Weekday dependence of German stock market returns

The so‐called ‘Monday effect’ has been found for various stock markets of the world. The empirical finding that Monday returns are significantly smaller than returns measured for the remaining days of the week calls the efficiency hypothesis for pricing processes operating on stock markets into question. Investigating an index series measured at the Frankfurt stock exchange the paper compares estimation results of parametric and non‐parametric autoregressive models with respect to possible weekday dependence of return data. Allowing for heteroskedastic error distributions the wild bootstrap is used to infer against time‐varying means and correlation of return data in parametric models and to obtain confidence bands for non‐parametric estimates. It is shown that time dependence is an important feature describing the dynamics of German stock market returns in the period 1960–1979. Within two subsamples obtained from the period 1980–1997 the evidence in favour of such effects is mitigated substantially. Copyright © 2000 John Wiley & Sons, Ltd.     

Consistency of kernel‐based quantile regression

Quantile regression is used in many areas of applied research and business. Examples are actuarial, financial or biometrical applications. We show that a non‐parametric generalization of quantile regression based on kernels shares with support vector machines the property of consistency to the Bayes risk. We further use this consistency to prove that the non‐parametric generalization approximates the conditional quantile function which gives the mathematical justification for kernel‐based quantile regression. Copyright © 2008 John Wiley & Sons, Ltd.     

Direct and iterative methods for interval parametric algebraic systems producing parametric solutions

This paper deals with interval parametric linear systems with general dependencies. Motivated by the so‐called parameterized solution introduced by Kolev, we consider the enclosures of the solution set in a revised affine form. This form is advantageous to a classical interval solution because it enables us to obtain both outer and inner bounds for the parametric solution set and, thus, intervals containing the endpoints of the hull solution, among others. We propose two solution methods, a direct method called the generalized expansion method and an iterative method based on interval‐affine Krawczyk iterations. For the iterative method, we discuss its convergence and show the respective sufficient criterion. For both methods, we perform theoretical and numerical comparisons with some other approaches. The numerical experiments, including also interval parametric linear systems arising in practical problems of structural and electrical engineering, indicate the great usefulness of the proposed methodology and its superiority over most of the existing approaches to solving interval parametric linear systems.     

Parametric representation of wave propagation in non‐uniform media (both in transmission and stop bands)

An analytical approach based on the parametric representation of the wave propagation in non‐uniform media was considered. In addition to the previously developed theory of parametric antiresonance describing the field attenuation in stop bands, in the present paper, the behaviour of the Bloch wave in a transmission band was investigated. A wide class of exact solutions was found, and the correspondence to the quasi‐periodic Floquet solutions was shown. Copyright © 2012 John Wiley & Sons, Ltd.     

Bifurcation analysis and chaos control in a discrete‐time plant quality and larch budmoth interaction model with Ricker equation

We investigate the dynamics of two‐dimensional discrete‐time model of leaf quality and larch budmoth interaction with Ricker equation. More precisely, the qualitative behavior of larch budmoth model is discussed in which the effect of food source upon the moth population is through intrinsic growth rate. We find the parametric conditions for local asymptotic stability of the unique positive fixed point. It is also proved that under certain parametric conditions, the system undergoes period‐doubling bifurcation with the help of center manifold theory. The parametric conditions for existence and direction of Neimark‐Sacker bifurcation at positive fixed point is investigated with the help of standard mathematical techniques of bifurcation theory. The chaos control in the system is discussed through implementation of hybrid control methodology. Finally, numerical simulations are provided to illustrate theoretical results. These results of numerical simulations demonstrate chaotic long‐term behavior over a broad range of parameters. The computation of the maximum Lyapunov exponents confirms the presence of chaotic behavior in the system.     

Non‐parametric modelling of time‐varying customer service times at a bank call centre

Call centres are becoming increasingly important in our modern commerce. We are interested in modelling the time‐varying pattern of average customer service times at a bank call centre. Understanding such a pattern is essential for efficient operation of a call centre. The call service times are shown to be lognormally distributed. Motivated by this observation and the important application, we propose a new method for inference about non‐parametric regression curves when the errors are lognormally distributed. Estimates and pointwise confidence bands are developed. The method builds upon the special relationship between the lognormal distribution and the normal distribution, and improves upon a naive estimation procedure that ignores this distributional structure. Our approach includes local non‐parametric estimation for both the mean function and the heteroscedastic variance function of the logged data, and uses local polynomial regression as a fitting tool. A simulation study is performed to illustrate the method. We then apply the method to model the time‐varying patterns of mean service times for different types of customer calls. Several operationally interesting findings are obtained and discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

