stability properties of implicit runge kutta methods new stability concepts bs stability and bsi stability internal bs stability are introduced bs stability is a modification and extension of b stability and enables the derivation of order results for runge kutta methods applied to general nonlinear stiff initial value problems these order results b consistency b convergence are not affected by stiffness several classes of implicit runge kutta methods are shown to be bs stable gauss radau ia and radau iia schemes

benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

rank based tests for randomness against first order serial dependence abstract optimal rank based procedures were derived in hallin ingenbleek and puri 1985 1987 and hallin and puri 1988 for some fundamental testing problems arising in time series analysis the optimality properties of these procedures are of an asymptotic nature however whereas much of the attractiveness of rank based methods lies in their small sample applicability and robustness features accordingly the objective of this article is twofold a a study of the finite sample behavior of the asymptotically optimal tests for randomness against first order autoregressive moving average dependence proposed in hallin et al 1985 both under the null hypothesis tables of critical values and under alternatives of serial dependence evaluation of the power function and b an heuristic investigation of the robustness properties of the proposed procedures with emphasis on the identification problem in the presence of outliers we begin sec 2 with a brief description of the rank based measu

on the algebraic equations in implicit runge kutta methods this paper is concerned with the system of nonlinear algebraic equations which arise in the application of implicit runge kutta methods to stir initial value problems without making the classical assumption that the stepsize h 0 is small we derive transparent conditions on the method that guarantee existence and uniqueness of solutions to the equations besides we discuss the sensitivity of the runge kutta procedure with respect to perturbations in the algebraic equations

global convergence of a cass of quasi newton methods on convex problems we study the global convergence properties of the restricted broyden class of quasi newton methods when applied to a convex objective function we assume that the line search satisfies a standard sufficient decrease condition and that the initial hessian approximation is any positive definite matrix we show global and superlinear convergence for this class of methods except for dfp this generalizes powell s well known result for the bfgs method the analysis gives us insight into the properties of these algorithms in particular it shows that dfp lacks a very desirable self correcting property possessed by bfgs

the modified newton method in the solution of stiff ordinary differential equations this paper presents an analysis of the modified newton method as it is used in codes implementing implicit formulae for integrating stiff ordinary differential equations we prove that near a smooth solution of the differential system when the jacobian is essentially negative dominant and slowly varying the modified newton iteration is contractive converging to the locally unique solution whose existence is hereby demonstrated of the implicit equations this analysis eliminates several common restrictive or unrealistic assumptions and provides insight for the design of robust codes 1 background results significance 1 1 prototype stiff problems their salient properties note the structure o the solution of the model differential equation 1 1 y ay cost a 1 namely y t eit y 0 2 1 2 sin t a cos t there is an initial transient of duration o ja 1 l log ji after which the tern eit is not active and the solution is as smooth as cos t under suitable conditions see 29 and infra solutions of the stiff time varying linear system n 1 2 y b t y g t y e r have the same structure y t is the sum of a smooth particular solution y t and a transient v t the transient a solution of the homogeneous equation v t b t v t v o y o 0 expires after a short time meanwhile ys t and its derivative have bounds expressible in terms of 1 dvb dvg 1 3 b t w b t v o 1 dtv received september 28 1989 revised august 10 1990 1980 mathematics subject classification 1985 revision primary 65l05 65h10

a nonlinear conjugate gradient method with a strong global convergence property conjugate gradient methods are widely used for unconstrained optimization especially large scale problems the strong wolfe conditions are usually used in the analyses and implementations of conjugate gradient methods this paper presents a new version of the conjugate gradient method which converges globally provided the line search satisfies the standard wolfe conditions the conditions on the objective function are also weak being similar to those required by the zoutendijk condition

