Studies on Binary Time Series Models with Applications to Empirical Macroeconomics and Finance

This thesis studies binary time series models and their applications in empirical macroeconomics and finance. In addition to previously suggested models, new dynamic extensions are proposed to the static probit model commonly used in the previous literature. In particular, we are interested in probit models with an autoregressive model structure. In Chapter 2, the main objective is to compare the predictive performance of the static and dynamic probit models in forecasting the U.S. and German business cycle recession periods. Financial variables, such as interest rates and stock market returns, are used as predictive variables. The empirical results suggest that the recession periods are predictable and dynamic probit models, especially models with the autoregressive structure, outperform the static model. Chapter 3 proposes a Lagrange Multiplier (LM) test for the usefulness of the autoregressive structure of the probit model. The finite sample properties of the LM test are considered with simulation experiments. Results indicate that the two alternative LM test statistics have reasonable size and power in large samples. In small samples, a parametric bootstrap method is suggested to obtain approximately correct size. In Chapter 4, the predictive power of dynamic probit models in predicting the direction of stock market returns are examined. The novel idea is to use recession forecast (see Chapter 2) as a predictor of the stock return sign. The evidence suggests that the signs of the U.S. excess stock returns over the risk-free return are predictable both in and out of sample. The new "error correction" probit model yields the best forecasts and it also outperforms other predictive models, such as ARMAX models, in terms of statistical and economic goodness-of-fit measures. Chapter 5 generalizes the analysis of univariate models considered in Chapters 2 4 to the case of a bivariate model. A new bivariate autoregressive probit model is applied to predict the current state of the U.S. business cycle and growth rate cycle periods. Evidence of predictability of both cycle indicators is obtained and the bivariate model is found to outperform the univariate models in terms of predictive power.

Non-linear couette flow with heat transfer using the B-G-K model

In recent years a large number of investigators have devoted their efforts to the study of flow and heat transfer in rarefied gases, using the BGK [1] model or the Boltzmann kinetic equation. The velocity moment method which is based on an expansion of the distribution function as a series of orthogonal polynomials in velocity space, has been applied to the linearized problem of shear flow and heat transfer by Mott-Smith [2] and Wang Chang and Uhlenbeck [3]. Gross, Jackson and Ziering [4] have improved greatly upon this technique by expressing the distribution function in terms of half-range functions and it is this feature which leads to the rapid convergence of the method. The full-range moments method [4] has been modified by Bhatnagar [5] and then applied to plane Couette flow using the B-G-K model. Bhatnagar and Srivastava [6] have also studied the heat transfer in plane Couette flow using the linearized B-G-K equation. On the other hand, the half-range moments method has been applied by Gross and Ziering [7] to heat transfer between parallel plates using Boltzmann equation for hard sphere molecules and by Ziering [83 to shear and heat flow using Maxwell molecular model. Along different lines, a moment method has been applied by Lees and Liu [9] to heat transfer in Couette flow using Maxwell's transfer equation rather than the Boltzmann equation for distribution function. An iteration method has been developed by Willis [10] to apply it to non-linear heat transfer problems using the B-G-K model, with the zeroth iteration being taken as the solution of the collisionless kinetic equation. Krook [11] has also used the moment method to formulate the equivalent continuum equations and has pointed out that if the effects of molecular collisions are described by the B-G-K model, exact numerical solutions of many rarefied gas-dynamic problems can be obtained. Recently, these numerical solutions have been obtained by Anderson [12] for the non-linear heat transfer in Couette flow,

An approximate analysis of non-linear non-conservative systems subjected to step function excitation

This paper deals with the approximate analysis of the step response of non-linear nonconservative systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on ultraspherical polynomial expansions. The Krylov-Bogoliubov results are given by a particular set of these polynomials. The method has been applied to study the step response of a cubic spring mass system in presence of viscous, material, quadratic, and mixed types of damping. The approximate results are compared with the digital and analogue computer solutions and a close agreement has been found between the analytical and the exact results.

