Mixed autoregressive-moving average multivariate processes with time-dependent coefficients

Conditions for mixed autoregressive-moving average processes with time-dependent coefficients to be purely nondeterministic and invertible can be obtained from classical difference equations theory. These conditions involve one-sided Green's functions or their matricial equivalents. A recursive computation of these functions is proposed, which allows one to drop the assumption of nondegeneracy classicaly made about the highest order matrix of difference operators; it constitutes thus a generalized definition of these functions.     

A measure of bullwhip effect in supply chains with a mixed autoregressive-moving average demand process

In this paper, we quantify the impact of the bullwhip effect – the phenomenon in which information on demand is distorted as moving up a supply chain – for a simple two-stage supply chain with one supplier and one retailer. Assuming that the retailer employs a base stock inventory policy, and that the demand forecast is performed via a mixed autoregressive-moving average model, ARMA(1, 1), we investigate the effects of the autoregressive coefficient, the moving average parameter, and the lead time on the bullwhip effect.     

The best parameter subset using the Chebychev curve fitting criterion

The Chebychev (also Minimax andL _∞ Norm) criterion has been widely studied as a method for curve fitting. Published computer codes are available to obtain the optimal parameter estimates to fit a linear function to a set of given points under the Chebychev criterion. The purpose of this paper is to study procedures for obtaining the best subset ofq parameters from a given set ofm parameters whereq is less-than-or-equal-tom.     

On the behavior of the recursive sequence

This paper deals with the global asymptotic behavior ef the nonlinear and nonautonomous dfference equaiion of nth order given in the title. The analysis is carried out by using methods from the theory of positive discrete dynamical systems. In particular, the recursive sequence considered defines self-mappings of a cone which are contractive with respect to the part-metric.     

A curious renewal process average

The lifetimes of a renewal process observed during a fixed interval (0, t] are smaller, on the average, than the process mean lifetime; it is shown that the mean observed lifetime has a particularly simple form.     

On recursive decompositions of measures

Recursive decompositions of a complex measure relative to a nonnegative measure are considered and properties of the decompositions and conditions for convergence are established.     

On the fitting length of NC-groups

In this paper NC-groups (i.e. finite groups G, in which for every Sylow p-subgroup P of G, N _G(Z(P))=C _G(Z(P)) are studied. Mainly the Authors give a way to construct solvable NC-groups with arbitrarely large fitting length and trivial center. Further some results about nonsolvable NC-groups are given.     

On the average number ofk-sets

In this paper we compute in closed form the average number ofk-sets of an allowable sequence. This work supported by a grant from the NSF.     

On the construction of a nonlinear recursive predictor

In this paper, we present a novel approach for constructing a nonlinear recursive predictor. Given a limited time series data set, our goal is to develop a predictor that is capable of providing reliable long-term forecasting. The approach is based on the use of an artificial neural network and we propose a combination of network architecture, training algorithm, and special procedures for scaling and initializing the weight coefficients. For time series arising from nonlinear dynamical systems, the power of the proposed predictor has been successfully demonstrated by testing on data sets obtained from numerical simulations and actual experiments.     

On the stability of solutions under recursive programming

Summary Recursive linear programming is defined by a sequence of linear programming problems in which a recursive relation is built into the system through either the coefficients of the objective function, the constraint matrix, or the right-hand side parameters. Here we consider the case where the right-hand side parameters are subject to a recursive time relation indicating how current period plans are related to past expectations and performance. Our object here is twofold: first, to analyze the stability properties of a linear recursive programming (LRP) model and second, to indicate some basic extensions of the LRP in the light of what is generally called the active approach of stochastic linear programming (SLP). Some simple theorems are developed in this connection and this is followed by a brief discussion of the possible lines of empirical applications.

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Zusammenfassung Rekursives lineares Programmieren wird als eine Aufeinanderfolge von linearen Programmproblemen definiert, bei denen eine rekursive Beziehung in das System eingebaut ist, und zwar entweder über die Koeffizienten der Zielfunktion, die Matrix der Beschränkungen oder die Parameter der rechten Seite. Wir betrachten hier den Fall, bei dem die Parameter der rechten Seite einer rekursiven Zeitrelation unterliegen, die den Zusammenhang zwischen den Plänen der gegenwärtigen Periode und früheren Erwartungen sowie deren Erfüllung angibt. Wir verfolgen zwei Ziele: Erstens wollen wir die Stabilitätseigenschaften eines linearen rekursiven Programm (LRP)-Modells analysieren, und zweitens wollen wir gewisse grundlegende Erweiterungen des LRP im Hinblick auf das sogenannte aktive Verhalten beim stochastischen Linearen Programmieren (SLP) angeben. Damit zusammenhängend werden einige einfache Theoreme entwickelt und eine kurze Diskussion der möglichen Richtungen empirischer Anwendungen angeschlossen.

