Modified relaxation method for mathematical programs with complementarity constraints

In this paper, we suggest a new relaxation method for solving mathematical programs with complementarity constraints. This method can be regarded as a modification of a method proposed in a recent paper (J. Opt. Theory Appl. 2003; 118 :81–116). We show that the main results remain true for the modified method and particularly, some conditions assumed in the previous paper can be removed. Copyright © 2007 John Wiley & Sons, Ltd.     

An exact formula for the move-to-front rule for self-organizing lists

A collection of items (e.g., books), each with an associated weight (or popularity), is arranged in a row. At each unit of time an item is removed with probability proportional to its weight and replaced at the left end of the row. Thismove-to-front rule gives a Markov chain on permutations often known as theTsetlin library. We derive an exact and tractable formula for the probability of any permutation after any number of moves. From the formula we read off previously studied quantities of interest associated with the chain, such as the stationary distribution and eigenvalues. Measuring discrepancy from stationarity by separation, we use the formula to find the initial arrangement giving the slowest convergence to stationarity. The time to stationarity in this case is a convolution of geometric random variables which we analyze for three natural choices of weights. We also assess the time required for an important functional, namely, expected search cost, to approach its stationary value.     

Fixed design regression for time series: Asymptotic normality

Consider the fixed regression model with general weights, and suppose that the error random variables are coming from a strictly stationary stochastic process, satisfying the strong mixing condition. The asymptotic normality of the proposed estimate is established under weak conditions. The applicability of the results obtained is demonstrated by way of two existing estimates, the Gasser-Müller estimate and that of Priestley and Chao. The asymptotic normality of these estimates is further illustrated by means of a concrete example from the class of autoregressive processes.     

A stochastic volatility factor model of heston type. Statistical properties and estimation

In this paper we study the properties of a new multidimensional continuous-time stochastic covariance process, the Stochastic Volatility Factor model. Two helpful conditional characteristic functions, one needed for estimation and the other used in the pricing of financial derivatives are provided, together with the properties of the instantaneous dependence structure. Conditions for stationarity, ergodicity and mixing properties of the increments are studied. The estimation of the model is performed using the Continuum-Generalized Method of Moments (CGMM). A simulation exercise is included showing parameters are recovered, confirming identifiability. The model is also calibrated to exemplary financial data.     

Mixed variational principle in elasticity theory and canonical systems of equations

The paper proposes a modification of the mixed variational principle from which stationarity conditions are derived in the form of a mixed system of equations resolved for the first derivatives of the displacement and stress components acting in a plane perpendicular to one of the coordinate axes. The variational principle allows decreasing the dimension of the problem of elasticity thus reducing the system of equations to a canonical form. The modified mixed principle helps immediately obtain a canonical system of equations for various applied theories. This possibility is demonstrated with the example of the Timoshenko theory of plates __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 55–62, May 2007.     

New method to obtain the acute sill of an ecological model with complex polynomial perturbation

This research aims to highlight and examine an example of ecological complexity. By taking into account the interference between predator and prey, we introduce an ecological system with a general functional response. This model is perturbed by a novel class of fluctuations in the polynomial form. Analytically, we present an alternative method to obtain the acute threshold between stationarity and predator disappearance. Our analysis enriches and improves the work of Zhou et al. (2021) by unifying the criteria of said asymptotic characteristics. Numerically, we audit the accuracy of our threshold in three particular situations: linear, quadratic and cubic perturbations. We establish that the increasing order of disturbance has a passive influence on the extinction time of predators. This finding highlights that complex noise sources have a positive role in the transient dynamics of ecological systems.     

Cointegration analysis of brand and category sales: Stationarity and long‐run equilibrium in market shares

The present study uses modern time series methodology to understand long‐run equilibrium in markets and provides additional evidence of the frequent existence of stationary market shares for frequently purchased consumer products. Dekimpe and Hanssens, Marketing Science 1995; 14(2):G109–121 using a database of over 400 prior studies, found that 78 per cent of the market share series they studied were stationary, but that 68 per cent of the sales series were evolving. Our findings reconcile these results. A major contribution of this paper is its demonstration that the prior empirical evidence that a majority of sales series is in evolution is consistent with stationary market shares, if brand sales and category sales are cointegrated. To the extent that competitive activities have an effect on market share, an implication of our findings is that these activities may, in general, only have a temporary effect on market share. Finally, we distinguish, from a strategic perspective, between sales and share response at the primary‐demand level (category sales), selective‐demand level (brand sales) and relative‐position level (market share) and identify strategic scenarios depending upon their stable/evolving nature. Copyright © 2000 John Wiley & Sons, Ltd.     

The stationarity and invertibility of a class of nonlinear ARMA models

We investigate some probabilistic properties of a new class of nonlinear time series models. A sufficient condition for the existence of a unique causal, strictly and weakly stationary solution is derived. To understand the proposed models better, we further discuss the moment structure and obtain some Yule-Walker difference equations for the second and third order cumulants, which can also be used for identification purpose. A sufficient condition for invertibility is also provided.     

有序聚类虚拟变量法及其应用

本文在对邹至庄检验和递归最小二乘法剖析基础上,综合有序聚类法和虚拟变量方法,提出了一种新的结构稳定性检验方法—有序聚类虚拟变量法,克服chow检验和递归最小二乘法等在系数稳定性检验中的缺陷,利用蒙特卡罗模拟方法比较了这三种方法的优劣。并利用这三种方法对从沪深300成份股中按πPS方法抽取出来的30只股票进行β系数稳定性检验比较。研究表明,有序聚类虚拟变量法在检验系数稳定性比邹至庄检验方法和递归最小二乘法更为有效。