automatic algorithm for monotone trend removal the available numerical algorithms for trend removal require a direct subjective intervention in choosing critical parameters in this paper an algorithm is presented which needs no initial subjective assumptions monotone trends are approximated by piecewise linear curves obtained by dividing into subintervals the signal values interval not the time interval the slope of each linear segment of the estimated trend is proportional to the average one step displacement of the signal values included into the corresponding subinterval the evaluation of the trend removal is performed on statistical ensembles of artificial time series with the random component given by realizations of autoregressive of order one stochastic processes or by fractional brownian motions the accuracy of the algorithm is compared with that of two well tested methods polynomial fitting and a nonparametric method based on moving average for stationary noise the results of the algorithm are slightly better but for nonstationary noise the preliminary results indicate that the polynomial fitting has the best accuracy as a verification on a real time series the time periods with monotone variation of global average temperature over the last 1800 phantom rule 0 3em 0ex text years are established the removal of a nonmonotone trend is also briefly discussed

optimal rank based procedures for time series analysis testing an arma model against other arma models the problem of testing a given arma model in which the density of the generating white noise is unspecified against other arma models is considered a distribution free asymptotically most powerful test based on a generalized linear serial rank statistic is provided against contiguous arma alternatives with specified coefficients in the case when the arma model in the alternative has unspecified coefficients the asymptotic sufficiency in the sense of le cam of a finite dimensional vector of rank statistics is established this asymptotic sufficiency is used to derive an asymptotically maximin most powerful test based on a generalized quadratic serial rank statistic the asymptotically maximin optimal test statistic can be interpreted as a rank based weighted version of the classical box pierce portmanteau statistic to which it reduces in some particular problems asymptotically and under gaussian assumptions

two new conjugate gradient methods based on modified secant equations following the approach proposed by dai and liao we introduce two nonlinear conjugate gradient methods for unconstrained optimization problems one of our proposed methods is based on a modified version of the secant equation proposed by zhang deng and chen and zhang and xu and the other is based on the modified bfgs update proposed by yuan an interesting feature of our methods is their account of both the gradient and function values under proper conditions we show that one of the proposed methods is globally convergent for general functions and that the other is globally convergent for uniformly convex functions to enhance the performance of the line search procedure we also propose a new approach for computing the initial steplength to be used for initiating the procedure we provide a comparison of implementations of our methods with the efficient conjugate gradient methods proposed by dai and liao and hestenes and stiefel numerical test results show the efficiency of our proposed methods

a nonparametric trend test for seasonal data with serial dependence statistical tests for monotonic trend in seasonal e g monthly hydrologic time series are commonly confounded by some of the following problems nonnormal data missing values seasonality censoring detection limits and serial dependence an extension of the mann kendall test for trend designed for such data is presented here because the test is based entirely on ranks it is robust against nonnormality and censoring seasonality and missing values present no theoretical or computational obstacles to its application monte carlo experiments show that in terms of type i error it is robust against serial correlation except when the data have strong long term persistence e g arma 1 1 monthly processes with 0 6 or short records 5 years when there is no serial correlation it is less powerful than a related simpler test which is not robust against serial correlation

a new conjugate gradient method with guaranteed descent and an efficient line search a new nonlinear conjugate gradient method and an associated implementation based on an inexact line search are proposed and analyzed with exact line search our method reduces to a nonlinear version of the hestenes stiefel conjugate gradient scheme for any inexact line search our scheme satisfies the descent condition bf g k sf t bf d k le frac 7 8 bf g k 2 moreover a global convergence result is established when the line search fulfills the wolfe conditions a new line search scheme is developed that is efficient and highly accurate efficiency is achieved by exploiting properties of linear interpolants in a neighborhood of a local minimizer high accuracy is achieved by using a convergence criterion which we call the approximate wolfe conditions obtained by replacing the sufficient decrease criterion in the wolfe conditions with an approximation that can be evaluated with greater precision in a neighborhood of a local minimum than the usual sufficient decrease criterion numerical comparisons are given with both l bfgs and conjugate gradient methods using the unconstrained optimization problems in the cute library

a note about wyl s conjugate gradient method and its applications this paper reviews the development of different versions of nonlinear conjugate gradient methods shortly the special attentions were given to the wyl method which was proposed by zengxin wei et al the convergence properties of some conjugate gradient methods applied mathematics and computation 183 2006 1341 1350 and its applications