Anomalous behavior of hydrodynamic modes in the two dimensional shear flow of a granular material

The growth rates of the hydrodynamic modes in the homogeneous sheared state of a granular material are determined by solving the Boltzmann equation. The steady velocity distribution is considered to be the product of the Maxwell Boltzmann distribution and a Hermite polynomial expansion in the velocity components; this form is inserted into them Boltzmann equation and solved to obtain the coeificients of the terms in the expansion. The solution is obtained using an expansion in the parameter epsilon =(1 - e)(1/2), and terms correct to epsilon(4) are retained to obtain an approximate solution; the error due to the neglect of higher terms is estimated at about 5% for e = 0.7. A small perturbation is placed on the distribution function in the form of a Hermite polynomial expansion for the velocity variations and a Fourier expansion in the spatial coordinates: this is inserted into the Boltzmann equation and the growth rate of the Fourier modes is determined. It is found that in the hydrodynamic limit, the growth rates of the hydrodynamic modes in the flow direction have unusual characteristics. The growth rate of the momentum diffusion mode is positive, indicating that density variations are unstable in the limit k--> 0, and the growth rate increases proportional to kslash} k kslash}(2/3) in the limit k --> 0 (in contrast to the k(2) increase in elastic systems), where k is the wave vector in the flow direction. The real and imaginary parts of the growth rate corresponding to the propagating also increase proportional to kslash k kslash(2/3) (in contrast to the k(2) and k increase in elastic systems). The energy mode is damped due to inelastic collisions between particles. The scaling of the growth rates of the hydrodynamic modes with the wave vector I in the gradient direction is similar to that in elastic systems. (C) 2000 Elsevier Science B.V. All rights reserved.

On the unreasonable effectiveness of Gutzmer's formula

In this article we plan to demonstrate the usefulness of `Gutzmer's formula' in the study of various problems related to the Segal-Bargmann transform. Gutzmer's formula is known in several contexts: compact Lie groups, symmetric spaces of compact and noncompact type, Heisenberg groups and Hermite expansions. We apply Gutzmer's formula to study holomorphic Sobolev spaces, local Peter-Weyl theorems, Paley-Wiener theorems and Poisson semigroups.

Architecture of Run-time Reconfigurable Channel Decoder

Modern wireline and wireless communication devices are multimode and multifunctional communication devices. In order to support multiple standards on a single platform, it is necessary to develop a reconfigurable architecture that can provide the required flexibility and performance. The Channel decoder is one of the most compute intensive and essential elements of any communication system. Most of the standards require a reconfigurable Channel decoder that is capable of performing Viterbi decoding and Turbo decoding. Furthermore, the Channel decoder needs to support different configurations of Viterbi and Turbo decoders. In this paper, we propose a reconfigurable Channel decoder that can be reconfigured for standards such as WCDMA, CDMA2000, IEEE802.11, DAB, DVB and GSM. Different parameters like code rate, constraint length, polynomials and truncation length can be configured to map any of the above mentioned standards. A multiprocessor approach has been followed to provide higher throughput and scalable power consumption in various configurations of the reconfigurable Viterbi decoder and Turbo decoder. We have proposed A Hybrid register exchange approach for multiprocessor architecture to minimize power consumption.

A systolic evaluator for linear, quadratic, and cubic expressions

High-speed evaluation of a large number of linear, quadratic, and cubic expressions is very important for the modeling and real-time display of objects in computer graphics. Using VLSI techniques, chips called pixel planes have actually been built by H. Fuchs and his group to evaluate linear expressions. In this paper, we describe a topological variant of Fuchs' pixel planes which can evaluate linear, quadratic, cubic, and higher-order polynomials. In our design, we make use of local interconnections only, i.e., interconnections between neighboring processing cells. This leads to the concept of tiling the processing cells for VLSI implementation.

