A proposal for a new specification for a conditionally heteroskedastic variance model: the Quadratic Moving-Average Conditional Heteroskedasticity and an application to the D. Mark-U.S. dollar Exchange Rate

Ever since the appearance of the ARCH model [Engle(1982a)], an impressive array of variance specifications belonging to the same class of models has emerged [i.e. Bollerslev's (1986) GARCH; Nelson's (1990) EGARCH]. This recent domain has achieved very successful developments. Nevertheless, several empirical studies seem to show that the performance of such models is not always appropriate [Boulier(1992)]. In this paper we propose a new specification: the Quadratic Moving Average Conditional heteroskedasticity model. Its statistical properties, such as the kurtosis and the symmetry, as well as two estimators (Method of Moments and Maximum Likelihood) are studied. Two statistical tests are presented, the first one tests for homoskedasticity and the second one, discriminates between ARCH and QMACH specification. A Monte Carlo study is presented in order to illustrate some of the theoretical results. An empirical study is undertaken for the DM-US exchange rate.

The third order Melnikov function of a quadratic center under quadratic perturbation

We study quadratic perturbations of the integrable system (1+x)dH; where H =(x²+y²)=2: We prove that the first three Melnikov functions associated to the perturbed system give rise at most to three limit cycles.

Asymptotics of orthogonal polynomials via the Koosis theorem

The main aim of this short paper is to advertize the Koosis theorem in the mathematical community, especially among those who study orthogonal polynomials. We (try to) do this by proving a new theorem about asymptotics of orthogonal polynomi- als for which the Koosis theorem seems to be the most natural tool. Namely, we consider the case when a SzegÄo measure on the unit circumference is perturbed by an arbitrary measure inside the unit disk and an arbitrary Blaschke sequence of point masses outside the unit disk.

Quadratic perturbations of a quadratic reversible Lotka-Volterra System

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Algebraic properties of isochronous centers of polynomial quadratic-like Hamiltonian systems

Projecte de recerca elaborat a partir d’una estada a la School of Mathematics and Statistics de la University of Plymouth, United Kingdom, entre abril juliol del 2007.Aquesta investigació és encara oberta i la memòria que presento constitueix un informe de la recerca que estem duent a terme actualment. En aquesta nota estudiem els centres isòcrons dels sistemes Hamiltonians analítics, parant especial atenció en el cas polinomial. Ens centrem en els anomenats quadratic-like Hamiltonian systems. Diverses propietats dels centres isòcrons d'aquest tipus de sistemes van ser donades a [A. Cima, F. Mañosas and J. Villadelprat, Isochronicity for several classes of Hamiltonian systems, J. Di®erential Equations 157 (1999) 373{413]. Aquell article estava centrat principalment en el cas en que A; B i C fossin funcions analítiques. El nostre objectiu amb l'estudi que estem duent a terme és investigar el cas en el que aquestes funcions són polinomis. En aquesta nota formulem una conjectura concreta sobre les propietats algebraiques que venen forçades per la isocronia del centre i provem alguns resultats parcials.

A functional equation related to the product in a quadratic number field

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On the zeroes of Goss polynomials

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A sharp Remez inequality for trigonometric polynomials

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Integral inequalities for algebraic and trigonometric polynomials

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Sobolev orthogonal polynomials on a simplex

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Approximation of quadratic irrationals and their pierce expansions

In this article two aims are pursued: on the one hand, to present arapidly converging algorithm for the approximation of square roots; on theother hand and based on the previous algorithm, to find the Pierce expansionsof a certain class of quadratic irrationals as an alternative way to themethod presented in 1984 by J.O. Shallit; we extend the method to findalso the Pierce expansions of quadratic irrationals of the form $2 (p-1)(p - \sqrt{p^2 - 1})$ which are not covered in Shallit's work.

Quadratic tranverse anisotropy term due to dislocations in Mn12 acetate crystals directly observed by EPR spectroscopy

High-sensitivity electron paramagnetic resonance experiments have been carried out in fresh and stressed Mn12 acetate single crystals for frequencies ranging from 40 GHz up to 110 GHz. The high number of crystal dislocations formed in the stressing process introduces a E(Sx2-Sy2) transverse anisotropy term in the spin Hamiltonian. From the behavior of the resonant absorptions on the applied transverse magnetic field we have obtained an average value for E=22 mK, corresponding to a concentration of dislocations per unit cell of c=10-3.

Sierpinski curve Julia sets for quadratic rational maps

We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.