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This work forms a part of a research project started originally at Iowa State University under the U.S. National Science Foundation Project NR 420-04-70 and continued presently by the authors. Some of the theoretical aspects closely related to this paper may be found in the following references: Sengupta, J. K., G. Tintner andC. Millham: On some theorems of stochastic linear programming with applications. Management Science, Vol. 10, October 1963, pp. 143–159. Sengupta, J. K., G. Tintner andB. Morrison: Stochastic linear programming with applications to economic models. Economica, August 1963, pp. 262–276. Sengupta, J. K.: Recursive constraints and stochastic linear programming. Accepted for publication Metrika. Sengupta, J. K., C. Millham andG. Tintner: On the stability of solutions under error in stochastic linear programming. Metrika No. 3, 1964. Sengupta, J. K. andT. Kumar: An application of sensitivity analysis to a linear programming problem. Unternehmungsforschung, Vol. 9, 1965, pp. 18–36. Sengupta, J. K.: On the stability of truncated solutions of stochastic linear programming. Mimeographed, December 20, 1963. Department of Economics, Iowa State University. (Sent for publication.) Sengupta, J. K., G. Tintner andC. Millham: A weak duality theorem for stochastic linear programming. Unternehmensforschung, Vol. 7, 1963, pp. 1–8.     

On the conic section fitting problem

Adjusted least squares (ALS) estimators for the conic section problem are considered. Consistency of the translation invariant version of ALS estimator is proved. The similarity invariance of the ALS estimator with estimated noise variance is shown. The conditions for consistency of the ALS estimator are relaxed compared with the ones of the paper Kukush et al. [Consistent estimation in an implicit quadratic measurement error model, Comput. Statist. Data Anal. 47(1) (2004) 123-147].     

On the direct construction of recursive MDS matrices

MDS matrices allow to build optimal linear diffusion layers in the design of block ciphers and hash functions. There has been a lot of study in designing efficient MDS matrices suitable for software and/or hardware implementations. In particular recursive MDS matrices are considered for resource constrained environments. Such matrices can be expressed as a power of simple companion matrices, i.e., an MDS matrix \(M = C_g^k\) for some companion matrix corresponding to a monic polynomial \(g(X) \in \mathbb {F}_q[X]\) of degree k. In this paper, we first show that for a monic polynomial g(X) of degree \(k\ge 2\), the matrix \(M = C_g^k\) is MDS if and only if g(X) has no nonzero multiple of degree \(\le 2k-1\) and weight \(\le k\). This characterization answers the issues raised by Augot et al. in FSE-2014 paper to some extent. We then revisit the algorithm given by Augot et al. to find all recursive MDS matrices that can be obtained from a class of BCH codes (which are also MDS) and propose an improved algorithm. We identify exactly what candidates in this class of BCH codes yield recursive MDS matrices. So the computation can be confined to only those potential candidate polynomials, and thus greatly reducing the complexity. As a consequence we are able to provide formulae for the number of such recursive MDS matrices, whereas in FSE-2014 paper, the same numbers are provided by exhaustively searching for some small parameter choices. We also present a few ideas making the search faster for finding efficient recursive MDS matrices in this class. Using our approach, it is possible to exhaustively search this class for larger parameter choices which was not possible earlier. We also present our search results for the case \(k=8\) and \(q=2^{16}\).     

On the complexity of curve fitting algorithms

We study a popular algorithm for fitting polynomial curves to scattered data based on the least squares with gradient weights. We show that sometimes this algorithm admits a substantial reduction of complexity, and, furthermore, find precise conditions under which this is possible. It turns out that this is, indeed, possible when one fits circles but not ellipses or hyperbolas.     

On the internal structure of random recursive circuits

We study the joint probability distribution of the number of nodes of fan-out k in random recursive circuits. For suitable norming we obtain a limiting multivariate normal distribution for the numbers of node of fan-out at most k, where we compute explicitly the limiting covariance matrix by solving a recurrence satisfied among its entries.     

Circular spline fitting using an evolution process

We propose a new method to approximate a given set of ordered data points by a spatial circular spline curve. At first an initial circular spline curve is generated by biarc interpolation. Then an evolution process based on a least-squares approximation is applied to the curve. During the evolution process, the circular spline curve converges dynamically to a stable shape. Our method does not need any tangent information. During the evolution process, the number of arcs is automatically adapted to the data such that the final curve contains as few arc arcs as possible. We prove that the evolution process is equivalent to a Gauss-Newton-type method.     

On maximal subgroups of the group of recursive permutations

The group G _R of all permutations belonging to R is considered for any partially recursively closed class of functions R. It is proved that the group G _R has a continuum number of maximal subgroups. Examples of constructive maximal subgroups of G _R are given.