Working Papers - JBHill (UNC)

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Home Page of Jonathan B. Hill

Assistant Professor of Economics

University of North Carolina – Chapel Hill

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WORKING PAPERS

(Under Submission or Invited Revision for Publication)

Are There Common Values in First-Price Auctions? A Tail-Index Nonparametric Test (2010, with A. Shneyerov): revised and resubmitted to Journal of Econometrics.

Paper: PDF (this version: Nov. 2011)

Appendix: PDF

We develop a consistent nonparametric test of common values in first-price auctions and apply it to British Columbia Timber Sales data. The test is based on the behavior of the CDF of bids near the reserve price. We show that the curvature of the CDF is drastically different under private values (PV) and common values (CV). We then show that the problem of discriminating between PV and CV is equivalent to estimating the lower tail index of the bid distribution. Our approach admits unobserved auction heterogeneity of an arbitrary form. We develop a Hill (1975)-type tail index estimator and find presence of common values BC Timber Sales.

Robust Estimation and Inference for Heavy Tailed Nonlinear GARCH (2012): submitted to Annals of Statistics

Paper: PDF

Supplemental Material: PDF

Extended Working Paper ("Robust M-Estimation for Heavy Tailed Nonlinear AR-GARCH "): PDF

We develop new tail-trimmed QML estimators for nonlinear GARCH models with possibly heavy tailed errors. Tail-trimming allows both identification of the true parameter and asymptotic normality. In heavy tailed cases the rate of convergence is below but arbitrarily close to root-n, the highest possible amongst M-estimators for GARCH with errors that have an infinite fourth moment, and faster than QML. We present a consistent estimator of the covariance matrix that permits classic inference without knowledge of the rate of convergence. Finally, a simulation study shows our estimators trump existing ones for sharpness and approximate normality, and we apply them to financial returns data.

Robust Score and Portmanteau Tests of Volatility Spillover (2012, with M. Aguilar)

Paper: PDF

This paper presents a variety of tests of volatility spillover that are robust to heavy tails. The tests are couched in semi-strong and strong GARCH frameworks 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 tail-trimmed 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 obtains a power of one asymptotically. A Monte Carlo study shows our tests provide significant improvements over extant GARCH-based tests of spillover, and we apply the tests to financial returns data.

Central Limit Theory for Tail-Trimmed Sums of Heavy-Tailed Dependent, Heterogeneous Data (2010): under revision for Stochastic Processes and theirApplications

Paper: PDF (under revision)

We present Gaussian central limit theorems for tail-trimmed sums of a heavy tailed weakly dependent process in the Feller class. We show how the results imply asymptotic normality for sample tail-trimmed variances and covariances, and a super-root(n)-convergent least squares estimator for infinite variance autoregressions.

Heavy-Tail and Plug-In Robust Consistent Conditional Moment Tests of Functional Form (2011): under revision for the Springer collected works in honor of Hal White

Paper: PDF

Appendix: PDF

We present asymptotic power-one test statistics for heavy tailed time series. Under the null the regression errors must have a finite mean, and otherwise they may have arbitrarily heavy tails. If the errors have an infinite variance then in principle any consistent plug-in is allowed, depending on the model, including those with non-Gaussian limits or a sub-root(n)-convergence rate. One statistic exploits an orthogonalized test equation that promotes plug-in robustness irrespective of tails. We derive chi-squared weak limits, characterize an empirical process method for selecting the trimming fractile, and study the finite sample properties.

GEL Estimation for Semi-Strong Non-Linear GARCH with Robust Empirical Likelihood Inference (2011: with Artem Prokhorov)

Paper: PDF

We construct Generalized Empirical Likelihood estimators for Nonlinear GARCH models with possibly heavy tailed non-iid errors. The estimators imbed tail-trimmed estimating equations allowing for over-identifying conditions, asymptotic normality and efficiency for very heavy-tailed data due to feedback or idiosyncratic noise. We show the empirical probabilities from Euclidean Empirical Likelihood optimize weight for usable large values, give large but not maximum weight on extremes, and give the lowest weight to non-leverage points. Finally, we use tail-trimmed GEL empirical probabilities for efficient and robust versions of Generalized Empirical Likelihood Ratio, Wald, and Lagrange Multiplier tests, and moment estimation with an application to heavy tail robust and efficient Expected Shortfall estimation.

Robust Score and Portmanteau Tests of Volatility Spillover (2012: with Mike Aguilar)

Paper: PDF

This paper presents a variety of tests of volatility spillover that are robust to heavy tails. The tests are couched in semi-strong and strong GARCH frameworks 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 tail-trimmed sample correlation coefficient for robust inference, and prove 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 obtains a power of one asymptotically. A Monte Carlo study shows our tests provide significant improvements over extant GARCH-based tests of spillover, and we apply the tests to financial returns data.

OLD WORKING PAPERS

Robust Estimation and Inference for Extremal Dependence in Time Series (2009)

Paper: PDF

Appendix C : Omitted Proofs : PDF

Appendix D : Omitted Figures and Tables : PDF

Gauss: code

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 semi-nonparametric and nonparametric measures, estimators and tests of bivariate tail dependence for non-iid data based on tail exceedances and events. The measures and estimators capture extremal dependence decay over time and can be re-scaled 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 non-extremal properties and joint distribution specifications. Finally, we study the extremal associations within and between equity returns in the U.S., U.K. and Japan.

Gaussian Tests of 'Extremal White Noise' for Dependent, Heterogeneous, Heavy Tailed Time Series with an Application (2008)

Paper: PDF (this version: Feb. 2008)

Appendix: PDF

Gauss: code

We develop a portmanteau test of extremal serial dependence. The test statistic is asymptotically chi-squared under a null of "extremal white noise", as long as extremes are Near-Epoch-Dependent, 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.