Home Page of Jonathan B. Hill

Assistant Professor of Economics

University of North Carolina – Chapel Hill

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CONTACT INFORMATION

Dept. of Economics Gardner Hall 300B University of North Carolina Chapel Hill, NC 27599-3305 jbhill at email dot unc dot edu.

RECENT PUBLICATIONS

On Tail Index Estimation for Dependent, Heterogeneous Data (2010) Econometric Theory 26, in press.

On Functional Central Limit Theorems for Dependent, Heterogeneous Arrays with Applications to Tail Index and Tail Dependence Estimation (2009) Journal of Statistical Planning and Inference 139, 2091-2110.

Heavy Tails and Mixed Distribution Hypothesis (2008) Encyclopedia of Quantitative Finance: forthcoming.

Consistent and Non-Degenerate Model Specification Tests Against Smooth Transition and Neural Network Alternatives (2008) Annales D’Economie et de Statistique: in press.

RESEARCH INTERESTS

Generalized Method of Moments and Trimmed Means

Several projects involve developing a theory of robust Minimum Distance Estimation for nonlinear models of the conditional mean and variance with arbitrarily heavy tails. The theory covers Tail Trimmed versions of GMM, QML, NLLS and LAD estimation under trivial assumptions on the GARCH component. This research includes asymptotic theory for tail-trimmed sums of dependent and heterogeneous processes, self-normalized by a kernel variance estimator, and several new robust estimators that can achieve greater than root-n consistency.

A related project involves fully characterizing the extremal (tail support) and non-extremal (tail-trimmed support) dependence properties of GARCH processes, including IGARCH and Explosive-GARCH. The results easily permit Gaussian asymptotic theory for a tail index and bivariate dependence estimator, and a tail-trimmed sum for this class of volatility process. The joint implication of these projects is a highly robust theory for GMM estimation of GARCH models.

Extreme Value Theory

My current research involves functional central limit theory for “tail arrays”. The theory allows for substantial generality in analyzing the properties of tail index estimators, tail dependence measures, and tail quantile functions when the data are dependent (short or long memory) and heterogeneous. Non-extremes are left unrestricted.

A related problem is the analysis of nonparametric tail dependence measures without relying on a bivariate tail shape, on a conditional volatility structure, or memory and heterogeneity properties of non-extremes. I am looking at extensions of projection theory based dependence measures to the tails, including Extremal-NED and Extremal-L₀-Approximabilty properties, as well as estimable tail correlations of exceedances and events. I explore the relationships between each measure, which classes of processes satisfy these tail dependence properties, and how they relate to the index of bivariate regular variation.

Applications include measures of extremal volatility spillover in asset and exchange rate markets, tests of exremal white noise and extremal nonlinearity, and the exact shape and decay rate of joint (serial and bivariate) GARCH and stochastic volatility tails.

A related problem is the dilemma of selecting the number of tail observations. I have developed parametric and nonparametric methods, including a unique Empirical Distribution Distance method for highly dependent, heterogeneous data.

Model Specification Tests

In other research I have studied consistent tests of functional form. Projects include analyses of when such tests are not degenerate, are never in-consistent (“super consistent”), have strictly integer or rational-valued nuisance parameters, and can be applied to Lp-regression model specification. Applications include a new interpretation of why the Bierens’ test in specific and neural nets in general work, and a weighted average test of model specification.