On BCH codes over arbitrary integer rings

Bose-C-Hocquenghem (BCH) atdes with symbols from an arbitrary fhite integer ring are derived in terms of their generator polynomials. The derivation is based on the factohation of x to the power (n) - 1 over the unit ring of an appropriate extension of the fiite integer ring. lke eomtruetion is thus shown to be similar to that for BCH codes over fink flelda.

Stability Analysis of Composite Skew Plates Using a Dynamic Method

Stability analysis is carried out considering free lateral vibrations of simply supported composite skew plates that are subjected to both direct and shear in-plane forces. An oblique stress component representation is used, consistent with the skew-geometry of the plate. A double series, expressed in Chebyshev polynomials, is used here as the assumed deflection surface and Ritz method of solution is employed. Numerical results for different combinations of side ratios, skew angle, and in-plane loadings that act individually or in combination are obtained. In this method, the in-plane load parameter is varied until the fundamental frequency goes to zero. The value of the in-plane load then corresponds to a critical buckling load. Plots of frequency parameter versus in-plane loading are given for a few typical cases. Details of crossings and quasi degeneracies of these curves are presented.

Invariant norm quantifying nonlinear content of Hamiltonian systems

Given a Hamiltonian system, one can represent it using a symplectic map. This symplectic map is specified by a set of homogeneous polynomials which are uniquely determined by the Hamiltonian. In this paper, we construct an invariant norm in the space of homogeneous polynomials of a given degree. This norm is a function of parameters characterizing the original Hamiltonian system. Such a norm has several potential applications. (C) 2010 Elsevier Inc. All rights reserved.

Methods and applications for improving parameter prediction models for stand structures in Finland

This thesis report attempts to improve the models for predicting forest stand structure for practical use, e.g. forest management planning (FMP) purposes in Finland. Comparisons were made between Weibull and Johnson s SB distribution and alternative regression estimation methods. Data used for preliminary studies was local but the final models were based on representative data. Models were validated mainly in terms of bias and RMSE in the main stand characteristics (e.g. volume) using independent data. The bivariate SBB distribution model was used to mimic realistic variations in tree dimensions by including within-diameter-class height variation. Using the traditional method, diameter distribution with the expected height resulted in reduced height variation, whereas the alternative bivariate method utilized the error-term of the height model. The lack of models for FMP was covered to some extent by the models for peatland and juvenile stands. The validation of these models showed that the more sophisticated regression estimation methods provided slightly improved accuracy. A flexible prediction and application for stand structure consisted of seemingly unrelated regression models for eight stand characteristics, the parameters of three optional distributions and Näslund s height curve. The cross-model covariance structure was used for linear prediction application, in which the expected values of the models were calibrated with the known stand characteristics. This provided a framework to validate the optional distributions and the optional set of stand characteristics. Height distribution is recommended for the earliest state of stands because of its continuous feature. From the mean height of about 4 m, Weibull dbh-frequency distribution is recommended in young stands if the input variables consist of arithmetic stand characteristics. In advanced stands, basal area-dbh distribution models are recommended. Näslund s height curve proved useful. Some efficient transformations of stand characteristics are introduced, e.g. the shape index, which combined the basal area, the stem number and the median diameter. Shape index enabled SB model for peatland stands to detect large variation in stand densities. This model also demonstrated reasonable behaviour for stands in mineral soils.

