Research Papers
Stochastic arbitrage with market index options
Joint with Brendan K. Beare
Opportunities for stochastic arbitrage in an options market arise when it is possible to construct a portfolio of options which provides a positive option premium and which, when combined with a direct investment in the underlying asset, generates a payoff which stochastically dominates the payoff from the direct investment in the underlying asset. We provide linear and linear integer programs for computing the stochastic arbitrage opportunity providing the maximum option premium to an investor. We apply our programs to 18 years of data on monthly put and call options on the Standard & Poors 500 index, confining attention to options with moderate moneyness. The selected option portfolios do not in fact generate stochastic arbitrage and are outperformed by a direct investment in the index. Our results serve as a cautionary tale about pursuing stochastic arbitrage opportunities when the behavior of the underlying asset is not well understood.
Functional data inference in a parametric quantile model applied to lifetime income curves
Joint with Jin Seo Cho and Peter C.B. Phillips
A parametric quantile function estimation procedure is developed for functional data. The approach involves minimizing the sum of integrated functional distances that measure the functional gap between each functional observation and the quantile curve in terms of the check function. The procedure is validated under both correctly specified and misspecified models by allowing for the presence of nuisance parameter estimation effects. Testing methodology is developed using Wald, Lagrange multiplier, and quasi-likelihood ratio procedures in this functional data setting. Finite sample performance is assessed using simulations and the methodology is applied to study how lifetime income paths differ between genders and among different education levels using continuous work history samples. The methodology enables the analysis of full career income paths with temporal and possibly persistent dependence structures embodied in the observations. The results capture both gender and education effects but these empirical differences are shown to be mitigated upon rescaling to take account of lifetime experience and job mobility.
Tie-break bootstrap for nonparametric rank statistics
Forthcoming in the Journal of Business & Economic Statistics.
In this paper, we propose a new bootstrap procedure for the empirical copula process. The procedure involves taking pseudo samples of normalized ranks in the same fashion as the classical bootstrap and applying small perturbations to break ties in the normalized ranks. Our procedure is a simple modification of the usual bootstrap based on sampling with replacement, yet it provides noticeable improvement in the finite sample performance. We also discuss how to incorporate our procedure into the time series framework. Since nonparametric rank statistics can be treated as functionals of the empirical copula, our proposal is useful in approximating the distribution of rank statistics in general. To provide an empirical illustration, we apply our bootstrap procedure to test the null hypotheses of positive quadrant dependence, tail monotonicity, and stochastic monotonicity, using data on the percentage changes in house prices across different states in the U.S.
Copula-based redundancy analysis
Joint with Jie Yeh Choi, Multivariate Behavioral Research (2022), 57 (6), 1007-1026.
Extended Redundancy Analysis (ERA) has recently been developed and widely applied to investigate component regression models. In this paper, we propose Copula-based Redundancy Analysis (CRA) to improve the performance of regression-based ERA. Our simulation results indicate that CRA is significantly superior to the regression-based ERA. We also discuss how to modify CRA to accommodate models with discrete, censored, truncated outcome variables, or a combination thereof, where ERA cannot be employed. For applications, we provide two empirical analyses: one on academic achievement and one on drug use and health.
Parametric inference on the mean of functional data applied to lifetime income curves
Joint with Jin Seo Cho and Peter C.B. Phillips, International Economic Review (2022), 63 (1), 391-456.
We propose a framework for estimation of the conditional mean function in a parametric model with function space covariates. The approach employs a functional mean squared error objective criterion and allows for possible model misspecification. Under regulatory conditions, consistency and asymptotic normality are established. The analysis extends to situations where the asymptotic properties are influenced by estimation errors arising from the presence of nuisance parameters. Wald, Lagrange multiplier, and quasi-likelihood ratio statistics are studied and asymptotic theory is provided. These procedures enable inference about curve shapes in the observed functional data. Several model specifications where our results are useful are analyzed, including random coefficient models, distributional mixtures, and copula mixture models. Simulations exploring the finite sample properties of our methods are provided. An empirical application conducts lifetime income path comparisons across different demographic groups according to years of work experience. Gender and education levels produce differences in mean income paths corroborating earlier research. However, the mean income paths are found to be proportional so that, upon rescaling, the paths match over gender and across education levels.[Codes]
A projection framework for testing shape restrictions that form convex cones
Joint with Zheng Fang, Econometrica (2021) 89 (5), 2439-2458.
This paper develops a uniformly valid and asymptotically nonconservative test based on projection for a class of shape restrictions. The key insight we exploit is that these restrictions form convex cones, a simple and yet elegant structure that has been barely harnessed in the literature. Based on a monotonicity property afforded by such a geometric structure, we construct a bootstrap procedure that, unlike many studies in nonstandard settings, dispenses with estimation of local parameter spaces, and the critical values are obtained in a way as simple as computing the test statistic. Moreover, by appealing to strong approximations, our framework accommodates nonparametric regression models as well as distributional/density-related and structural settings. Since the test entails a tuning parameter (due to the nonstandard nature of the problem), we propose a data-driven choice and prove its validity. Monte Carlo simulations confirm that our test works well.
