so that x 1 x n have a common distribution 1 and the remaining x n 1 x n have a common distribution 2 1 for some 0 1 the change point as well as the distributions are unknown a family of tests is introduced for the nonstandard change point problem h 0 0 versus h 1 0 where 0 is an arbitrary subset of 0 1 the tests are shown to be asymptotic level tests and to be consistent on a large class of alternatives the same holds for the corresponding bootstrap versions of the tests moreover we present a detailed investigation of the local power

a goodness of fit test for copulas based on martingale transformation abstract this paper proposes an asymptotically distribution free test for copulas with dynamic marginal distributions such as garch and arma processes the test is based on the empirical copula process with parametrically estimated marginal distributions by applying the khmaladze 1982 1988 1993 martingale transformation method the transformed empirical process converges to a standard gaussian process so the resulting test statistics are asymptotically distribution free monte carlo simulations show that the test performs well in finite samples an empirical application to test copulas between eur usd and gbp usd exchange rates is provided

a semiparametric changepoint model a semiparametric changepoint model is considered and the empirical likelihood method is applied to detect the change from a distribution to a weighted distribution in a sequence of independent random variables the maximum likelihood changepoint estimator is shown to be consistent the empirical likelihood ratio test statistic is proved to have the same limit null distribution as that with parametric models a data based test for the validity of the models is also proposed simulation shows the sensitivity and robustness of the semiparametric approach the methods are applied to some classical datasets such as the nile river data and stock price data

the modified decomposition method applied to unsteady flow of gas through a porous medium in this paper an analytic solution for the unsteady flow of gas through a porous medium is constructed our approach rests on the recently developed modification of the adomian decomposition method the diagonal pade approximants are effectively used in the analysis to capture the essential behavior of y x and to determine the initial slope y 0 the proposed scheme avoids the complexity provided by using perturbation techniques

change point detection for long range dependent sequences in a general setting abstract we consider a sequence of observations x i i 1 n with a marginal distribution that is given by x i p n if i n n and x i q n if i n n the parameter 0 n 1 is the location of the change point which must be estimated and may depend on the sequence length we consider the general case in which the change point can converge to one of the end points of the interval 0 1 as the sequence length n tends to infinity the sequence can be long range dependent short range dependent or independent and may be nonstationary we study a class of nonparametric estimators and prove that they are consistent and that the rate of convergence is 1 n we also deal with the case in which the distance between the distributions p n and q n tends to zero as n tends to infinity

optimal rate of convergence for nonparametric change point estimators for nonstationary sequences let x i i 1 ldots n be a possibly nonstationary sequence such that mathscr l x i p n if i leq n theta and mathscr l x i q n if i gt n theta where 0 lt theta lt 1 is the location of the change point to be estimated we construct a class of estimators based on the empirical measures and a seminorm on the space of measures defined through a family of functions mathcal f we prove the consistency of the estimator and give rates of convergence under very general conditions in particular the 1 n rate is achieved for a wide class of processes including long range dependent sequences and even nonstationary ones the approach unifies generalizes and improves on the existing results for both parametric and nonparametric change point estimation applied to independent short range dependent and as well long range dependent sequences

model checks for regression an innovation process approach in the context of regression analysis it is known that the residual cusum process may serve as a basis for the construction of various omnibus smooth and directional goodness of fit tests since a deeper analysis requires the decomposition of the cusums into their principal components and this is difficult to obtain we propose to replace this process by its innovation martingale it turns out that the resulting tests are asymptotically distribution free under composite null models and may be readily performed a simulation study is included which indicates that the distributional approximations already work for small to moderate sample sizes

evaluating garch models in this paper a unified framework for testing the adequacy of an estimated garch model is presented parametric lagrange multiplier lm or lm type tests of no arch in standardized errors linearity and parameter constancy are proposed the asymptotic null distributions of the tests are standard which makes application easy versions of the tests that are robust against nonnormal errors are provided the finite sample properties of the test statistics are investigated by simulation the robust tests prove superior to the nonrobust ones when the errors are nonnormal they also compare favourably in terms of power with misspecification tests previously proposed in the literature

a reliable modification of adomian decomposition method in this paper we propose a powerful modification of adomian decomposition method that will accelerate the rapid convergence of the series solution the validity of the modified technique is verified through illustrative examples in all cases of differential and integral equations we obtained excellent performance from the modified algorithm the modification could lead to a promising approach for many applications in applied sciences

