Exponential moving average versus moving?exponential?average

In this note we discuss the mathematical tools to define trend indicators which are used to describe market trends. We explain the relation between averages and moving averages on the one hand and the so called exponential moving average (EMA) on the other hand. We present a lot of examples and give the definition of the most frequently used trend indicator, the MACD.     

Functional regular variation of Lévy-driven multivariate mixed moving average processes

We consider the functional regular variation in the space $\mathbb {D}$ of càdlàg functions of multivariate mixed moving average (MMA) processes of the type $X_t = \int \int f(A, t - s) \Lambda (d A, d s)$ . We give sufficient conditions for an MMA process $(X_t)$ to have càdlàg sample paths. As our main result, we prove that $(X_t)$ is regularly varying in $\mathbb {D}$ if the driving Lévy basis is regularly varying and the kernel function f satisfies certain natural (continuity) conditions. Finally, the special case of supOU processes, which are used, e.g., in applications in finance, is considered in detail.     

Complete q-order moment convergence of moving average processes under φ-mixing assumptions

Let {Y _i , ?∞ < i < ∞} be a doubly infinite sequence of identically distributed φ-mixing random variables, and {a _i , ?∞ < i < ∞} an absolutely summable sequence of real numbers. We prove the complete q-order moment convergence for the partial sums of moving average processes $\left\{ {X_n = \sum\limits_{i = - \infty }^\infty {a_i + Y_{i + n} ,n \geqslant 1} } \right\}$ based on the sequence {Y _i , ?∞ < i < ∞} of φ-mixing random variables under some suitable conditions. These results generalize and complement earlier results.     

Risk preference modeling with conditional average: an application to portfolio optimization

The paper introduces a new risk measure called Conditional Average (CAVG), which was designed to cover typical attitudes towards risk for any type of distribution. It can be viewed as a generalization of Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), two commonly used risk measures. The preference structure induced by CAVG has the interpretation in Yaari’s dual theory of choice under risk and relates to Tversky and Kahneman’s cumulative prospect theory. The measure is based on the new stochastic ordering called dual prospect stochastic dominance, which can be considered as a dual stochastic ordering to recently developed prospect stochastic dominance. In general, CAVG translates into a nonconvex quadratic programming problem, but in the case of a finite probability space it can also be expressed as a mixed-integer program. The paper also presents the results of computational studies designed to assess the preference modeling capabilities of the measure. The experimental analysis was performed on the asset allocation problem built on historical values of S&P 500 sub-industry indexes. The research was supported by the grant PBZ-KBN-016/P03/99 from the State Committee for Scientific Research.     

A smoothing sample average approximation method for stochastic optimization problems with CVaR risk measure

This paper is concerned with solving single CVaR and mixed CVaR minimization problems. A CHKS-type smoothing sample average approximation (SAA) method is proposed for solving these two problems, which retains the convexity and smoothness of the original problem and is easy to implement. For any fixed smoothing constant ε, this method produces a sequence whose cluster points are weak stationary points of the CVaR optimization problems with probability one. This framework of combining smoothing technique and SAA scheme can be extended to other smoothing functions as well. Practical numerical examples arising from logistics management are presented to show the usefulness of this method.     

Complete moment convergence of moving average processes under <Emphasis Type="Italic">ρ</Emphasis>-mixing assumption

Let {Y _i : ?∞ < i < ∞} be a doubly infinite sequence of identically distributed ρ-mixing random variables, and {a _i : ?∞ < i < ∞} an absolutely summable sequence of real numbers. In this paper we prove the complete moment convergence for the partial sums of moving average processes \(\{ X_n = \sum\limits_{i = - \infty }^\infty {a_i Y_{i + n,} n \geqslant 1} \} \) based on the sequence {Y _i : ?∞ < i < ∞} of ρ-mixing random variables under some suitable conditions.     

Strong Normalizability of Typed Lambda-Calculi for Substructural Logics

The strong normalization theorem is uniformly proved for typed λ-calculi for a wide range of substructural logics with or without strong negation. We would like to thank the referees for their valuable comments and suggestions. This research was supported by the Alexander von Humboldt Foundation. The second author is grateful to the Foundation for providing excellent working conditions and generous support of this research. This work was also supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology, Grant-in-Aid for Young Scientists (B) 20700015, 2008.     

