Time Inhomogeneous Multiple Volatility Modeling

Price variations at speculative markets exhibit positive autocorrelationand cross correlation. Due to large parameter spaces necessaryfor joint modeling of variances and covariances, multivariateparametric volatility models become easily intractable in practice.We propose an adaptive procedure that identifies periods ofsecond-order homogeneity for each moment in time. To overcomethe high dimensionality of the problem we transform the multivariateseries into a set of univariate processes. We discuss thoroughlythe implementation of the adaptive technique. Theoretical andMonte Carlo results are given. We provide two applications ofthe new method. For a bivariate exchange rate series we comparethe multivariate GARCH approach with our method and find thelatter to be more in line with the underlying assumption ofindependently distributed innovations. Analyzing a 23-dimensionalvector of asset returns we underscore the case for adaptivemodeling in high-dimensional systems.     

A Dynamic Analysis of Fixed- and Adjustable-Rate Mortgage Terminations

This paper provides a side-by-side comparison of loan-level statistical models for fixed- and adjustable-rate mortgages. Multinomial logit models for quarterly conditional probabilities of default and prepayment are estimated. We find that the estimated impacts of embedded option values for prepayment and default are generally quite similar across both FRM and ARM loans, providing additional empirical support for the basic predictions of the options theory. We also find that differences in estimates of conditional probabilities of prepayment and default associated with mortgage age, origination period, original LTV, and relative loan size, indicate the continued significance of these other economic and demographic factors for empirical models of mortgage terminations.     

Consistent estimation in the bilinear multivariate errors-in-variables model

A bilinear multivariate errors-in-variables model is considered. It corresponds to an overdetermined set of linear equations AXB=C, A∈ℝ^m×n, B∈ℝ^p×q, in which the data A, B, C are perturbed by errors. The total least squares estimator is inconsistent in this case.  An adjusted least squares estimator is constructed, which converges to the true value X, as m →∞, q →∞. A small sample modification of the estimator is presented, which is more stable for small m and q and is asymptotically equivalent to the adjusted least squares estimator. The theoretical results are confirmed by a simulation study. Acknowledgements. We thank two anonymous reviewers for their suggestions and corrections.? A. Kukush is supported by a postdoctoral research fellowship of the Belgian office for Scientific, Technical and Cultural Affairs, promoting Scientific and Technical Collaboration with Central and Eastern Europe.? S. Van Huffel is a full professor with the Katholieke Universiteit Leuven.? I. Markovsky is a research assistant with the Katholieke Universiteit Leuven.? This paper presents research results of the Belgian Programme on Interuniversity Poles of Attraction (IUAP V-22), initiated by the Belgian State, Prime Minister's Office – Federal Office for Scientific, Technical and Cultural Affairs of the Concerted Research Action (GOA) projects of the Flemish Government MEFISTO-666 (Mathematical Engineering for Information and Communication Systems Technology), of the IDO/99/03 project (K.U. Leuven) “Predictive computer models for medical classification problems using patient data and expert knowledge”, of the FWO projects G.0078.01, G.0200.00, and G0.0270.02.? The scientific responsibility is assumed by its authors.     

Environmental Valuation with Imperfect Information The Case of the Random Utility Model

This paper considers welfare analysis with therandom utility model (RUM) when perceptions ofenvironmental quality differ from objectivemeasures of environmental quality. Environmental quality is assumed to be anexperience good, so that while perceptions ofquality determine choices, ex postutility is determined by objective quality. Given this assumption, I derive a measure ofthe welfare impact of changes in environmentalquality, and I show how this new welfaremeasure differs from the traditional welfaremeasure developed by Hanemann (1982). This newwelfare measure provides an approach tomeasuring the value of information aboutenvironmental quality within the framework ofthe random utility model.     

