A simple modification to improve the finite sample properties of Ng and Perron's unit root tests

2007 ◽  
Vol 94 (1) ◽  
pp. 12-19 ◽  
Author(s):  
Pierre Perron ◽  
Zhongjun Qu
Keyword(s):  
Unit Root ◽  
Unit Root Tests ◽  
Finite Sample ◽  
Simple Modification ◽  
Finite Sample Properties

scholarly journals THE IMPACT OF PERSISTENT CYCLES ON ZERO FREQUENCY UNIT ROOT TESTS

2013 ◽  
Vol 29 (6) ◽  
pp. 1289-1313 ◽  
Author(s):  
Tomás del Barrio Castro ◽  
Paulo M.M. Rodrigues ◽  
A.M. Robert Taylor
Keyword(s):  
Unit Root ◽  
Unit Root Test ◽  
American Statistical Association ◽  
Unit Root Tests ◽  
Statistical Association ◽  
Finite Sample ◽  
Finite Sample Properties ◽  
Augmented Dickey Fuller ◽  
Frequency Unit ◽  
The Impact

In this paper we investigate the impact of persistent (nonstationary or near nonstationary) cycles on the asymptotic and finite-sample properties of standard unit root tests. Results are presented for the augmented Dickey–Fuller (ADF) normalized bias and t-ratio-based tests (Dickey and Fuller, 1979, Journal of the American Statistical Association 745, 427–431; Said and Dickey, 1984; Biometrika 71, 599–607). the variance ratio unit root test of Breitung (2002, Journal of Econometrics 108, 343–363), and the M class of unit-root tests introduced by Stock (1999, in Engle and White (eds.), A Festschrift in Honour of Clive W.J. Granger) and Perron and Ng (1996, Review of Economic Studies 63, 435–463). We show that although the ADF statistics remain asymptotically pivotal (provided the test regression is properly augmented) in the presence of persistent cycles, this is not the case for the other statistics considered and show numerically that the size properties of the tests based on these statistics are too unreliable to be used in practice. We also show that the t-ratios associated with lags of the dependent variable of order greater than two in the ADF regression are asymptotically normally distributed. This is an important result as it implies that extant sequential methods (see Hall, 1994, Journal of Business & Economic Statistics 17, 461–470; Ng and Perron, 1995, Journal of the American Statistical Association 90, 268–281) used to determine the order of augmentation in the ADF regression remain valid in the presence of persistent cycles.

scholarly journals Simulation Analysis of Threshold Autoregressive Unit Root Tests

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Steve Cook
Keyword(s):  
Unit Root ◽  
Simulation Analysis ◽  
Unit Root Tests ◽  
Robust Methods ◽  
Finite Sample ◽  
Threshold Estimation ◽  
Matrix Estimation ◽  
Threshold Autoregressive ◽  
Finite Sample Properties ◽  
The Impact

Using numerical simulation, the finite-sample properties of threshold autoregressive (TAR) and momentum-threshold (MTAR) autoregressive-based unit root tests under both deterministic and consistent methods of threshold estimation are examined in the presence of generalised autoregressive conditional heteroskedasticity (GARCH). Previous research is extended by considering both the impact of alternative robust methods of covariance matrix estimation and the behaviour of the secondary tests of asymmetry associated with the TAR and MTAR models. The results obtained reveal many interesting features, in particular the distortionary effects of consistent-threshold estimation. In summary, the findings presented indicate that caution should be exercised when interpreting the results of these frequently employed threshold-based testing methods.

scholarly journals Finite-Sample Properties of the GLS-Based Dickey-Fuller Test in the Presence of Breaks in Innovation Variance

2016 ◽  
Vol 33 (3) ◽  
Author(s):  
Steven Cook
Keyword(s):  
Sample Size ◽  
Unit Root ◽  
Unit Root Tests ◽  
Finite Sample ◽  
Higher Power ◽  
Finite Sample Properties ◽  
Innovation Variance ◽  
Finite Sample Size

Using local-to-unity detrending, the GLS-based Dickey-Fuller test has been shown to possess higher power than other available unit root tests. As a result, application of this easily implemented test has increased in recent years. In the present study the finite-sample size and power of the GLS-based Dickey-Fuller test is examined in the presence of breaks in innovation variance under the null. In contrast to the original Dickey-Fuller test which has been shown to suffer severe distortion in such circumstances, the GLS-basedtest latter exhibits robustness to all but the most extreme breaks in variance.The results derived show the GLS-based test to be more robust to variance breaks than other modified Dickey-Fuller tests previously considered in the literature.

Unit root tests in panel data: asymptotic and finite-sample properties

2002 ◽  
Vol 108 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Andrew Levin ◽  
Chien-Fu Lin ◽  
Chia-Shang James Chu
Keyword(s):  
Panel Data ◽  
Unit Root ◽  
Unit Root Tests ◽  
Finite Sample ◽  
Finite Sample Properties

ASYMPTOTICALLY UMP PANEL UNIT ROOT TESTS—THE EFFECT OF HETEROGENEITY IN THE ALTERNATIVES

2014 ◽  
Vol 31 (3) ◽  
pp. 539-559 ◽  
Author(s):  
I. Gaia Becheri ◽  
Feike C. Drost ◽  
Ramon van den Akker
Keyword(s):  
Unit Root ◽  
Generalized Least Squares ◽  
Applied Economics ◽  
Unit Root Tests ◽  
Finite Sample ◽  
Asymptotic Power ◽  
Optimal Tests ◽  
Independent Panel ◽  
Local Asymptotic Power ◽  
Uniformly Most Powerful

In a Gaussian, heterogeneous, cross-sectionally independent panel with incidental intercepts, Moon, Perron, and Phillips (2007, Journal of Econometrics 141, 416–459) present an asymptotic power envelope yielding an upper bound to the local asymptotic power of unit root tests. In case of homogeneous alternatives this envelope is known to be sharp, but this paper shows that it is not attainable for heterogeneous alternatives. Using limit experiment theory we derive a sharp power envelope. We also demonstrate that, among others, one of the likelihood ratio based tests in Moon et al. (2007, Journal of Econometrics 141, 416–459), a pooled generalized least squares (GLS) based test using the Breitung and Meyer (1994, Applied Economics 25, 353–361) device, and a new test based on the asymptotic structure of the model are all asymptotically UMP (Uniformly Most Powerful). Thus, perhaps somewhat surprisingly, pooled regression-based tests may yield optimal tests in case of heterogeneous alternatives. Although finite-sample powers are comparable, the new test is easy to implement and has superior size properties.

Near Observational Equivalence and Theoretical size Problems with Unit Root Tests

1996 ◽  
Vol 12 (4) ◽  
pp. 724-731 ◽  
Author(s):  
Jon Faust
Keyword(s):  
Unit Root ◽  
Sufficient Conditions ◽  
Unit Root Test ◽  
Asymptotic Distributions ◽  
Unit Root Tests ◽  
Finite Sample ◽  
Test Procedures ◽  
Asymptotic Size ◽  
Finite Sample Size ◽  
Topological Sense

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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