Jonathan B.
Hill
(updated Oct. 2009)
CONTACT
INFORMATION
Jonathan B. Hill
Department of Economics
University of North Carolina
Gardener Hall CB # 3305
Chapel Hill, NC
RESEARCH
FIELDS
Econometric Theory, Mathematical Statistics,
Time Series Econometrics, Financial Econometrics
RESEARCH INTERESTS
o Extreme value theory
tail shape,
tail fractile, tail dependence, extremal causality;
applications
in finance and macroeconomics.
o Non-parametric statistics
tests
of functional form, tail dependence and tail-trimming.
o Robust estimation
tail-trimmed
GMM, QML, NLLS; analysis of dependent, heterogeneous extremes.
o Asymptotic theory
weak
limit theory for D-valued non-iid arrays; weak limit theory for nonlinear
non-iid
tail arrays; central limit theory for non-iid tail-trimmed sums.
CURRENT
ACADEMIC APPOINTMENTS
Assistant Professor of Economics, University
of North Carolina-Chapel Hill, 2008-
RESEARCH
VISITS
Visiting Research Fellow, CentER, University
of Tilburg (Fall 2009)
Visiting Fellow, CIREQ and Concordia
University (March 1-7, 2010)
PREVIOUS
ACADEMIC APPOINTMENTS
Visiting Assistant Professor of Economics,
University of North Carolina-Chapel Hill (2007-08)
Assistant Professor of Economics, Florida
International University (2003-2007)
Visiting Professor of Statistics, China
Agricultural University, Beijing (Summer 2001, Summer 2002)
Visiting Lecturer of Econometrics,
University of California-San Diego (2001- 2003)
EDUCATION
Ph.D., Economics, 2001, University of Colorado-Boulder
B.A.'s, Economics, Sociology and
Anthropology, 1990, University of Colorado
PUBLISHED
AND FORTHCOMING PAPERS
PAPERS UNDER
REVIEW OR REVISION FOR PUBLICATION
8. Tail and Non-Tail
Memory with Applications to Extreme Value and Robust Statistics (2008) Revised and resubmitted to Econometric Theory
9. Consistent
GMM Residuals-Based Tests of Functional Form (2008) Revised and
resubmitted to Econometric Reviews.
13. Robust Estimation and
Inference for Extremal Dependence in Time Series (2009), Appendix C
(proofs), Appendix D
(figures and tables)
14. Are There Common Values on BC Timber
Sales? A Tail-Index Nonparametric Test (2009, with A. Shneyerov)
15. Stochastically Weighted
Average Conditional Moment Tests of Functional Form (2008)
PAPERS IN PROGRESS
Generalized Method of
Moments with Tail Trimming (with Eric Renault)
We develop a new GMM
estimator by trimming an asymptotically vanishing portion of the sampl estimating
equations. The estimator is consistent and asymptotically normal for
arbitrarily heavy tailed stationary processes including linear and nonlinear
ARMA-GARCH with infinite variance shocks and any GARCH parameter values within
the stationary range. Standard √n-convergence is achieved for thin-tailed
data, and we explicitly prove the estimator may be super-√n-consistent
for heavy tailed linear dynamic and ARCH models. Simulation evidence shows the
new estimator dominates GMM and QML when these estimators are not, or have not
been shown to be, asymptotically normal; and super-consistency is achievable in
heavy tailed models.
Minimum Distance Estimation
under Non-Standard Conditions with Applications to Robust QML
We analyze the asymptotic
properties of Minimum Distance Estimators where the criterion function need not
be differentiable for small or large samples, and may be dependent on sample
size. The small sample problem arises from criterion discontinuities due to
model nonlinearity and/or trimming or truncation (e.g. Threshold GARCH, Least
Trimmed Squares). The large sample problem arises from moment condition failure
due to heavy tails, in which case the criterion Jacobian is unbounded
asymptotically (e.g. GMM for Threshold IGARCH). We establish sufficient
conditions for consistency and asymptotic normality for a general class of
MDE's that covers Method of Moments and M-estimators, including GMM, QML, LAD
and NLLS when the criterion is differentiable (e.g. GMM for ARMA),
non-differentiable with a smooth limit (e.g. QML for Threshold GARCH), or never
differentiable (e.g. GMM for Threshold GARCH with infinite kurtosis). The
results are applied to generalized versions of GMM and M-estimation that unify
Least Trimmed Squares, Maximum Trimmed Squares, Least Abolute Weighted
Deviations, Method of Trimmed Moments, and so on. Finally, we show how our
results cover existing and new estimators, and deliver two new robust
estimators: Tail Trimmed QMLE couched within a new GMM framework, and Least
Tail Trimmed Squares framed as a robust M-estimator. We prove asymptotic
normality and super-√n-consistency for simple models of the conditional
mean and variance.
Tail Dependence for Time
Series : Non-Parametric Characterization, Estimation and Inference
We develop new
representations of tail dependence for time series that provide significant
details on what tail index and tail copula notions of tail dependence actually
represent. We reveal significant shortcomings in these standard measures
including mis-classification of tail dependence, inabilities to detect tail
dependence, and the inability to model tail dependence decay between x_{t-h}
and y_{t} as the lag h increases for all distribution classes repeatedly
exploited in this literature. We deliver a complete non-parametric methodology
for measuring, estimating and testing for tail dependence, covering a multitude
of time series processes, and easily capturing persistence decay where extant
methods fail. On the theory side we prove joint weak convergence for tail
dependence estimates at multiple lags where non-extremal properties are
irrelevant and we do not require a model of the bivariate tail probability.