Anisotropic curve shortening flow in higher codimension

We consider the evolution of parametric curves by anisotropic mean curvature flow in ?ⁿ for an arbitrary n?2. After the introduction of a spatial discretization, we prove convergence estimates for the proposed finite‐element model. Numerical tests and simulations based on a fully discrete semi‐implicit stable algorithm are presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Detecting change points in the stress‐strength reliability P(X < Y)

We address the statistical problem of detecting change points in the stress‐strength reliability R=P(X<Y) in a sequence of paired variables (X,Y). Without specifying their underlying distributions, we embed this nonparametric problem into a parametric framework and apply the maximum likelihood method via a dynamic programming approach to determine the locations of the change points in R. Under some mild conditions, we show the consistency and asymptotic properties of the procedure to locate the change points. Simulation experiments reveal that, in comparison with existing parametric and nonparametric change‐point detection methods, our proposed method performs well in detecting both single and multiple change points in R in terms of the accuracy of the location estimation and the computation time. Applications to real data demonstrate the usefulness of our proposed methodology for detecting the change points in the stress‐strength reliability R. Supplementary materials are available online.     

SO(∀∃*) Sentences and Their Asymptotic Probabilities

We prove a 0‐1 law for the fragment of second order logic SO(∀∃*) over parametric classes of finite structures which allow only one unary atomic type. This completes the investigation of 0‐1 laws for fragments of second order logic defined in terms of first order quantifier prefixes over, e.g., simple graphs and tournaments. We also prove a low oscillation law, and establish the 0‐1 law for Σ¹₄(∀∃*) without any restriction on the number of unary types.     

An efficient numerical treatment of fourth‐order fractional diffusion‐wave problems

In this paper, we consider the numerical treatment of a fourth‐order fractional diffusion‐wave problem. Our proposed method includes the use of parametric quintic spline in the spatial dimension and the weighted shifted Grünwald‐Letnikov approximation of fractional integral. The solvability, stability, and convergence of the numerical scheme are rigorously proved. It is shown that the theoretical convergence order improves those of earlier work. Simulation is further carried out to demonstrate the numerical efficiency of the proposed scheme and to compare with other methods.     

An evaluation of the multivariate dispersion charts with estimated parameters under non‐normality

Various charts such as |S|, W, and G are used for monitoring process dispersion. Most of these charts are based on the normality assumption, while exact distribution of the control statistic is unknown, and thus limiting distribution of control statistic is employed which is applicable for large sample sizes. In practice, the normality assumption of distribution might be violated, while it is not always possible to collect large sample size. Furthermore, to use control charts in practice, the in‐control state usually has to be estimated. Such estimation has a negative effect on the performance of control chart. Non‐parametric bootstrap control charts can be considered as an alternative when the distribution is unknown or a collection of large sample size is not possible or the process parameters are estimated from a Phase I data set. In this paper, non‐parametric bootstrap multivariate control charts |S|, W, and G are introduced, and their performances are compared against Shewhart‐type control charts. The proposed method is based on bootstrapping the data used for estimating the in‐control state. Simulation results show satisfactory performance for the bootstrap control charts. Ultimately, the proposed control charts are applied to a real case study.     

A moments approach for omitted variables in residential histories and other panel data

This paper reviews the problems of omitted variables in panel data analysis. Results obtained from previous analyses have been shown to be sensitive to the particular parametric forms assumed for the distribution of omitted variables. An alternative non‐parametric approach is described in which the effects of omitted variables enter the model through the non‐central moments of an error term distribution. A reparametrisation ensures that the constraints on the moments of a probability distribution are not violated. The model is applied to data on the residential mobility history of a sample of households in Cardiff, Wales.     

Bifurcations and parametric representations of traveling wave solutions for the (2+1)‐dimensional Boiti–Leon–Pempinelle system

By using the method of bifurcation theory of planar dynamical systems to the traveling wave system of the (2+1)‐dimensional Boiti–Leon–Pempinelle system, exact explicit parametric representations of the traveling wave solutions are obtained in different parameter regions. Copyright © 2010 John Wiley & Sons, Ltd.     