Can adaption help on the average?

Summary We study adaptive information for approximation of linear problems in a separable Hilbert space equipped with a probability measure . It is known that adaption does not help in the worst case for linear problems. We prove that adaption also doesnot help on the average. That is, there exists nonadaptive information which is as powerful as adaptive information. This result holds for orthogonally invariant measures. We provide necessary and sufficient conditions for a measure to be orthogonally invariant. Examples of orthogonally invariant measures include Gaussian measures and, in the finite dimensional case, weighted Lebesgue measures.This research was supported in part by the National Science Foundation under Grant MCS-7823676     

Magnetically-Induced Buckling of a Whirling Conducting Rod with Applications to Electrodynamic Space Tethers

We study the effect of a magnetic field on the behaviour of a slender conducting elastic structure, motivated by stability problems of electrodynamic space tethers. Both static (buckling) and dynamic (whirling) instability are considered and we also compute post-buckling configurations. The equations used are the geometrically exact Kirchhoff equations. Magnetic buckling of a welded rod is found to be described by a surprisingly degenerate bifurcation, which is unfolded when both transverse anisotropy of the rod and angular velocity are considered. By solving the linearised equations about the (quasi-) stationary solutions, we find various secondary instabilities. Our results are relevant for current designs of electrodynamic space tethers and potentially for future applications in nano- and molecular wires.     

Inexact Josephy–Newton framework for generalized equations and its applications to local analysis of Newtonian methods for constrained optimization

We propose and analyze a perturbed version of the classical Josephy–Newton method for solving generalized equations. This perturbed framework is convenient to treat in a unified way standard sequential quadratic programming, its stabilized version, sequential quadratically constrained quadratic programming, and linearly constrained Lagrangian methods. For the linearly constrained Lagrangian methods, in particular, we obtain superlinear convergence under the second-order sufficient optimality condition and the strict Mangasarian–Fromovitz constraint qualification, while previous results in the literature assume (in addition to second-order sufficiency) the stronger linear independence constraint qualification as well as the strict complementarity condition. For the sequential quadratically constrained quadratic programming methods, we prove primal-dual superlinear/quadratic convergence under the same assumptions as above, which also gives a new result.     

Combinatorial Integer Labeling Theorems on Finite Sets with Applications

Tucker’s well-known combinatorial lemma states that, for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set {±1,±2,…,±n} with the property that antipodal vertices on the boundary of the cube are assigned opposite labels, the triangulation admits a 1-dimensional simplex whose two vertices have opposite labels. In this paper, we are concerned with an arbitrary finite set D of integral vectors in the n-dimensional Euclidean space and an integer labeling that assigns to each element of D a label from the set {±1,±2,…,±n}. Using a constructive approach, we prove two combinatorial theorems of Tucker type. The theorems state that, under some mild conditions, there exists two integral vectors in D having opposite labels and being cell-connected in the sense that both belong to the set {0,1} ⁿ +q for some integral vector q. These theorems are used to show in a constructive way the existence of an integral solution to a system of nonlinear equations under certain natural conditions. An economic application is provided.     

Non-Walker Self-Dual Neutral Einstein Four-Manifolds of Petrov Type III

The local structure of the manifolds named in the title is described. Although curvature homogeneous, they are not, in general, locally homogeneous. Not all of them are Ricci-flat, which answers an existence question about type III Jordan-Osserman metrics, raised by Díaz-Ramos, García-Río and Vázquez-Lorenzo (J. Geom. Anal. 16, 39–52, 2006). Work begun during the author’s visit to the University of Santiago de Compostela, supported by Grant MTM2006-01432 (Spain).     