the proof of the sufficient descent condition of the wei yao liu conjugate gradient method under the strong wolfe powell line search abstract in z wei et al the convergence properties of some conjugate gradient methods appl math comput 183 2006 1341 1350 wei et al proposed a new conjugate gradient method called wyl method which has good numerical experiments under the sufficient descent condition and wwp line search the given method s convergent results have been established by wei et al so the sufficient descent condition is important for the wyl method in this paper we prove that by restricting the parameter 1 4 under the swp line search condition the wyl method possess the sufficient descent condition which deduces the global convergent results of the wyl method under swp line search

the inefficiency of cryptocurrency and its cross correlation with dow jones industrial average abstract as a form of cryptocurrency the issue of informational efficiency of bitcoin has received much attention recently we add to the literature by investigating nine forms of cryptocurrencies i e bitcoin ripple ethereum nem stellar litecoin dash monero and verge with a battery of efficiency tests and the empirical results indicate that all these cryptocurrencies are inefficient markets what is more we further construct a value weighted cryptocurrency composite index cci and show that cci and dow jones industrial average are persistently cross correlated

estimation of nonlinear trends in water quality an improved approach using generalized additive models 1 this paper advocates the use of generalized additive models gams for the estimation of nonlinear trends in water quality in the presence of serially correlated errors the gam methodology is applicable to a range of physical chemical and biological water quality variates comparison with the estimate based on seasonal kendall s slope and robust regression is discussed an example is given concerning log transformed stream electrical conductivity which is adjusted for flow the monthly data have first order autocorrelation exceeding 0 5 and the trend is markedly nonlinear seasonal effects are shown to have been changing over time

on coverage probability independence and normality in batch means algorithms abstract we consider the batching approach to interval estimation of the mean of a stochastic process based upon simulation output in particular using batch means processes generated from underlying ar 1 processes and m m 1 queueing systems we study the effects of undetected autocorrelation on both the probability of coverage and the performance of the shapiro wilk test of normality we also conduct power comparisons of two tests used to detect first order autocorrelation in batch means processes the von neumann ratio test and a rank version thereof proposed by bartels 1982 our results indicate that a large number of batches perhaps at least 100 be used when testing for the presence of autocorrelation

new conjugacy condition and related new conjugate gradient methods for unconstrained optimization the conjugate gradient cg method has played a special role in solving large scale nonlinear optimization due to the simplicity of their iterations and their very low memory requirements based on a new quasi newton equation proposed in z wei g li l qi new quasi newton methods for unconstrain optimization preprint z wei g yu g yuan z lian the superlinear convergence of a modified bfgs type method for unconstrained optimization comput optim appl 29 3 2004 315 332 we establish a new conjugacy condition for cg methods and propose several new cg methods it is a interesting feature that these new cg methods take both the gradient and function value information under some suitable conditions the global convergence is achieved for these methods the numerical results show that one of our new cg methods is very encouraging

the convergence properties of some new conjugate gradient methods abstract in this paper a new conjugate gradient formula k is given to compute the search directions for unconstrained optimization problems general convergence results for the proposed formula with some line searches such as the exact line search the wolfe powell line search and the grippo lucidi line search are discussed under the above line searches and some assumptions the global convergence properties of the given methods are discussed the given formula k 0 and has the similar form with k prp preliminary numerical results show that the proposed methods are efficient

using exogenous variables in testing for monotonic trends in hydrologic time series one approach that has been used in performing a nonparametric test for monotonic trend in a hydrologic time series consists of a two stage analysis first a regression equation is estimated for the variable being tested as a function of an exogenous variable a nonparametric trend test such as the kendall test is then performed on the residuals from the equation by analogy to stagewise regression and through monte carlo experiments it is demonstrated that this approach will tend to underestimate the magnitude of the trend and to result in some loss in power as a result of ignoring the interaction between the exogenous variable and time an alternative approach referred to as the adjusted variable kendall test is demonstrated to generally have increased statistical power and to provide more reliable estimates of the trend slope in addition the utility of including an exogenous variable in a trend test is examined under selected conditions

the rank version of von neumann s ratio test for randomness abstract although rank tests for randomness were proposed in the literature as early as 1943 no such test has gained wide acceptance comparable to say spearman s rho test this may be due to the lack of small sample theory and of tables of critical values to enable such a test to be carried out on small samples in this article we consider the rank version of the von neumann ratio statistic and we obtain the critical values of this statistic under the randomization hypothesis in a monte carlo experiment we then show that the resulting nonparametric test for randomness has far greater power than the test based on the number of runs up and down moreover under normality its power vis a vis the normal theory von neumann ratio test is also very good it is therefore suggested that with the tables presented in this article the rank von neumann ratio test for randomness provides an easy and powerful alternative to nonparametric tests now in common use

