Improved ARMA spectral estimation

The autoregressive (AR) spectral estimator has been studied by several authors, Parzen [10], Burg [3], and Marple [7] to name but a few. Even though the results of Burg and later results of Nuttal [9], Ulrych and Clayton [14] and also Marple [7] significantly improved the AR spectral estimator, it still is somewhat disappointing for narrow band signals or for nearly noninvertible auroregressive moving average (ARMA) data. To circumvent the difficulties, while at the same time introducing a more robust estimator, several authors have suggested the use of the ARMA spectral estimator (e.g. Morton and Gray [8] and Cadzow [4]). In this paper, a new ARMA spectral estimator is introduced which, using a recent result of Tiao and Tsay [12], makes use of dynamic prefiltering. It seems to perform better than previously defined ARMA spectral estimators and the AR spectral estimators of Burg or Marple. Examples are given which include data which is ARMA and data which is not ARMA. Several references to work in this area are included.     

Parameter estimation and topology identification of uncertain fractional order complex networks

This paper focuses on a significant issue in the research of fractional order complex network, i.e., the identification problem of unknown system parameters and network topologies in uncertain complex networks with fractional-order node dynamics. Based on the stability analysis of fractional order systems and the adaptive control method, we propose a novel and general approach to address this challenge. The theoretical results in this paper have generalized the synchronization-based identification method that has been reported in several literatures on identifying integer order complex networks. We further derive the sufficient condition that ensures successful network identification. An uncertain complex network with four fractional-order Lorenz systems is employed to verify the effectiveness of the proposed approach. The numerical results show that this approach is applicable for online monitoring of the static or changing network topology. In addition, we present a discussion to explore which factor would influence the identification process. Certain interesting conclusions from the discussion are obtained, which reveal that large coupling strengths and small fractional orders are both harmful for a successful identification.     

Conditions of reverse bullwhip effect in pricing for price-sensitive demand functions

Supply chain mechanisms that exacerbate price variation needs special attention, since price variation is one of the root causes of the bullwhip effect. In this study, we investigate conditions that create an amplification of price variation moving from the upstream suppliers to the downstream customers in a supply chain, which is referred as the “reverse bullwhip effect in pricing” (RBP). Considering initially a single-stage supply chain in which a retailer faces a random and price-sensitive demand, we derive conditions on a general demand function for which the retail price variation is higher than that of the wholesale price. The investigation is extended to a multi-stage supply chain in which the price at each stage is determined by a game theoretical framework. We illustrate the use of the conditions in identifying commonly used demand functions that induce RBP analytically and by means of several numerical examples.     

Mono-implicit Runge-Kutta schemes for the parallel solution of initial value ODEs

Among the numerical techniques commonly considered for the efficient solution of stiff initial value ordinary differential equations are the implicit Runge-Kutta (IRK) schemes. The calculation of the stages of the IRK method involves the solution of a nonlinear system of equations usually employing some variant of Newton's method. Since the costs of the linear algebra associated with the implementation of Newton's method generally dominate the overall cost of the computation, many subclasses of IRK schemes, such as diagonally implicit Runge-Kutta schemes, singly implicit Runge-Kutta schemes, and mono-implicit (MIRK) schemes, have been developed to attempt to reduce these costs. In this paper we are concerned with the design of MIRK schemes that are inherently parallel in that smaller systems of equations are apportioned to concurrent processors. This work builds on that of an earlier investigation in which a special subclass of the MIRK formulas were implemented in parallel. While suitable parallelism was achieved, the formulas were limited to some extent because they all had only stage order 1. This is of some concern since in the application of a Runge-Kutta method to a system of stiff ODEs the phenomenon of order reduction can arise; the IRK method can behave as if its order were only its stage order (or its stage order plus one), regardless of its classical order. The formulas derived in the current paper represent an improvement over the previous investigation in that the full class of MIRK formulas is considered and therefore it is possible to derive efficient, parallel formulas of orders 2, 3, and 4, having stage orders 2 or 3.     

Identification of Refined ARMA Echelon Form Models for Multivariate Time Series

In the present article, we are interested in the identification of canonical ARMA echelon form models represented in a “refined” form. An identification procedure for such models is given by Tsay (J. Time Ser. Anal.10(1989), 357-372). This procedure is based on the theory of canonical analysis. We propose an alternative procedure which does not rely on this theory. We show initially that an examination of the linear dependency structure of the rows of the Hankel matrix of correlations, with originkin (i.e., with correlation at lagkin position (1, 1)), allows us not only to identify the Kronecker indicesn₁, …, n_d, whenk=1, but also to determine the autoregressive ordersp₁, …, p_d, as well as the moving average ordersq₁, …, q_dof the ARMA echelon form model by settingk>1 andk<1, respectively. Successive test procedures for the identification of the structural parametersn_i,p_i, andq_iare then presented. We show, under the corresponding null hypotheses, that the test statistics employed asymptotically follow chi-square distributions. Furthermore, under the alternative hypothesis, these statistics are unbounded in probability and are of the formNδ{1+o_p(1)}, whereδis a positive constant andNdenotes the number of observations. Finally, the behaviour of the proposed identification procedure is illustrated with a simulated series from a given ARMA model.     