topological and non topological solitons of the generalized klein gordon equations this paper obtains the 1 soliton solution of five various forms of the generalized nonlinear klein gordon equations the solitary wave ansatz is used to obtain the soliton solutions of each of these cases both topological as well as non topological soliton solutions are obtained depending on the type of nonlinearity in question the conserved quantities are also calculated for each of these five forms of generalized nonlinear klein gordon equations each of these forms reduce to the previously known results as special cases

the sample autocorrelations of heavy tailed processes with applications to arch we study the sample acvf and acf of a general stationary sequence under a weak mixing condition and in the case that the marginal distributions are regularly varying this includes linear and bilinear processes with regularly varying noise and arch processes their squares and absolute values we show that the distributional limits of the sample acf can be random provided that the variance of the marginal distribution is infinite and the process is nonlinear this is in contrast to infinite variance linear processes if the process has a finite second but infinite fourth moment then the sample acp is consistent with scaling rates that grow at a slower rate than the standard root n consequently asymptotic confidence bands are wider than those constructed in the classical theory we demonstrate the theory in full detail far an arch 1 process

an improvement on the exp function method when balancing the highest order linear and nonlinear terms abstract the exp function method has been widely used to solve different kinds of nonlinear partial differential equations these nonlinear partial differential equations are transformed first into nonlinear ordinary differential equations and then the ansatz of the exp function method u n c p a n exp n m d q b m exp m is applied to obtain the solution however a part of the solution using this method is to construct the relations between c p d and q by balancing the highest order linear term with the highest order nonlinear term it is proved in the present paper that c d and p q are the only relations that can be obtained by applying this method to any nonlinear ordinary differential equation therefore the additional calculations of balancing the highest order linear term with the highest order nonlinear term are not longer required in future hence the method becomes more straightforward

statistical method for detecting structural change in the growth process due to competition among individual trees and other exogenous factors that change the growth environment each tree grows following its own growth trend with some structural changes in growth over time in the present article a new method is proposed to detect a structural change in the growth process we formulate the method as a simple statistical test for signal detection without constructing any specific model for the structural change to evaluate the p value of the test the tube method is developed because the regular distribution theory is insufficient using two sets of tree diameter growth data sampled from planted forest stands of cryptomeria japonica in japan we conduct an analysis of identifying the effect of thinning on the growth process as a structural change our results demonstrate that the proposed method is useful to identify the structural change caused by thinning we also provide the properties of the method in terms of the size and power of the test

testing for structural change in regression quantiles abstract most studies in the structural change literature focus solely on the conditional mean while under various circumstances structural change in the conditional distribution or in conditional quantiles is of key importance this paper proposes several tests for structural change in regression quantiles two types of statistics are considered namely a fluctuation type statistic based on the subgradient and a wald type statistic based on comparing parameter estimates obtained from different subsamples the former requires estimating the model under the null hypothesis and the latter involves estimation under the alternative hypothesis the tests proposed can be used to test for structural change occurring in a pre specified quantile or across quantiles which can be viewed as testing for change in the conditional distribution with a linear specification of the conditional quantile function both single and multiple structural changes are considered we derive the limiting distributions under the null hypothesis and show they are nuisance parameter free and can be easily simulated a simulation study is conducted to assess the size and power in finite samples

empirical process of the squared residuals of an arch sequence we derive the asymptotic distribution of the sequential empirical process of the squared residuals of an arch p sequence unlike the residuals of an arma process these residuals do not behave in this context like asymptotically independent random variables and the asymptotic distribution involves a term depending on the parameters of the model we show that in certain applications including the detection of changes in the distribution of the unobservable innovations our result leads to asymptotically distribution free statistics

estimating the stable index alpha in order to measure tail thickness a critique stable laws are often fit to outlier prone data and if the index alpha is estimated to be much less than two then the normal law is rejected in favor of an infinite variance stable law this paper derives the theoretical properties of such a procedure when the true distribution is stable the distribution of the m l e of alpha is non regular if alpha 2 when the true distribution is not stable the estimate of alpha is not a robust measure of the rate of decrease of the tail probabilities a more robust procedure is developed and a statistic for describing and comparing the tail shapes of arbitrary samples is proposed