
Home Page of Jonathan B. Hill
Associate Professor of Economics University of North Carolina – Chapel Hill


CV (pdf) 



LINKS 

(Under
Submission or Invited Revision for Publication) GEL Estimation for
GARCH Models with Robust Empirical Likelihood Inference (2013: with Artem
Prokhorov): under revision for Journal
of Econometrics (1^{st} round)
We construct a Generalized Empirical Likelihood
estimator for a GARCH(1,1) model with possibly heavy tailed errors. The
estimator imbeds tailtrimmed estimating equations allowing for
overidentifying conditions, asymptotic normality and efficiency for very
heavytailed data due to feedback or idiosyncratic noise. We show the
empirical probabilities from the tailtrimmed Continuously Updated Estimator
or CUEGMM elevate weight for usable large values, assign large but not
maximum weight to extreme observations, and give the lowest weight to
nonleverage points. Finally, we present robust versions of Generalized
Empirical Likelihood Ratio, Wald, and Lagrange Multiplier tests, and an
efficient and robust moment estimator with an application to expected
shortfall estimation. Robust
Generalized Empirical Likelihood for Heavy Tailed Autoregressions with
Conditionally Heteroscedastic Errors (2013)
: submitted.
We present a robust Generalized
Empirical Likelihood estimator and confidence region for the parameters of an
autoregression that may have a heavy tailed heteroscedastic error. The
estimator exploits two transformations for heavy tail robustness: a
redescending transformation of the error that robustifies against innovation
outliers, and weighted least squares instruments that ensure robustness
against heavy tailed regressors. Our estimator is consistent for the true
parameter and asymptotically normally distributed irrespective of heavy
tails. Robust
Score and Portmanteau Tests of Volatility Spillover (2012: with M. Aguilar): revised and resubmitted to Journal of Econometrics (2^{nd} round).
This paper presents a variety of tests
of volatility spillover that are robust to heavy tails generated by large
errors or GARCHtype feedback. The tests are couched in a general conditional
heteroskedasticity framework with idiosyncratic shocks that are only required
to have a finite variance if they are independent. We negligibly trim test equations,
or components of the equations, and construct heavy tail robust score and
portmanteau statistics. We develop the tailtrimmed sample correlation
coefficient for robust inference, and prove that its Gaussian limit under the
null hypothesis of no spillover has the same standardization irrespective of
tail thickness. Further, if spillover occurs within a specified horizon, our
test statistics obtain power of one asymptotically. A Monte Carlo study shows
our tests provide significant improvements over extant GARCHbased tests of
spillover, and we apply the tests to financial returns data. Heavy
Tail Robust Frequency Domain Estimation (2014: with A. McCloskey) : submitted.
We develop heavy tail robust frequency
domain estimators for covariance stationary time series with a parametric
spectrum, including ARMA, GARCH and stochastic volatility. We use robust
techniques to reduce the moment requirement down to only a finite variance.
In particular, we negligibly transform the data with a redescending function
that permits identification of the parameter for the candidate model, and
asymptotic normality, while leading to a classic limit theory when the data
have a finite fourth moment. The transform itself can lead to asymptotic bias
in our estimators, hence we correct the bias. In the case of symmetrically
distributed data we compute the meansquarederror of our biased estimator
and characterize the meansquarederror minimization number of sample
extremes. A simulation experiment shows our QML estimator works well and in
general has lower bias than the standard estimator, even when the process is
Gaussian, suggesting robust methods have merit even for thin tailed
processes. Robust
Estimation for Average Treatment Effects (2013: with S. Chaudhuri) : submitted.
We study the probability tail
properties of the Inverse Probability Weighting (IPW) estimators of the
Average Treatment Effect when there is limited overlap in the covariate
distribution. Our main contribution is a new robust estimator that performs
substantially better than existing IPW estimators. In the literature either
the propensity score is assumed bounded away from 0 and 1, or a fixed or
shrinking sample portion of the random variable Z that identifies the average
treatment effect by E[Z] = ATE is trimmed when covariate values are large. In
a general setting we propose an asymptotically normal estimator that
negligibly trims Z adaptively by its large values which sidesteps
dimensionality, bias and poor correspondence properties associated with
trimming by the covariates, and provides a simple solution to the typically
ad hoc choice of trimming threshold. The estimator is asymptotically normal
and unbiased whether there is limited overlap or not. In the event there is
only one covariate, we also propose an improved robust IPW estimator that
trims when the covariate is large. We then work within a latent variable
model of the treatment assignment and characterize the probability tail decay
of Z. We show when Z exhibits power law tail decay due to limited overlap,
and when it has an infinite variance in which case existing estimators do not
necessarily have a Gaussian distribution limit. We demonstrate the tail decay
property of Z, and study the tailtrimmed estimators by Monte Carlo
experiments. We show that our estimator has lower bias and meansquarederror,
and is closer to normal than an existing robust IPW estimator in its
suggested form, and in the improved form we propose here. Testing for Granger Causality with Mixed
Frequency Data (2014: with E. Ghysels and K. Motegi): submitted.
