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Bootstrap
testing for the null of no cointegration in a threshold vector error
correction model, Journal of Econometrics, Volume 134, Issue 1, September 2006, Pages 129-150.
Abstract:
We develop a test for the linear no cointegration null hypothesis in a
threshold vector error correction model. We adopt a sup-Wald type test and
derive its null asymptotic distribution. A residual-based bootstrap is
proposed, and the first-order consistency of the bootstrap is established.
A set of Monte Carlo simulations shows that the bootstrap corrects size
distortion of asymptotic distribution in finite samples, and that its
power against the threshold cointegration alternative is significantly
greater than that of conventional cointegration tests. Our method is
illustrated with used car price indexes.
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A smoothed least
squares estimator for threshold regression models, with Oliver
Linton, Journal of Econometrics,
Vol 141, Issue 2, December 2007, Pages 704-735: Collection of Simulations
We propose a smoothed least squares estimator of the parameters of a threshold regression model. Our model generalizes that considered in Hansen (2000) to allow the thresholding to depend on a linear index of observed regressors, thus allowing discrete variables to enter. We also do not assume that the threshold effect is vanishingly small. Our estimator is shown to be consistent and asymptotically normal thus facilitating standard inference techniques based on estimated standard errors or standard bootstrap for the slope and threshold parameters. We compare our confidence intervals with those of Hansen (2000) in a simulation study and show that our methods outperform his for large values of the threshold.
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Semiparametric
estimation of a binary response model with a change-point due to a covariate
threshold,
Journal of Econometrics
(2008), 144, 492-499, with Sokbae Lee.
This paper is concerned with semiparametric
estimation of a threshold binary response model. The estimation method
considered in the paper is semiparametric since the parameters for a
regression function are finite-dimensional, while allowing for
heteroskedasticity of unknown form. In particular, the paper considers
Manski (1975, 1985)¨s
maximum score estimator. The model in this paper is irregular because of a
change-point due to an unknown threshold in a covariate. This irregularity
coupled with the discontinuity of the objective function of the maximum
score estimator complicates the analysis of the asymptotic behavior of the
estimator. Sufficient conditions for the identification of parameters are
given and the consistency of the estimator is obtained. It is shown that
the estimator of the threshold parameter
is n-consistent and the estimator of the remaining
regression parameters is cube root n-consistent.
Furthermore, we obtain the asymptotic distribution of the estimators.
It turns out that a suitably normalized estimator of
the
regression parameters converges weakly to
the distribution to which it would
converge
weakly if the true threshold value
were known and likewise for
the threshold estimator.
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Unit root test in a
threshold autoregression: Asymptotic theory and residual-based bootstrap,
Econometric Theory
(2008), 24,
1699-1716.
This paper develops a test of the unit root null hypothesis against a
stationary threshold process. This
testing problem is nonstandard and complicated because a parameter is
unidentified and the process is nonstationary under the null hypothesis.
We derive an asymptotic distribution for the test, which is not pivotal
without simplifying assumptions. A residual-based block bootstrap is
proposed to calculate the asymptotic p-values. The asymptotic validity of
the bootstrap is established and a set of Monte Carlo simulations
demonstrates its .nite sample performance. In particular, the test
exhibits considerable power gains over the ADF test that neglects
threshold effects.
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Estimation of
Nonlinear Error Correction Models, Econometric Theory (2011),
volume 27, issue 02, pp. 201-234. updated from the previous version
titled as "Estimation of Threshold Cointegration."
This paper explores the asymptotic properties of the least squares estimators of nonlinear vector error correction models (VECM) that exhibits regime-specific short-run dynamics. The model is irregular due to the presence of cointegration. We make the following contributions. First, we establish the consistency of the estimator of the cointegrating vector allowing for both smooth and discontinuous transition. Second, we derive the convergence rate of the cointegrating vector estimate in the discontinuous threshold VECM. The rate is nonstandard and extremely fast, which is n^{3/2}. Third, we obtain the asymptotic distributions for the smoothed least squares estimators of all the model parameters in the threshold VECM. Those of the cointegrating vector and the threshold parameter is a functional of a vector Brownian motion and independent of those of the slope parameters, which are Normal. It is also shown that the smoothed estimator of the threshold is asymptotically normal as if the true cointegrating vector were known, if we plug in the unsmoothed estimator of the cointegrating vector.
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Testing for Non-Nested Conditional Moment
Restrictions using
Unconditional Empirical
Likelihood,
Journal of Econometrics, forthcoming, 2010,
with Yoon-Jae Whang and Taisuke
Otsu.
We propose non-nested hypotheses tests for
conditional moment restriction models based on the
method of generalized empirical likelihood (GEL). By
utilizing the implied GEL probabilities from a sequence of
unconditional moment restrictions that contains
equivalent information of the conditional moment
restrictions, we construct Kolmogorov-Smirnov and Cram\'{e}r-von
Mises type\ moment encompassing tests. Advantages of our tests over
Otsu and Whang's (2007) tests are: (i) they are
free from smoothing parameters, (ii) they can be
applied to weakly dependent data, and (iii) they allow
non-smooth moment functions. We derive the null distributions,
validity of a bootstrap procedure, and local and
global power properties of our tests. The
simulation results show that our tests have reasonable size and power
performance in finite
samples.
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Testing for threshold effects in regression models,
Journal of the American Statistical Association (Theory and
Methods)
(2011), 106, 220-231 with Sokbae Lee and Youngki Shin.
Working paper version
In this article, we develop a
general method for testing threshold effects in regression models, using
sup-likelihood-ratio (LR)-type statistics. Although the sup-LR-type test
statistic has been considered in the literature, our method for establishing
the asymptotic null distribution is new and nonstandard. The standard
approach in the literature for obtaining the asymptotic null distribution
requires that there exist a certain quadratic approximation to the objective
function. We provide an alternative, novel method that can be used to
establish the asymptotic null distribution, even when the usual quadratic
approximation is intractable. We illustrate the usefulness of our approach
in the examples of the maximum score estimation, maximum likelihood
estimation, quantile regression, and maximum rank correlation estimation. We
also establish consistency and local power properties of the test. We
provide some simulation results and also an empirical application to tipping
in racial segregation. This article has supplementary materials online.
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