Finally, we analyze daily returns in international equity markets.
Flexibly Trimmed Method
Moments
We generalized the method of
tail trimmed moments to allow for individualized ("flexible") rates
of trimming for regression errors and regressors, based on either fixed or tail
quantiles. The result fully generalizes robust M-estimation and GMM estimation
into one composite theory.
Trimmed Least Square for
Dynamic Linear Regressions Models with Heterogeneous Errors
We develop two robust least
squares estimators for the slope parameter in a stationary dynamic linear
regression model. We either trim a fixed or vanishing tail quantile of the
sample normal equations which govern asymptotics, and deliver trimmed least
squares estimators by a method of trimmed moments. The resulting Trimmed and
Tail Trimmed Least Squares estimators are asymptotically normal for arbitrarily
heavy tailed data, we only require the error term to satisfy martingale
difference and mixing properties, allowing random volatility errors (e.g.
GARCH). Further, we establish conditions that ensure uniform consistency over a
trimming quantile parameter, and deliver a consistent estimator of the
asymptotic covariance matrix. We demonstrate tail trimming leads to sub-√n
or super-√n consistency depending on the relative tail thickness of the
errors and regressors. Super-√n consistency is always exhibited for
infinite variance autoregressions, where the rate approaches the untrimmed
least squares rate as the trimming rate shrinks. Finally, a simulation study
reveals TTLS leads to a potentially massive improvement in efficiency over TLS
and conventional Least Trimmed Squares for heavy tailed dynamic regressions.
CONFERENCES,
WORKSHOPS, and INVITED TALKS
Computing in Economics and Finance Conference, Boston, June 1999.
Econometric Society European Summer Meeting, Madrid, Sept. 1999, (discussant)
Econometric Society North American Summer Meeting, Seattle, Aug. 2000
Society for Nonlinear Dynamics in Econometrics 12th Annual
Symposium, Atlanta, March 2004
Econometric Society North American Winter Meeting, Providence, June
2004 (chair)
Econometric Society European Summer Meeting, Madrid,, Aug. 2004
Midwestern Econometrics Group, Chicago , Oct. 2004
European Meeting of Statisticians, Olso, July 2005
Econometric Society World Congress, London , Aug. 2005
Vilnius Conference on Mathematical Statistics, June 2006
European Meeting of Statisticians, Turon, July 2006 (accepted)
Statistical and Applied Mathematical Sciences Institute: Risk, Extreme Events and Decision Theory, Sept. 2007
Triangle Econometrics Conference, Durham NC, Dec. 2007.
Computational and Financial Econometrics – Neuchâtel, Switzerland, June 2008 (invited speaker, chair)
Econometric Society North American Summer Meeting, Pittsburgh, June 2008
Joint Statistical Meetings – Denver, Aug. 2008
Royal Statistical Society – Nottingham, Sept. 2008
UNC-NCSU Econometrics Workshop, Oct. 2008
SEMINARS,
COLLOQUIA, TALKS
Colorado
State University, Dept. of Statistics
Indiana
University, Dept. of Economics
University
of California – San Diego, Dept. of Economics
Vrije
Universiteit Amsterdam, Dept. of Econometrics
University
of Amsterdam, Dept. of Econometrics
University
of Mannheim, Dept. of Statistics
Lancaster
University, Dept. of Mathematics and Statistics
University
of North Carolina-Chapel Hill, Dept. of Statistics and O.R.
University
of Toronto, Dept. of Economics
Duke
University, Dept. of Economics
London
School of Economics, Dept. of Economics
Oxford
University, Dept. of Economics
University
of North Carolina – Chapel Hill, Dept. of Economics
University
of Toronto, Dept. of Statistics
University
of California – Davis, Dept. of Statistics
Georgia
Tech, Dept. of Mathematics
CentER
Econometrics and Statistics Seminar at University of Tilburg
RECENT
and FORTHCOMING TALKS
JOURNAL,
ACADEMIC PRESS and GRANT PROPOSAL REFEREE
Econometrica, Journal of the American Statistical Association, Econometric Theory, Annals of Statistical Mathematics, Journal of Nonparametric Statistics, Journal of Multivariate Analysis, Journal of Business and Economic Statistics, Journal of Econometrics, Stochastic Processes and their Applications, Journal of Time Series Analysis, Oxford Bulletin of Economics and Statistics, Statistical Methods and Applications, IMA Journal of Management Mathematics, Studies in Nonlinear Dynamics and Econometrics, Journal of the Korean Statistical Society, Economic Modeling, Computational Statistics and Data Analysis, Physica A: Statistical Mechanics, Physica D: Nonlinear Phenomena, Econometrics Journal, International Economics and Finance Journal, National Science Foundation, Yale University Press
AFFILIATIONS
Institute of Mathematical Statistics,
Econometric Society,
American Economic Association,
TEACHING
Undergraduate:
Mathematical Economics, Econometrics I,II,III, Time Series Forecasting, Public
Finance, Microeconomics: principles,
intermediate
Graduate: Nonlinear
Time Series Econometrics, Mathematical Economics, Microeconometrics, Time
Series, Time Series Forecasting, Public Finance