some robust exact results on sample autocorrelations and tests of randomness abstract several exact results on the second moments of sample autocorrelations for both gaussian and non gaussian series are presented general formulae for the means variances and covariances of sample autocorrelations are given for the case where the variables in a sequence are exchangeable bounds for the variances and covariances of sample autocorrelations from an arbitrary random sequence are derived exact and explicit formulae for the variances and covariances of sample autocorrelations from a gaussian white noise are given it is observed that the latter results hold for all spherically symmetric distributions a simulation experiment with gaussian series indicates that normalizing each sample autocorrelation with its exact mean and variance instead of the usual approximate moments can improve considerably the accuracy of the asymptotic n 0 1 distribution to obtain critical values for tests of randomness the exact second moments of rank autocorrelations are also studied

a nonparametric multivariate test for monotone trend with pharmaceutical applications abstract during a drug trial each subject may have many blood constituents measured at regular time intervals the traditional method of evaluating such data using normal ranges has undergone much controversy in the clinical chemistry literature we propose a new multivariate test for monotone trend based on kendall s statistic as a way to test for change in blood constituents over the course of a drug experiment the new test avoids the unrealistic assumptions and repeated testing problem of the normal range method an example illustrates the new procedure

techniques of trend analysis for monthly water quality data some of the characteristics that complicate the analysis of water quality time series are non normal distributions seasonality flow relatedness missing values values below the limit of detection and serial correlation presented here are techniques that are suitable in the face of the complications listed above for the exploratory analysis of monthly water quality data for monotonie trends the first procedure described is a nonparametric test for trend applicable to data sets with seasonality missing values or values reported as less than the seasonal kendall test under realistic stochastic processes exhibiting seasonality skewness and serial correlation it is robust in comparison to parametric alternatives although neither the seasonal kendall test nor the alternatives can be considered an exact test in the presence of serial correlation the second procedure the seasonal kendall slope estimator is an estimator of trend magnitude it is an unbiased estimator of the slope of a linear trend and has considerably higher precision than a regression estimator where data are highly skewed but somewhat lower precision where the data are normal the third procedure provides a means for testing for change over time in the relationship between constituent concentration and flow thus avoiding the problem of identifying trends in water quality that are artifacts of the particular sequence of discharges observed e g drought effects in this method a flow adjusted concentration is defined as the residual actual minus conditional expectation based on a regression of concentration on some function of discharge these flow adjusted concentrations which may also be seasonal and non normal can then be tested for trend by using the seasonal kendall test

misspecification tests in econometrics based on ranks abstract this paper introduces a class of rank statistics for use in testing econometric models for misspecification these statistics are ideally suited to survey data since endogenous and exogenous variables in econometric models may therefore be considered exchangeable thus residuals from a wide class of models e g linear regression non linear regression simultaneous equations etc are also exchangeable since rank statistics are distribution free when based on exchangeable data it follows the rank statistics based on these residuals are also distribution free simulation studies in the linear regression case suggest that they have good power characteristics and are distributionally robust in comparison to the usual classical procedures

further studies on the wei yao liu nonlinear conjugate gradient method the wei yao liu wyl method proposed by wei et al z wei s yao l liu the convergence properties of some new conjugate gradient methods appl math comput 183 2006 1341 1350 has been proved to converge globally for uniformly convex functions with exact line search and nonconvex functions with the strong wolfe line search if the parameter email protected 0 1 4 in this paper we further study the global convergence properties of the wyl method we show that this method still converges globally for nonconvex optimization when the strong wolfe line search with the parameter s 1 4 or some armijo type line searches are used

permutational extreme values of autocorrelation coefficients and a pitman test against serial dependence somewhat more difficult this problem which is shown to reduce to a particular case of the well known travelling salesman problem is explicitly solved here for the autocorrelation coefficient of order one allowing for a simple computation of permutational critical values for pitman tests against serial dependence the case of higher order autocorrelations is however of a different nature and requires another approach

