Yoon-Jae Whang

Consistent bootstrap tests of parametric regression functions

Abstract This paper introduces specification tests of parametric mean-regression models. The null hypothesis of interest is that the parametric regression function is correctly specified. The proposed tests are generalizations of the Kolmogorov–Smirnov and Cramer–von Mises tests to the regression framework. They are consistent against all alternatives to the null hypothesis, powerful against 1/ n local alternatives, not dependent on any smoothing parameters and simple to compute. A wild-bootstrap procedure is suggested to obtain critical values for the tests and is justified asymptotically. A small-scale Monte Carlo experiment shows that our tests (especially Cramer–von Mises test) have outstanding small sample performance compared to some of the existing tests.

A multiple variance ratio test using subsampling

Abstract This paper considers a test of the random walk hypothesis by comparing jointly the variance ratios at multiple observation intervals with unity. We suggest a subsampling procedure to approximate the asymptotic null distribution. Simulation results provide some favorable finite sample performance.

The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series

This paper derives the asymptotic distribution of a smoothing-based estimator of the Lyapunov exponent for a stochastic time series under two general scenarios. In the first case, we are able to establish root-T consistency and asymptotic normality, while in the second case, which is more relevant for chaotic processes, we are only able to establish asymptotic normality at a slower rate of convergence. We provide consistent confidence intervals for both cases. We apply our procedures to simulated data.

TOPICS IN ADVANCED ECONOMETRICS: ESTIMATION, TESTING, AND SPECIFICATION OF CROSS-SECTION AND TIME SERIES MODELS

This book, Topics in Advanced Econometrics , is written primarily as a textbook for an advanced graduate econometrics course. The topics covered include consistent model specification testing, unit roots and cointegration, and nonparametric regression estimation; they are mainly the topics in which Professor Bierens has made significant contributions to the literature over the last 15 years. This book is unusual as a textbook in the sense that it treats both cross-sectional and time series (i.e., both subscript i and t ) issues in econometrics at an advanced level. Most of the results given, other than those available in standard econometrics or statistics textbooks, are drawn from the published work of the author. The book is very useful because it puts together a number of important current issues that have been treated separately in the literature and presents them systematically using a well-organized set of statistical tools. Another advantage of this book is that the materials given are almost self-contained, making this book suitable for self-tuition. This book thus ideally suits students who need tools for independent research especially in the area of nonlinear and nonparametric models and time series analysis. It will also be useful to more advanced researchers who are interested in a thorough understanding of some of the authors original and influential work in these areas.

Consistent specification testing for conditional moment restrictions

Abstract This paper introduces specification tests for conditional moment restrictions. The proposed tests are generalizations of the Kolmogorov–Smirnov and Cramer–von Mises tests and they are consistent against all alternatives to the null hypothesis, powerful against 1/ n local alternatives and not dependent on any smoothing parameter. A nonparametric bootstrap procedure based on recentered criterion function is suggested to obtain critical values for the tests and is justified asymptotically.

Nonparametric Estimation With Aggregated Data

We introduce a kernel-based estimator of the density function and regression function for data that have been grouped into family totals. We allow for a common intrafamily component but require that observations from different families be independent. We establish consistency and asymptotic normality for our procedures. As usual, the rates of convergence can be very slow depending on the behavior of the characteristic function at infinity. We investigate the practical performance of our method in a simple Monte Carlo experiment.

A TEST OF AUTOCORRELATION IN THE PRESENCE OF HETEROSKEDASTICITY OF UNKNOWN FORM

This paper develops a test of autocorrelation in the presence of heteroskedasticity of unknown form in the nonlinear regression model. The test statistic is based on the sample autocovariance of the residuals standardized by a nonparametric kernel estimate of the unknown heteroskedasticity function. Under appropriate conditions, the test statistic is shown to have a limiting chi-square distribution. Local power and consistency results for the test are also established. Monte Carlo experiments show that the test has reasonable size performance and generally dominates some of the existing tests in terms of finite-sample power.

A test of normality using nonparametrlic residuals

In this paper, we develop a test of the normality assumption of the errors using the residuals from a nonparametric kernel regression. Contrary to the existing tests based on the residuals from a parametric regression, our test is thus robust to misspecification of the regression function. The test statistic proposed here is a Bera-Jarque type test of skewness and kurtosis. We show that the test statistic has the usual x2(2) limit distribution under the null hypothesis. In contrast to the results of Rilstone (1992), we provide a set of primitive assumptions that allow weakly dependent observations and data dependent bandwidth parameters. We also establish consistency property of the test. Monte Carlo experiments show that our test has reasonably good size and power performance in small samples and perfornu better than some of the alternative tests in various situations.

A Semiparametric Analysis of the Life Cycle-Permanent Income Hypothesis

This paper considers a semiparametric regression model to test the various implications of the Life Cycle-Permanent Income (LCP) hypothesis proposed by Hall (1978). The semiparametric regression model does not require any parametric assumption on the functional form of the unknown utility function in our analysis. In contrast, the linear regression models frequently used in the literature are justified under specific parametric forms of the utility function and may lead to a misleading conclusion on the LCP hypothesis if the parameterization is incorrect. Using both linear and semiparametric regression models, tests of the martingale property of consumption along with several specification tests are performed on the U. S quarterly data from 1947 to 1990. The results from the semiparametric model do not differ significantly from those from the linear model and suggest some evidences against the implications of the LCP hypothesis. [C14]