Asymptotic expansion of S-estimators of location and covariance

By means of a straightforward application of empirical process theory, we show that S-estimators of multivariate location and covariance are asymptotically equivalent to a sum of independent vector and matrix valued random elements respectively. This provides an alternative proof of asymptotic normality of S-estimators and clearly explains the limiting covariance structure. It also leads to a relatively simple proof of asymptotic normality of the length of the shortest α-fraction.     

SELECTION BIAS CORRECTIONS BASED ON THE MULTINOMIAL LOGIT MODEL: MONTE CARLO COMPARISONS

Abstract.  This survey presents the set of methods available in the literature on selection bias correction, when selection is specified as a multinomial logit model. It contrasts the underlying assumptions made by the different methods and shows results from a set of Monte Carlo experiments. We find that, in many cases, the approach initiated by Dubin and MacFadden (1984) as well as the semi-parametric alternative recently proposed by Dahl (2002) are to be preferred to the most commonly used Lee (1983) method. We also find that a restriction imposed in the original Dubin and MacFadden paper can be waived to achieve more robust estimators. Monte Carlo experiments also show that selection bias correction based on the multinomial logit model can provide fairly good correction for the outcome equation, even when the IIA hypothesis is violated.     

A new bivariate distribution in natural exponential family

We propose a new bivariate distribution following a GLM form i.e., natural exponential family given the constantly correlated covariance matrix. The proposed distribution can represent an independent bivariate gamma distribution as a special case. In order to derive the distribution we utilize an integrating factor method to satisfy the integrability condition of the quasi-score function. The derived distribution becomes a mixture of discrete and absolute continuous distributions. The proposal of our new bivariate distribution will make it possible to develop some bivariate generalized linear models. Further the discrete correlated bivariate distribution will also arise from an independent bivariate Poisson mass function by compounding our proposed distribution (Iwasaki and Tsubaki, 2002).Received March 2003     

Evaluation of the social and economic impact of carbon dioxide (CO2) emissions on sustainable mobility using cumulative ordinal models: trend odds model

In the context of environmental sustainability evaluation, grouped under climate change, health and ecosystem themes, an impact that could be investigated is the Global Warming Potential (GWP), whose sources are a multitude. In urban areas the evaluation of real vehicles emissions is an essential activity in order to suggest possible solution to local administrators. They still express the need to improve and maintain the characteristics of the breathing air at the best possible quality level. Moreover, these solutions, such as planning measures or traffic control management in respect of pollution, would be apply at different geographical levels, i.e. national, regional or urban scale. Another factor to be investigated is the effect of technologies and emission control systems to comply more stringent limits (Euro 4/5/6) and improve air quality to a lower environmental impact. GWP, indicator of climate change, is measured in terms of CO₂ equivalency emission values variable. To perform this activity an experimental campaign was carried out with several vehicles from different manufacturers and with a wide variety in terms of mass, power, engine displacement and type approval technology. The experimental plan includes some repetitions of the urban section in Naples city centre.The purpose of this paper is twofold: first, to provide a strategy on the choice of a logistic model with ordinal data and with trend, and, second, to evaluate the usefulness of such models for environmental sustainability (CO₂ and other vehicular pollutant emissions), with particular emphasis on model formulation, the interpretation of model coefficients, and the implications of such models.     

Convenient estimators for the panel probit model: Further results

Bertschek and Lechner (1998) propose several variants of a GMM estimator based on the period specific regression functions for the panel probit model. The analysis is motivated by the complexity of maximum likelihood estimation and the possibly excessive amount of time involved in maximum simulated likelihood estimation. But, for applications of the size considered in their study, full likelihood estimation is actually straightforward, and resort to GMM estimation for convenience is unnecessary. In this note, we reconsider maximum likelihood based estimation of their panel probit model then examine some extensions which can exploit the heterogeneity contained in their panel data set. Empirical results are obtained using the data set employed in the earlier study. Helpful comments and suggestions by Irene Bertschek and Michael Lechner are gratefully acknowledged. This paper has also benefited from comments by two anonymous referees and from seminar participants at the Center for Health Economics at the University of York. Any remaining errors are the responsibility of the author.