Modified Unit Root Tests with Nuisance Parameter Free Asymptotic Distributions

Said and Dickey (1984,Biometrika71, 599–608) and Phillips and Perron (1988,Biometrika75, 335–346) have derived unit root tests that have asymptotic distributions free of nuisance parameters under very general maintained models. Under models as general as those assumed by these authors, the size of the unit root test procedures will converge to one, not the size under the asymptotic distribution. Solving this problem requires restricting attention to a model that is small, in a topological sense, relative to the original. Sufficient conditions for solving the asymptotic size problem yield some suggestions for improving finite-sample size performance of standard tests.

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A Note on the Asymptotic Distributions of Unit Root Tests in the Additive Outlier Model With Breaks

Brazilian Review of Econometrics ◽

10.12660/bre.v13n21993.2981 ◽

1993 ◽

Vol 13 (2) ◽

pp. 8 ◽

Cited By ~ 2

Author(s):

Pierre Perron ◽

Timothy J. Vogelsang

Keyword(s):

Unit Root ◽

Asymptotic Distributions ◽

Unit Root Tests ◽

Additive Outlier

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Unit Root Tests Based on M Estimators

Econometric Theory ◽

10.1017/s0266466600009191 ◽

1995 ◽

Vol 11 (2) ◽

pp. 331-346 ◽

Cited By ~ 58

Author(s):

André Lucas

Keyword(s):

Linear Combination ◽

Unit Root ◽

Asymptotic Theory ◽

Simulation Experiment ◽

Unit Root Test ◽

Ordinary Least Squares ◽

Asymptotic Distributions ◽

Unit Root Tests ◽

Nuisance Parameters ◽

M Estimator

This paper considers unit root tests based on M estimators. The asymptotic theory for these tests is developed. It is shown how the asymptotic distributions of the tests depend on nuisance parameters and how tests can be constructed that are invariant to these parameters. It is also shown that a particular linear combination of a unit root test based on the ordinary least-squares (OLS) estimator and on an M estimator converges to a normal random variate. The interpretation of this result is discussed. A simulation experiment is described, illustrating the level and power of different unit root tests for several sample sizes and data generating processes. The tests based on M estimators turn out to be more powerful than the OLS-based tests if the innovations are fat-tailed.

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Asymptotic Distribution of Unit Root Tests Base on ESTAR Model with Flexible Fourier Form

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2021/v14i130321 ◽

2021 ◽

pp. 41-51

Author(s):

Murtala Adam Muhammad ◽

Junjuan Hu

Keyword(s):

Brownian Motion ◽

Asymptotic Distribution ◽

Unit Root ◽

Asymptotic Distributions ◽

Unit Root Tests ◽

Nuisance Parameters ◽

Not Given

In this paper, the asymptotic distribution of Fourier ESTAR model (FKSS) proposed by [1], which was not given in the original paper are derived. Result shows that the asymptotic distributions are functions of brownian motion, only depends on K and free from nuisance parameters.

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