Randomization tests for equality in dependence structure
Journal of Business & Economic Statistics (2021) 39 (4), 1026-1037.
We develop a new statistical procedure to test whether the dependence structure is identical between two groups. Rather than relying on a single index such as Pearson's correlation coefficient or Kendall's tau , we consider the entire dependence structure by investigating the dependence functions (copulas). The critical values are obtained by a modified randomization procedure designed to exploit asymptotic group invariance conditions. Implementation of the test is intuitive and simple, and does not require any specification of a tuning parameter or weight function. At the same time, the test exhibits excellent finite sample performance, with the null rejection rates almost equal to the nominal level even when the sample size is extremely small. Two empirical applications concerning the dependence between income and consumption, and the Brexit effect on European financial market integration are provided. [Appendix] [Codes] [Data]
Randomization tests of copula symmetry
Joint with Brendan K. Beare, Econometric Theory (2020) 36 (6), 1025-1063.
New nonparametric tests of copula exchangeability and radial symmetry are proposed. The novel aspect of the tests is a resampling procedure that exploits group invariance conditions associated with the relevant symmetry hypothesis. They may be viewed as modified versions of randomization tests, the latter being inapplicable due to the unobservability of margins. Our tests are simple to compute, control size asymptotically, consistently detect arbitrary forms of asymmetry, and do not require the specification of a tuning parameter. Simulations indicate excellent small sample properties compared to existing procedures involving the bootstrap. [Codes]
Tests of stochastic monotonicity with improved power
Journal of Econometrics (2018) 207 (1), 53-70.
We develop improved statistical procedures for testing the null hypothesis of stochastic monotonicity. Stochastic monotonicity can be reformulated in terms of the concavity of cross-sections of a copula function; our test statistic is based on an empirical measure of departures from concavity. While existing tests of stochastic monotonicity deliver a limiting rejection rate equal to the nominal significance level at one point and below the nominal significance level elsewhere in the null, our test raises the limiting rejection rate to the nominal significance level over a wide region of the null. This improves power against relevant local alternatives. Implementation of our procedure is based on preliminary estimation of a contact set, similar to procedures developed recently in other contexts. To show the validity of our approach we draw on recent results on the directional differentiability of the least concave majorant operator, and on bootstrap inference when smoothness conditions sufficient to apply the functional delta method for the bootstrap are not satisfied. An application to intergenerational income mobility is provided. [Codes] [Data]
Cointegrated linear processes in Hilbert space
Joint with Brendan K. Beare and Won-Ki Seo, Journal of Time Series Analysis (2017) 38 (6), 1010-1027.
We extend the notion of cointegration for multivariate real valued time series to a potentially infinite dimensional setting in which our time series takes values in a complex separable Hilbert space. In this setting, standard linear processes with nonzero long run covariance operator play the role of I(0) processes. We show that the cointegrating space for an I(1) process may be sensibly defined as the kernel of the long run covariance operator of its difference. The inner product of an I(1) process with an element of the cointegrating space is a stationary complex valued process. Our main result is a version of the Granger-Johansen representation theorem: we obtain a geometric reformulation of the Johansen I(1) condition that extends naturally to a Hilbert space setting, and show that an autogressive Hilbertian process satisfying this condition, and possibly also a compactness condition, admits an I(1) representation.
Vine copula specifications for stationary multivariate Markov chains
Joint with Brendan K. Beare, Journal of Time Series Analysis (2015) 36 (2), 228-246.
Vine copulae provide a graphical framework in which multiple bivariate copulae may be combined in a consistent fashion to yield a more complex multivariate copula. In this paper we discuss the use of vine copulae to build flexible semiparametric models for stationary multivariate higher-order Markov chains. We propose a new vine structure, the M-vine, that is particularly well suited to this purpose. Stationarity may be imposed by requiring the equality of certain copulae in the M-vine, while the Markov property may be imposed by requiring certain copulae to be independence copulae. [Corrigendum]
Time irreversible copula-based Markov models
Joint with Brendan K. Beare, Econometric Theory (2014) 30 (5), 923-960.
Economic and financial time series frequently exhibit time irreversible dynamics. For instance, there is considerable evidence of asymmetric fluctuations in many macroeconomic and financial variables, and certain game theoretic models of price determination predict asymmetric cycles in price series. In this paper we make two primary contributions to the econometric literature on time reversibility. First, we propose a new test of time reversibility, applicable to stationary Markov chains. Compared to existing tests, our test has the advantage of being consistent against arbitrary violations of reversibility. Second, we explain how a circulation density function may be used to characterize the nature of time irreversibility when it is present. We propose a copula-based estimator of the circulation density, and verify that it is well behaved asymptotically under suitable regularity conditions. We illustrate the use of our time reversibility test and circulation density estimator by applying them to five years of Canadian gasoline price markup data.