A semiparametric Bayesian generalized linear mixed model for the reliability of Kevlar fibers

We analyze the reliability of NASA composite pressure vessels by using a new Bayesian semiparametric model. The data set consists of lifetimes of pressure vessels, wrapped with a Kevlar fiber, grouped by spool, subject to different stress levels; 10% of the data are right censored. The model that we consider is a regression on the log‐scale for the lifetimes, with fixed (stress) and random (spool) effects. The prior of the spool parameters is nonparametric, namely they are a sample from a normalized generalized gamma process, which encompasses the well‐known Dirichlet process. The nonparametric prior is assumed to robustify inferences to misspecification of the parametric prior. Here, this choice of likelihood and prior yields a new Bayesian model in reliability analysis. Via a Bayesian hierarchical approach, it is easy to analyze the reliability of the Kevlar fiber by predicting quantiles of the failure time when a new spool is selected at random from the population of spools. Moreover, for comparative purposes, we review the most interesting frequentist and Bayesian models analyzing this data set. Our credibility intervals of the quantiles of interest for a new random spool are narrower than those derived by previous Bayesian parametric literature, although the predictive goodness‐of‐fit performances are similar. Finally, as an original feature of our model, by means of the discreteness of the random‐effects distribution, we are able to cluster the spools into three different groups. Copyright © 2012 John Wiley & Sons, Ltd.     

Speed limit quasi splines and their application to interpolation with bounded first order derivative

The problem of computing spline‐like functions for ideal data, subject to two‐sided inequality constraints on the first‐order derivative, are considered, focusing primarily on constant constraints and then generalizing. Using a variational approach, in which the inequality constraints are not explicitly imposed, a special type of exponential splines we call speed limit quasi splines is introduced. A simple, non‐parametric, efficient, and robust iterative solver is suggested, which is suitable for a wide range of inequality constraints. Analysis of the convergence factor of this algorithm is provided and supported by extensive numerical tests. Copyright © 2014 John Wiley & Sons, Ltd.     

Semi‐analytical integration of the 8‐node plane element stiffness matrix using symbolic computation

The semi‐analytical integration of an 8‐node plane strain finite element stiffness matrix is presented in this work. The element is assumed to be super‐parametric, having straight sides. Before carrying out the integration, the integral expressions are classified into several groups, thus avoiding duplication of calculations. Symbolic manipulation and integration is used to obtain the basic formulae to evaluate the stiffness matrix. Then, the resulting expressions are postprocessed, optimized, and simplified in order to reduce the computation time. Maple symbolic‐manipulation software was used to generate the closed expressions and to develop the corresponding Fortran code. Comparisons between semi‐analytical integration and numerical integration were made. It was demonstrated that semi‐analytical integration required less CPU time than conventional numerical integration (using Gaussian‐Legendre quadrature) to obtain the stiffness matrix. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Global bifurcations and single‐pulse homoclinic orbits of a plate subjected to the transverse and in‐plane excitations

The Shilnikov‐type single‐pulse homoclinic orbits and chaotic dynamics of a simply supported truss core sandwich plate subjected to the transverse and the in‐plane excitations are investigated in detail. The resonant case considered here is principal parametric resonance and 1:2 internal resonance. Based on the normal form theory, the desired form for the global perturbation method is obtained. By using the global perturbation method developed by Kovacic and Wiggins, explicit sufficient conditions for the existence of a Shilnikov‐type homoclinic orbit are obtained, which implies that chaotic motions may occur for this class of truss core sandwich plate in the sense of Smale horseshoes. Numerical results obtained by using the fourth‐order Runge–Kutta method agree with theoretical analysis at least qualitatively. Copyright © 2017 John Wiley & Sons, Ltd.     

Monte Carlo exact goodness‐of‐fit tests for nonhomogeneous Poisson processes

Nonhomogeneous Poisson processes (NHPPs) are often used to model failure data from repairable systems, and there is thus a need to check model fit for such models. We study the problem of obtaining exact goodness‐of‐fit tests for parametric NHPPs. The idea is to use conditional tests given a sufficient statistic under the null hypothesis model. The tests are performed by simulating conditional samples given the sufficient statistic. Algorithms are presented for testing goodness‐of‐fit for the power law and the log‐linear law NHPP models. It is noted that while exact algorithms for the power law case are well known in the literature, the availability of such algorithms for the log‐linear case seems to be less known. A data example, as well as simulations, are considered. Copyright © 2010 John Wiley & Sons, Ltd.     

A parametric lifetime model for a multicomponents system with spatial interactions

In this paper, we consider a system made of n components displayed on a structure (eg, a steel plate). We define a parametric model for the hazard function, which includes covariates and spatial interaction between components. The state (nonfailed or failed) of each component is observed at some inspection times. From these data, we consider the problem of model parameter estimation. To achieve this, we suggest to use the SEM algorithm based on a pseudo‐likelihood function. A definition for the time‐to‐failure of the system is given, generalizing the classical cases. A study based on numerical simulations is provided to illustrate the proposed approach.