This paper introduces an ARCH model (exponential ARCH) that (1) allows correlation between returns and volatility innovations (an important feature of stock market volatility changes), (2) eliminates the need for inequality constraints on parameters, and (3) allows for a straightforward interpretation of the "persistence" of shocks to volatility. In the above respects, it is an improvement over the widely-used GARCH model. The model is applied to study volatility changes and the risk premium on the CRSP Value-Weighted Market Index from 1962 to 1987. Copyright 1991 by The Econometric Society.

Conditional heteroskedasticity in asset returns: a new approach

This paper focuses on the class of speech enhancement systems which capitalize on the major importance of the short-time spectral amplitude (STSA) of the speech signal in its perception. A system which utilizes a minimum mean-square error (MMSE) STSA estimator is proposed and then compared with other widely used systems which are based on Wiener filtering and the "spectral subtraction" algorithm. In this paper we derive the MMSE STSA estimator, based on modeling speech and noise spectral components as statistically independent Gaussian random variables. We analyze the performance of the proposed STSA estimator and compare it with a STSA estimator derived from the Wiener estimator. We also examine the MMSE STSA estimator under uncertainty of signal presence in the noisy observations. In constructing the enhanced signal, the MMSE STSA estimator is combined with the complex exponential of the noisy phase. It is shown here that the latter is the MMSE estimator of the complex exponential of the original phase, which does not affect the STSA estimation. The proposed approach results in a significant reduction of the noise, and provides enhanced speech with colorless residual noise. The complexity of the proposed algorithm is approximately that of other systems in the discussed class.

Speech enhancement using a minimum-mean square error short-time spectral amplitude estimator

Since the work of Bishop and Heberlein, a number of contingent valuation experiments have appeared involving discrete responses which are analyzed by logit or similar techniques. This paper addresses the issues of how the logit models should be formulated to be consistent with the hypothesis of utility maximization and how measures of compensating and equivalent surplus should be derived from the fitted models. Two distinct types of welfare measures are introduced and then estimated from Bishop and Heberlein's data.

Welfare Evaluations in Contingent Valuation Experiments with Discrete Responses

A new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved This new method can therefore be more efficient than the usual finite element methods An additional feature of the partition-of-unity method is that finite element spaces of any desired regularity can be constructed very easily This paper includes a convergence proof of this method and illustrates its efficiency by an application to the Helmholtz equation for high wave numbers The basic estimates for a posteriori error estimation for this new method are also proved © 1997 by John Wiley & Sons, Ltd

The Partition of Unity Method

Random matrix theory has found many applications in physics, statistics and engineering since its inception. Although early developments were motivated by practical experimental problems, random matrices are now used in fields as diverse as Riemann hypothesis, stochastic differential equations, condensed matter physics, statistical physics, chaotic systems, numerical linear algebra, neural networks, multivariate statistics, information theory, signal processing and small-world networks. This article provides a tutorial on random matrices which provides an overview of the theory and brings together in one source the most significant results recently obtained. Furthermore, the application of random matrix theory to the fundamental limits of wireless communication channels is described in depth.

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Random Matrix Theory and Wireless Communications

0 Introduction 1 Elementary Functions 2 Indefinite Integrals of Elementary Functions 3 Definite Integrals of Elementary Functions 4.Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integrals of Special Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequalities 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform

M. Y. Tseytlin

Papers

Table of Integrals, Series, and Products

Preface to the fourth edition