It is well known that temporal aggregation has adverse effects
on Granger causality tests. Time series are often sampled at different
frequencies. This is typically ignored, and data are merely aggregated to the
common lowest frequency. We develop a set of Granger causality tests that
explicitly take advantage of data sampled at different frequencies. We show
that taking advantage of mixed frequency data allows us to better recover
causal relationships when compared to the conventional common low frequency
approach. We also show that the mixed frequency causality tests have higher
local asymptotic power as well as more power in finite samples compared to
conventional tests. An Empirical Process PValue Test when a
Nuisance Parameter is Present under Either or Both Hypotheses (2013): submitted.
We present an empirical process method for transforming
a test statistic pvalue in the presence of a nuisance parameter under either
hypothesis. The pvalue transform represents the uniform measure of the
parameter space, or occupation time [OT], on which the null hypothesis is
rejected. We reject at significance level a when the OT is greater than a, and the
asymptotic probability of a Type I error is bounded by α. Thus,
conveniently the OT both operates like a test statistic because large values
indicate rejection of the null, and like a pvalue compliment because its
values are bounded between 0 and 1 and rejection of the null occurs when the
OT is above a. Further, power in the original test naturally
translates to the OT test, while the OT test achieves a nontrivial power
improvement over the original test: even if the original test is not
consistent, as long as it has power on a dense subset of the nuisance
parameter space with Lebesgue measure greater than α then the OT test is
consistent. Finally, computation time is dramatically shorter than a popular
bootstrapsimulation method. Examples and numerical experiments are given
involving tests of functional form, GARCH effects and white noise robust to
heavy tails. Central Limit Theory for TailTrimmed Sums of
HeavyTailed Dependent, Heterogeneous Data (2010):
under revision for Stochastic Processes
and their Applications.
We present Gaussian central limit
theorems for tailtrimmed sums of a heavy tailed weakly dependent process in the
Feller class. We show how the results imply asymptotic normality for sample
tailtrimmed variances and covariances, and a superroot(n)convergent least
squares estimator for infinite variance autoregressions.
Robust
MEstimation for Heavy Tailed Nonlinear ARGARCH (2011).
We
develop new tailtrimmed Mestimation methods for heavy tailed Nonlinear
ARGARCH models. Tailtrimming allows both identification of the true
parameter and asymptotic normality for nonlinear models with asymmetric
errors. In heavy tailed cases the rate of convergence is infinitesimally
close to the highest possible amongst Mestimators for a particular loss
function, hence super root(n)convergence can be achieved in nonlinear AR
models with infinite variance errors, and arbitrarily near
root(n)convergence for GARCH with errors that have an infinite fourth
moment. We present a consistent estimator of the covariance matrix that
permits classic inference without knowledge of the rate of convergence, and
explore asymptotic covariance and bootstrap meansquarederror methods for
selecting trimming parameters. A simulation study shows the estimator trumps
existing ones for AR and GARCH models based on sharpness, approximate
normality, rate of convergence, and test accuracy. We then use the estimator
to study asset returns data. Robust Estimation and Inference for Extremal
Dependence in Time Series
(2009)
Dependence between extreme
values is predominantly measured by first assuming a parametric joint
distribution function, and almost always for otherwise marginally iid
processes. We develop seminonparametric and nonparametric measures,
estimators and tests of bivariate tail dependence for noniid data based on
tail exceedances and events. The measures and estimators capture extremal
dependence decay over time and can be rescaled to provide robust estimators
of canonical conditional tail probability and tail copula notions of tail
dependence. Unlike extant offerings, the tests obtain asymptotic power of one
against infinitessimal deviations from tail independence. Further, the
estimators apply to dependent, heterogeneous processes with or without
extremal dependence and irrespective of nonextremal properties and joint
distribution specifications. Finally, we study the extremal associations
within and between equity returns in the Gaussian
Tests of 'Extremal White Noise' for Dependent, Heterogeneous, Heavy Tailed
Time Series with an Application
(2008)
We
develop a portmanteau test of extremal serial dependence. The test statistic
is asymptotically chisquared under a null of "extremal white
noise", as long as extremes are NearEpochDependent, covering linear
and nonlinear distributed lags, stochastic volatility, and GARCH processes
with possibly unit or explosive roots. We apply tail specific tests to equity
market and exchange rate returns. 

Econometrics Workshops 



Software 



Econometrics Links 



Data Sources 



Research Resources 



Journals 



Statistics Links 



Miscellaneous Links 

Academic 



Personal
(places I’ve lived) 

Beijing 

San Fran. 

San Diego 
Miami 

Seattle 



Personal (favorite
places) 

Montreal 
Quebec City 

Bergen 
Tromso 

Eureka 
Cape Anne 

Edinburg 

Big
Sur 

Toledo Spain 
Connemara 



Photos 









































































































































































































































































































































































