High-order convergent deferred correction schemes based on parameterized Runge–Kutta–Nyström methods for second-order boundary value problems

Iterated deferred correction is a widely used approach to the numerical solution of first-order systems of nonlinear two-point boundary value problems. Normally, the orders of accuracy of the various methods used in a deferred correction scheme differ by 2 and, as a direct result, each time deferred correction is used the order of the overall scheme is increased by a maximum of 2. In [16], however, it has been shown that there exist schemes based on parameterized Runge–Kutta methods, which allow a higher increase of the overall order. A first example of such a high-order convergent scheme which allows an increase of 4 orders per deferred correction was based on two mono-implicit Runge–Kutta methods. In the present paper, we will investigate the possibility for high-order convergence of schemes for the numerical solution of second-order nonlinear two-point boundary value problems not containing the first derivative. Two examples of such high-order convergent schemes, based on parameterized Runge–Kutta-Nyström methods of orders 4 and 8, are analysed and discussed.     

STABILITY ANALYSIS OF H-R NEURON MODEL WITH FRACTIONAL ORDERS

In this paper,we are concerned with a Hindmarsh-Rose(H-R) neuron model of fractional orders.By employing stability theory,we present some sufficient conditions ensuring the equilibrium of system to be stable.The simulations are provided to verify the theoretical results.     

指令驱动市场中的组合下单策略研究

已有研究一般直接假设指令驱动市场中的知情交易者总是选择市价单进行交易，本文则基于现实交易状况．建立了一个理论模型．分析拥有私有信息的知情交易者组合使用限价委托单和市价委托单的决策问题．具体给出了不同私有信息状态下知情交易者的组合下单选择。     

On the cusum of squares test for variance change in nonstationary and nonparametric time series models

In this paper we consider the problem of testing for a variance change in nonstationary and nonparametric time series models. The models under consideration are the unstable AR(q) model and the fixed design nonparametric regression model with a strong mixing error process. In order to perform a test, we employ the cusum of squares test introduced by Inclán and Tiao (1994,J. Amer. Statist. Assoc.,89, 913–923). It is shown that the limiting distribution of the test statistic is the sup of a standard Brownian bridge as seen in iid random samples. Simulation results are provided for illustration.     

Customer Enquiry Management: Part of a Hierarchical System to Control Lead Times in Make-to-Order Companies

The authors are currently developing a hierarchical production planning system specifically designed for the ‘make-to-order’ sector of industry. Its aim is to control the delivery and manufacturing lead times of all orders processed by a firm. Two major decision levels are identified - the customer enquiry stage and the order release stage. Input/output control is exercised at both stages. This paper is concerned with the control mechanisms used at the customer enquiry stage. Two important backlogs of work, along with their associated backlog lengths, are identified. The system aims to maintain these backlogs between predetermined minimum and maximum lengths in order to process all orders within an acceptable length of time. It is shown that the two backlogs are linked in a manner that enables them to be controlled simultaneously. Hence, a procedure for dealing with incoming customer orders is presented.     

Efficient Scheduling Rules in a Combined Make-to-Stock and Make-to-Order Manufacturing System

In this paper, we consider a mixed MTS/MTO policy to manage a single manufacturing facility producing two classes of end-products. A few end-products have high volume demands, whereas a fairly large number of end-products have low volume demands. In this situation, it is appealing to try to produce the high volume products according to an MTS policy and the low volume products according to an MTO policy. The purpose of this paper is to analyze and compare the impact of the choice of the scheduling policy on the overall performance of the system. We consider two policies: the classical FIFO policy and a priority policy (PR). The PR policy gives priority to production orders corresponding to low volume products over production orders corresponding to high volume products. Under some simple stochastic modeling assumptions, we develop analytical/numerical solutions to optimise each system. We then provide insights regarding this issue with the help of numerical examples. It appears that for some range of parameters, the PR rule can outperform the FIFO rule in the sense that, to achieve the same service level constraint, the corresponding cost under the PR rule is much lower. This situation is encountered when the low volume products can be managed with an MTO policy under the PR scheduling rule, while they have to be managed according to an MTS policy under the FIFO scheduling rule. We also derive some theoretical properties that support our empirical findings.     

Superconvergence and Asymptotic Expansions for Bilinear Finite Volume Element Approximations

Aiming at the isoparametric bilinear finite volume element scheme, we initially derive an asymptotic expansion and a high accuracy combination formula of the derivatives in the sense of pointwise by employing the energy-embedded method on uniform grids. Furthermore, we prove that the approximate derivatives are convergent of order two. Finally, numerical examples verify the theoretical results.     