applicability of prewhitening to eliminate the influence of serial correlation on the mann kendall test 1 prewhitening has been used to eliminate the influence of serial correlation on the mann kendall mk test in trend detection studies of hydrological time series however its ability to accomplish such a task has not been well documented this study investigates this issue by monte carlo simulation simulated time series consist of a linear trend and a lag 1 autoregressive ar 1 process with a noise simulation results demonstrate that when trend exists in a time series the effect of positive negative serial correlation on the mk test is dependent upon sample size magnitude of serial correlation and magnitude of trend when sample size and magnitude of trend are large enough serial correlation no longer significantly affects the mk test statistics removal of positive ar 1 from time series by prewhitening will remove a portion of trend and hence reduces the possibility of rejecting the null hypothesis while it might be false contrarily removal of negative ar 1 by prewhitening will inflate trend and leads to an increase in the possibility of rejecting the null hypothesis while it might be true therefore prewhitening is not suitable for eliminating the effect of serial correlation on the mk test when trend exists within a time series

another improved wei yao liu nonlinear conjugate gradient method with sufficient descent property abstract recently zhang 13 take a little modification to the wei yao liu nonlinear conjugate gradient method proposed by wei et al 10 such that the modified method called nprp method in zhang 13 satisfies sufficient descent condition with greater parameter 0 1 2 in the strong wolfe line search and converges globally for nonconvex minimization with the strong wolfe line search in this paper we take a little modification to the nprp method such that the modified nprp method possesses better properties than the nprp method in zhang 13 firstly the modified nprp method possesses the sufficient descent property without any line searches secondly the modified nprp method converges globally for nonconvex minimization with wolfe line search or armijo line search moreover we extend these results to the hestenes stiefel hs method and prove that the modified hs method also possesses sufficient descent property and global convergence with the standard wolfe conditions numerical results are reported by utilizing some test problems in the cute library

serial correlation in water quality variables estimation and implications for trend analysis 1 serial correlation in water quality time series invalidates tests of significance such as seasonal kendall analysis that assume independence one approach to analyzing such data is to estimate the magnitude of the serial correlation and then use the degree of serial correlation to adjust the variance and make valid inferences four methods for estimating serial correlation lag parameters are evaluated r estimation outperformed the alternative methods considered in case studies of water quality time series the nonparametric rank von neumann s ratio test of randomness is used to test for the presence of serial correlation and r estimation is used to estimate the severity of the serial correlation case study results demonstrate that serial correlation is common in monthly water quality data and does not disappear when bimonthly intervals are used adjustment for flow and seasonal effects generally reduced estimates of serial correlation however even after flow adjustment and deseasonalization the assumption of independence was often unreasonable

statistical estimation and interpretation of trends in water quality time series three approaches to trend analysis of water quality time series are discussed 1 seasonal model with a test for trend based on ranks of observations with observations assumed to be m dependent 2 transfer function noise model in which covariate series may be included by means of transfer functions with the remaining noise modeled as a seasonal autoregressive moving average process and 3 component model with the noise decomposed into series which describe trends and irregular and seasonal variation models are studied with regards to their ability to include covariate series possibility of interpretation of trends treatment of seasonal variation and serial dependence and robustness for outliers we regard the component model being the most realistic and the most informative of the three approaches models are applied to series of monthly phosphorus concentration in the ljungbyan river in southern sweden

some global convergence properties of the wei yao liu conjugate gradient method with inexact line search abstract in z wei s yao l liu the convergence properties of some new conjugate gradient methods applied mathematics and computation 183 2006 1341 1350 wei et al proposed a new conjugate gradient method called wyl method which has good numerical experiments and some excellent properties such as k wyl 0 in this paper we prove that while t k 1 c 2 l g k 2 d k 2 the sufficient descent condition can be satisfied at each iteration of the wyl method based on this the global convergence of the wyl method with the standard armijo line search and the generalized wolfe powell line search is established