Entropy and dynamics of water in hydration layers of a bilayer

We compute the entropy and transport properties of water in the hydration layer of dipalmitoylphosphatidylcholine bilayer by using a recently developed theoretical scheme two-phase thermodynamic model, termed as 2PT method; S.-T. Lin et al., J. Chem. Phys. 119, 11792 (2003)] based on the translational and rotational velocity autocorrelation functions and their power spectra. The weights of translational and rotational power spectra shift from higher to lower frequency as one goes from the bilayer interface to the bulk. Water molecules near the bilayer head groups have substantially lower entropy (48.36 J/mol/K) than water molecules in the intermediate region (51.36 J/mol/K), which have again lower entropy than the molecules (60.52 J/mol/K) in bulk. Thus, the entropic contribution to the free energy change (T Delta S) of transferring an interface water molecule to the bulk is 3.65 kJ/mol and of transferring intermediate water to the bulk is 2.75 kJ/mol at 300 K, which is to be compared with 6.03 kJ/mol for melting of ice at 273 K. The translational diffusion of water in the vicinity of the head groups is found to be in a subdiffusive regime and the rotational diffusion constant increases going away from the interface. This behavior is supported by the slower reorientational relaxation of the dipole vector and OH bond vector of interfacial water. The ratio of reorientational relaxation time for Legendre polynomials of order 1 and 2 is approximately 2 for interface, intermediate, and bulk water, indicating the presence of jump dynamics in these water molecules. (C) 2010 American Institute of Physics. doi:10.1063/1.3494115]

A Smooth Finite Element Method Based on Reproducing Kernel DMS-Splines

The element-based piecewise smooth functional approximation in the conventional finite element method (FEM) results in discontinuous first and higher order derivatives across element boundaries Despite the significant advantages of the FEM in modelling complicated geometries, a motivation in developing mesh-free methods has been the ease with which higher order globally smooth shape functions can be derived via the reproduction of polynomials There is thus a case for combining these advantages in a so-called hybrid scheme or a `smooth FEM' that, whilst retaining the popular mesh-based discretization, obtains shape functions with uniform C-p (p >= 1) continuity One such recent attempt, a NURBS based parametric bridging method (Shaw et al 2008b), uses polynomial reproducing, tensor-product non-uniform rational B-splines (NURBS) over a typical FE mesh and relies upon a (possibly piecewise) bijective geometric map between the physical domain and a rectangular (cuboidal) parametric domain The present work aims at a significant extension and improvement of this concept by replacing NURBS with DMS-splines (say, of degree n > 0) that are defined over triangles and provide Cn-1 continuity across the triangle edges This relieves the need for a geometric map that could precipitate ill-conditioning of the discretized equations Delaunay triangulation is used to discretize the physical domain and shape functions are constructed via the polynomial reproduction condition, which quite remarkably relieves the solution of its sensitive dependence on the selected knotsets Derivatives of shape functions are also constructed based on the principle of reproduction of derivatives of polynomials (Shaw and Roy 2008a) Within the present scheme, the triangles also serve as background integration cells in weak formulations thereby overcoming non-conformability issues Numerical examples involving the evaluation of derivatives of targeted functions up to the fourth order and applications of the method to a few boundary value problems of general interest in solid mechanics over (non-simply connected) bounded domains in 2D are presented towards the end of the paper

A field-consistent and variationally correct representation of transverse shear strains in the nine-noded plate element

We present a biquadratic Lagrangian plate bending element with consistent fields for the constrained transverse shear strain functions. A technique involving expansion of the strain interpolations in terms of Legendre polynomials is used to redistribute the kinematically derived shear strain fields so that the field-consistent forms (i.e. avoiding locking) are also variationally correct (i.e. do not violate the variational norms). Also, a rational method of isoparametric Jacobian transformation is incorporated so that the constrained covariant shear strain fields are always consistent in whatever general quadrilateral form the element may take. Finally the element is compared with another formulation which was recently published. The element is subjected to several robust bench mark tests and is found to pass all the tests efficiently.

A novel property of an Auto-Correlation Sequence and some Applications

In this article, we use some spectral properties of polynomials presented in 1] and map an auto-correlation sequence to a set of Line Spectral Frequencies(LSFs) and reflection coefficients. This novel characterization of an auto-correlation sequence is used to obtain a lattice structure of a Linear-Phase(LP) FIR filter.