A review of the recent contribution of systems thinking to operational research and management science

The systems approach, or systems thinking, has been intimately connected with the development of OR and management science initially through the work of founders such as Churchman and Ackoff and latterly through innovations such as soft systems. In this paper we have undertaken a review of the contribution that systems thinking has been making more recently, especially to the practice of OR. Systems thinking is a discipline in its own right, with many theoretical and methodological developments, but it is also applicable to almost any problem area because of its generality, and so such a review must always be selective. We have looked at the literature from both a theoretical and an applications orientation. In the first part we consider the main systems theories and methodologies in terms of their recent developments and also their applications. This covers: the systems approach, complexity theory, cybernetics, system dynamics, soft OR and PSMs, critical systems and multimethodology. In the second part we review the main domains of application: strategy, information systems, organisations, production and operations, ecology and agriculture, and medicine and health. Our overall conclusion is that while systems may not be well established institutionally, in terms of academic departments, it is incredibly healthy in terms of the quantity and variety of its applications.     

A note on the stochastic properties of a scale change random effects model

The scale change model in survival analysis incorporates unobserved heterogeneity through a frailty that enters the baseline hazard function to change the time scale. In this paper we examine the stochastic properties of the mixtures of scale change model and build dependence between the overall population variable and the frailty variable. We also carry out stochastic comparisons between overall population variables when their respective frailty or baseline variables are ordered in the sense of various stochastic orders. Finally, we demonstrate how the variation of the baseline variable has an effect on the model.     

Explicit Calculations and Asymptotic Behavior of a Distance Measure Between Finite Abelian Groups

A metric on the space of finite abelian groups was introduced by Wolf. Though numerically computable for given groups, up to now hardly any theoretical results for this metric have been known. With a slight modification of the original definition, we are able to give a closed form for some distances and also gain some insight into the asymptotic behavior, i.e. the behavior as the group orders go to infinity.     

Innovation algorithm in ARMA process

Most of the works in Time Series Analysis are based on the Auto Regressive Integrated Moving Average (ARIMA) models presented by Box and Jenkins(1976). If the data exhibits no apparent deviation from stationarity and if it has rapidly decreasing autocorrelation function then a suitable ARMA(p,q) model is fit to the given data. Selection of the orders of p and q is one of the crucial steps in Time Series Analysis. Most of the methods to determine p and q are based on the autocorrelation function and partial autocorrelation function as suggested by Box and Jenkins (1976). Many new techniques have emerged in the literature and it is found that most of them are of very little use in determining the orders of p and q when both of them are non-zero. The Durbin-Levinson algorithm and Innovation algorithm (Brockwell and Davis, 1987) are used as recursive methods for computing best linear predictors in an ARMA(p,q) model. These algorithms are modified to yield an effective method for ARMA model identification so that the values of order p and q can be determined from them. The new method is developed and its validity and usefulness is illustrated by many theoretical examples. This method can also be applied to any real world data.     

Nim games with arbitrary periodic moving orders

A well known two person game called Nim consists in two players, alternately taking matches from a single heap of matches. In our paper we extend this game to arbitrary periodic moving orders, for exampleAABAB, whereA andB are the players. The main result states, that the player moving more frequently always can force a win, provided there are “enough” matches in the heap initially. Thus in the exampleA will win.     

Measurement and optimization of responsiveness in supply chain networks with queueing structures

In this paper we consider supply chains with multiple stages of serial or network structure. The supply chains are endogenous in the sense that they involve queues because each order’s lead-time is dependent on the orders already in the system. We define supply chain responsiveness as the probability of fulfilling customer orders within a promised lead-time and study the problems of measuring and optimizing supply chain responsiveness using queueing network models. We first consider a single-server multi-stage serial supply chain and find a closed form expression for the fulfilment time distribution. For the multi-server multi-stage problem, the closed form evaluation of the fulfilment time distribution becomes intractable due to the dependency of the lead-times in different stages. We circumvent this difficulty by proposing a novel FCFS discipline which enables a closed-form analysis. For the multi-server multi-stage Jackson-type supply chain network, to enable analysis, we convert the system into an equivalent single server single stage system with state-dependent rates. For each case, we present detailed numerical examples for both measurement and the optimization of supply chain responsiveness.     

Unreliable newsboy problem with a forecast update

In this paper, we derive an optimal ordering policy for an unreliable newsboy who can place two sequential orders before the start of a single selling season by using a demand forecast update. Supply yield is modeled using a uniform distribution considering both the minimum order guarantee and the maximum yield. Our results indicate that a firm should focus on increasing the minimum order guarantee from a first stage supplier to reduce its total supply chain cost.     

Numerical integration based on bivariate quadratic spline quasi-interpolants on Powell-Sabin partitions

In this paper we generate and study new cubature formulas based on spline quasi-interpolants in the space of quadratic Powell-Sabin splines on nonuniform triangulations of a polygonal domain in ?². By using a specific refinement of a generic triangulation, optimal convergence orders are obtained for some of these rules. Numerical tests are presented for illustrating the theoretical results.