on the unique solvability of the runge kutta equations we consider the existence of a unique solution to the systems of equations that arise when we apply a runge kutta method to a stiff nonlinear system of differential equationsu f t u withf satisfying a one sided lipschitz condition with constant for any given product h whereh denotes the step size we present algebraic conditions on the runge kutta matrixa which are necessary and sufficient for unique solvability of the equations as a second topic we consider the question whether the solution to the system of equations is stable with respect to perturbations known as bsi stability for this property also necessary and sufficient algebraic conditions ona are presented

a robust goodness of fit test for generalized autoregressive conditional heteroscedastic models summary the estimation of time series models with heavy tailed innovations has been widely discussed but corresponding goodness of fit tests have attracted less attention primarily because the autocorrelation function commonly used in constructing goodness of fit tests necessarily imposes certain moment conditions on the innovations as a bounded random variable has finite moments of all orders we address the problem by first transforming the residuals with a bounded function more specifically we consider the sample autocorrelation function of the transformed absolute residuals of a fitted generalized autoregressive conditional heteroscedastic model with the corresponding residual empirical distribution function naturally employed as the transformation a robust goodness of fit test is then constructed the asymptotic distributions of the test statistic under the null hypothesis and local alternatives are derived and monte carlo experiments are conducted to examine finite sample properties the proposed test is shown to be more powerful than existing tests when the innovations are heavy tailed

a class of one parameter conjugate gradient methods this paper proposes a class of one parameter conjugate gradient methods which can be regarded as some kinds of convex combinations of some modified form of prp and hs methods the scalar k has the form of k k 1 k the convergence of the given methods is analyzed by some unified tools which show the global convergence of the proposed methods numerical experiments with the cute collections show that the proposed methods are promising

an improved wei yao liu nonlinear conjugate gradient method for optimization computation in this paper we take a little modification to the wei yao liu nonlinear conjugate gradient method proposed by wei et al z wei s yao l liu the convergence properties of some new conjugate gradient methods appl math comput 183 2006 1341 1350 such that the modified method possesses better convergence properties in fact we prove that the modified method satisfies sufficient descent condition with greater parameter email protected 0 12 in the strong wolfe line search and converges globally for nonconvex minimization we also extend these results to the hestenes stiefel method and prove that the modified hs method is globally convergent for nonconvex functions with the standard wolfe conditions numerical results are reported by using some test problems in the cute library

multivariate tests for trend in water quality several methods of testing for multivariate trend have been discussed in the statistical and water quality literature we review both parametric and nonparametric approaches and compare their performance using synthetic data a new method based on a robust estimation and testing approach suggested by sen and puri performed very well for serially independent observations a modified version of the covariance inversion approach presented by dietz and killeen also performed well for serially independent observations for serially correlated observations the covariance eigenvalue method suggested by lettenmaier was the best performer

a nonlinear conjugate gradient algorithm with an optimal property and an improved wolfe line search in this paper we seek the conjugate gradient direction closest to the direction of the scaled memoryless bfgs method and propose a family of conjugate gradient methods for unconstrained optimization an improved wolfe line search is also proposed which can avoid a numerical drawback of the original wolfe line search and guarantee the global convergence of the conjugate gradient method under mild conditions to accelerate the algorithm we introduce adaptive restarts along negative gradients based on the extent to which the function approximates some quadratic function during previous iterations numerical experiments with the cuter collection show that the proposed algorithm is promising

permutation tests for correlation in regression errors abstract this article is about tests for serial spatial or other correlation in e the error vector in the linear model y x e the errors need not come from a particular parametric distribution such as the normal p values are computed using permutations of the regression residuals in the special cases that y e or x is a vector of is the tests are valid and consistent in general regression residuals are not exchangeable so the tests are only approximate it is shown however that under mild conditions the permutation tests are asymptotically valid and consistent the test statistics are asymptotically normal in the serial case the tests are closely related to the durbin watson dw test the spatial case is illustrated with a test based on a triangulation of observation locations in addition to providing a spatial analog to the dw test the permutation tests circumvent two of the dw test s difficulties dependency on the normality of errors and the need to accommodate indifference zones

suitability of runge kutta methods in this paper we introduce the concept of suitability which means that the nonlinear equations to be solved in a runge kutta method have a unique solution we give several results about suitability and prove that the butcher i ii and iii and the lobatto iiia and iiib methods are suitable