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.

Conjugacy of piecewise linear Lorenz map that expand on average

For piecewise linear Lorenz map that expand on average, we show that it admits a dichotomy: it is either periodic renormalizable or prime. As a result, such a map is conjugate to a ß-transformation.

Nuclear magnetic resonance chemical shifts with the statistical average of orbital-dependent model potentials in Kohn-Sham density functional theory

The performance of the SAOP potential for the calculation of NMR chemical shifts was evaluated. SAOP results show considerable improvement with respect to previous potentials, like VWN or BP86, at least for the carbon, nitrogen, oxygen, and fluorine chemical shifts. Furthermore, a few NMR calculations carried out on third period atoms (S, P, and Cl) improved when using the SAOP potential

Influence of average size and interface passivation on the spectral emission of Si nanocrystals embedded in SiO2

The correlation between the structural (average size and density) and optoelectronic properties [band gap and photoluminescence (PL)] of Si nanocrystals embedded in SiO2 is among the essential factors in understanding their emission mechanism. This correlation has been difficult to establish in the past due to the lack of reliable methods for measuring the size distribution of nanocrystals from electron microscopy, mainly because of the insufficient contrast between Si and SiO2. With this aim, we have recently developed a successful method for imaging Si nanocrystals in SiO2 matrices. This is done by using high-resolution electron microscopy in conjunction with conventional electron microscopy in dark field conditions. Then, by varying the time of annealing in a large time scale we have been able to track the nucleation, pure growth, and ripening stages of the nanocrystal population. The nucleation and pure growth stages are almost completed after a few minutes of annealing time at 1100°C in N2 and afterward the ensemble undergoes an asymptotic ripening process. In contrast, the PL intensity steadily increases and reaches saturation after 3-4 h of annealing at 1100°C. Forming gas postannealing considerably enhances the PL intensity but only for samples annealed previously in less time than that needed for PL saturation. The effects of forming gas are reversible and do not modify the spectral shape of the PL emission. The PL intensity shows at all times an inverse correlation with the amount of Pb paramagnetic centers at the Si-SiO2 nanocrystal-matrix interfaces, which have been measured by electron spin resonance. Consequently, the Pb centers or other centers associated with them are interfacial nonradiative channels for recombination and the emission yield largely depends on the interface passivation. We have correlated as well the average size of the nanocrystals with their optical band gap and PL emission energy. The band gap and emission energy shift to the blue as the nanocrystal size shrinks, in agreement with models based on quantum confinement. As a main result, we have found that the Stokes shift is independent of the average size of nanocrystals and has a constant value of 0.26±0.03 eV, which is almost twice the energy of the Si¿O vibration. This finding suggests that among the possible channels for radiative recombination, the dominant one for Si nanocrystals embedded in SiO2 is a fundamental transition spatially located at the Si¿SiO2 interface with the assistance of a local Si-O vibration.

Linear least squares estimation of the first order moving average parameter

We propose an iterative procedure to minimize the sum of squares function which avoids the nonlinear nature of estimating the first order moving average parameter and provides a closed form of the estimator. The asymptotic properties of the method are discussed and the consistency of the linear least squares estimator is proved for the invertible case. We perform various Monte Carlo experiments in order to compare the sample properties of the linear least squares estimator with its nonlinear counterpart for the conditional and unconditional cases. Some examples are also discussed

Semiclassical evaluation of average nuclear one- and two-body matrix elements

Thomas-Fermi theory is developed to evaluate nuclear matrix elements averaged on the energy shell, on the basis of independent particle Hamiltonians. One- and two-body matrix elements are compared with the quantal results, and it is demonstrated that the semiclassical matrix elements, as function of energy, well pass through the average of the scattered quantum values. For the one-body matrix elements it is shown how the Thomas-Fermi approach can be projected on good parity and also on good angular momentum. For the two-body case, the pairing matrix elements are considered explicitly.

Average ground-state energy of finite Fermi systems

Semiclassical theories such as the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in systems with a fixed number of particles N, these methods overbind the actual average of the quantum energy as N is varied. We describe a theory that accounts for this effect. Numerical illustrations are discussed for fermions trapped in a harmonic oscillator potential and in a hard-wall cavity, and for self-consistent calculations of atomic nuclei. In the latter case, the influence of deformations on the average behavior of the energy is also considered.

Linear least squares estimation of the first order moving average parameter

We propose an iterative procedure to minimize the sum of squares function which avoids the nonlinear nature of estimating the first order moving average parameter and provides a closed form of the estimator. The asymptotic properties of the method are discussed and the consistency of the linear least squares estimator is proved for the invertible case. We perform various Monte Carlo experiments in order to compare the sample properties of the linear least squares estimator with its nonlinear counterpart for the conditional and unconditional cases. Some examples are also discussed

The Uncertain generalized probabilistic weighted average and its application in the theory of expertons

A new model for dealing with decision making under risk by considering subjective and objective information in the same formulation is here presented. The uncertain probabilistic weighted average (UPWA) is also presented. Its main advantage is that it unifies the probability and the weighted average in the same formulation and considering the degree of importance that each case has in the analysis. Moreover, it is able to deal with uncertain environments represented in the form of interval numbers. We study some of its main properties and particular cases. The applicability of the UPWA is also studied and it is seen that it is very broad because all the previous studies that use the probability or the weighted average can be revised with this new approach. Focus is placed on a multi-person decision making problem regarding the selection of strategies by using the theory of expertons.

Average performance analysis of circular and hyperbolic geolocation

A comparative performance analysis of four geolocation methods in terms of their theoretical root mean square positioning errors is provided. Comparison is established in two different ways: strict and average. In the strict type, methods are examined for a particular geometric configuration of base stations(BSs) with respect to mobile position, which determines a givennoise profile affecting the respective time-of-arrival (TOA) or timedifference-of-arrival (TDOA) estimates. In the average type, methodsare evaluated in terms of the expected covariance matrix ofthe position error over an ensemble of random geometries, so thatcomparison is geometry independent. Exact semianalytical equationsand associated lower bounds (depending solely on the noiseprofile) are obtained for the average covariance matrix of the positionerror in terms of the so-called information matrix specific toeach geolocation method. Statistical channel models inferred fromfield trials are used to define realistic prior probabilities for therandom geometries. A final evaluation provides extensive resultsrelating the expected position error to channel model parametersand the number of base stations.