A Mathematica package for q-holonomic sequences and power series

We describe a Mathematica package for dealing with q-holonomic sequences and power series. The package is intended as a q-analogue of the Maple package gfun and the Mathematica package GeneratingFunctions. It provides commands for addition, multiplication, and substitution of these objects, for converting between various representations (q-differential equations, q-recurrence equations, q-shift equations), for computing sequence terms and power series coefficients, and for guessing recurrence equations given initial terms of a sequence. C. Koutschan partially supported by the Austrian Science Foundation (FWF) grants SFB F1305.     

Do we self-regulate actions or perceptions? A test of two computational models

Self-regulation theories in applied psychology disagree about whether action or perceptions are the focus of regulation. Computational models based on the two conceptualizations were constructed and simulated. In one scenario, they performed identically and in conjunction with participants in a study of the goal-level effect (Vancouver et al., Organ Res Methods 8:100–127, 2005). In another scenario they created differentiating predictions and only the computational model based on the self-regulation of perceptions matched the data of participants. Implications for research and practice are discussed.

The average distance on the Sierpiński gasket

Summary The canonical distance of points on the Sierpiski gasket is considered and its expectation deduced. The solution is surprising, both for the value and for the method derived from an analysis of graphs connected with the Tower of Hanoi problem.     

Units of ℤ(Cp × C2) and ℤ(Cp × C2 × C2)

The goal of this article is to describe a multiplicatively independent set, which generates the group of units of the integral group ring ?G, where G is either the cyclic group of order 2p or C₂ × C₂ × C_p, for a prime number p that satisfies some suitable conditions that will be specified later.     

Existence of a periodic solution for continuous and discrete periodic second-order equations with variable potentials

Green’s functions for new second-order periodic differential and difference equations with variable potentials are found, then used as kernels in integral operators to guarantee the existence of a positive periodic solution to continuous and discrete second-order periodic boundary value problems with periodic coefficient functions. A new version of the Leggett-Williams fixed point theorem is employed.     

Asymptotic behavior for non-oscillatory solutions of difference equations with several delays in the neutral term

In this paper, we first consider difference equations with several delays in the neutral term of the form * $$\Delta\left(y_{n}+\sum_{i=1}^{L}p_{i}y_{n-{k_{i}}}-\sum_{j=1}^{M}r_{j}y_{n-{\rho_{j}}}\right)+q_{n}y_{n-\tau}=0\quad \mbox{for}\ n\in\mathbb{Z}^{+}(0),$$ study various cases of coefficients in the neutral term and obtain the asymptotic behavior for non-oscillatory solution of (*) under some hypotheses. Moreover, we consider reaction-diffusion difference equations with several delays in the neutral term of the form $$\begin{array}{l}\Delta_{1}\left(u_{n,m}+\displaystyle \sum_{i=1}^{L}p_{i}u_{n-{k_{i}},m}-\displaystyle \sum_{j=1}^{M}r_{j}u_{n-{\rho_{j}},m}\right)+q_{n,m}u_{n-\tau,m}\\[18pt]\quad {}=a^{2}\Delta_{2}^{2}u_{n+1,m-1}\end{array}$$ for (n,m)∈?⁺(0)×Ω, study various cases of coefficients in the neutral term and obtain the asymptotic behavior for non-oscillatory solution under some hypotheses.     

Limit Property for Regular and Weak Generalized Convolution

We denote by ? \((\mathcal{P_{+}})\) the set of all probability measures defined on the Borel subsets of the real line (the positive half-line [0,∞)). K. Urbanik defined the generalized convolution as a commutative and associative ?₊-valued binary operation ? on ? ₊ ² which is continuous in each variable separately. This convolution is distributive with respect to convex combinations and scale changes T _a (a>0) with δ ₀ as the unit element. The key axiom of a generalized convolution is the following: there exist norming constants c _n and a measure ν other than δ ₀ such that \(T_{c_{n}}\delta_{1}^{\bullet n}\to\nu\).In Sect. 2 we discuss basic properties of the generalized convolution on ? which hold for the convolutions without the key axiom. This rather technical discussion is important for the weak generalized convolution where the key axiom is not a natural assumption. In Sect. 4 we show that if the weak generalized convolution defined by a weakly stable measure μ has this property, then μ is a factor of strictly stable distribution.