scholarly journals A FIXED-b PERSPECTIVE ON THE PHILLIPS–PERRON UNIT ROOT TESTS

2012 ◽  
Vol 29 (3) ◽  
pp. 609-628 ◽  
Author(s):  
Timothy J. Vogelsang ◽  
Martin Wagner
Keyword(s):  
Unit Root ◽  
Theoretical Explanation ◽  
Unit Root Tests ◽  
Nuisance Parameters ◽  
Finite Sample ◽  
Asymptotic Power ◽  
Long Run ◽  
Local Asymptotic Power ◽  
One Step ◽  
The One

In this paper we extend fixed-b asymptotic theory to the nonparametric Phillips–Perron (PP) unit root tests. We show that the fixed-b limits depend on nuisance parameters in a complicated way. These nonpivotal limits provide an alternative theoretical explanation for the well-known finite-sample problems of the PP tests. We also show that the fixed-b limits depend on whether deterministic trends are removed using one-step or two-step detrending approaches. This is in contrast to the asymptotic equivalence of the one- and two-step approaches under a consistency approximation for the long-run variance estimator. Based on these results we introduce modified PP tests that allow for asymptotically pivotal fixed-b inference. The theoretical analysis is cast in the framework of near-integrated processes, which allows us to study the asymptotic behavior both under the unit root null hypothesis and for local alternatives. The performance of the original and modified PP tests is compared by means of local asymptotic power and a small finite-sample simulation study.

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.

scholarly journals LOCAL ASYMPTOTIC POWER OF THE IM-PESARAN-SHIN PANEL UNIT ROOT TEST AND THE IMPACT OF INITIAL OBSERVATIONS

2009 ◽  
Vol 26 (1) ◽  
pp. 311-324 ◽  
Author(s):  
David Harris ◽  
David I. Harvey ◽  
Stephen J. Leybourne ◽  
Nikolaos D. Sakkas
Keyword(s):  
Unit Root ◽  
Initial Conditions ◽  
Unit Root Test ◽  
Finite Sample ◽  
Asymptotic Power ◽  
Panel Unit Root ◽  
Practical Applications ◽  
Power Of The Test ◽  
Local Asymptotic Power ◽  
The Impact

In this note we derive the local asymptotic power function of the standardized averaged Dickey–Fuller panel unit root statistic of Im, Pesaran, and Shin (2003, Journal of Econometrics, 115, 53–74), allowing for heterogeneous deterministic intercept terms. We consider the situation where the deviation of the initial observation from the underlying intercept term in each individual time series may not be asymptotically negligible. We find that power decreases monotonically as the magnitude of the initial conditions increases, in direct contrast to what is usually observed in the univariate case. Finite-sample simulations confirm the relevance of this result for practical applications, demonstrating that the power of the test can be very low for values of T and N typically encountered in practice.

scholarly journals Structural Breaks and Explosive Behavior in the Long-Run: The Case of Australian Real House Prices, 1870–2020

2021 ◽  
Vol 15 (1) ◽  
pp. 72-84
Author(s):  
Vicente Esteve ◽  
Maria A. Prats
Keyword(s):  
Time Series ◽  
Unit Root ◽  
Structural Breaks ◽  
House Prices ◽  
Unit Root Tests ◽  
Annual Data ◽  
Bubble Behavior ◽  
Long Period ◽  
Long Run ◽  
Long Time

Abstract In this article, we use tests of explosive behavior in real house prices with annual data for the case of Australia for the period 1870–2020. The main contribution of this paper is the use of very long time series. It is important to use longer span data because it offers more powerful econometric results. To detect episodes of potential explosive behavior in house prices over this long period, we use the recursive unit root tests for explosiveness proposed by Phillips et al. (2011), (2015a,b). According to the results, there is a clear speculative bubble behavior in real house prices between 1997 and 2020, speculative process that has not yet been adjusted.

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.

scholarly journals ON AUGMENTED HEGY TESTS FOR SEASONAL UNIT ROOTS

2012 ◽  
Vol 28 (5) ◽  
pp. 1121-1143 ◽  
Author(s):  
Tomás del Barrio Castro ◽  
Denise R. Osborn ◽  
A.M. Robert Taylor
Keyword(s):  
Unit Root ◽  
Unit Roots ◽  
Linear Process ◽  
Unit Root Tests ◽  
Nuisance Parameters ◽  
Martingale Difference ◽  
Linear Processes ◽  
Seasonal Unit Roots ◽  
Null Distributions ◽  
Augmented Dickey Fuller

In this paper we extend the large-sample results provided for the augmented Dickey–Fuller test by Said and Dickey (1984, Biometrika 71, 599–607) and Chang and Park (2002, Econometric Reviews 21, 431–447) to the case of the augmented seasonal unit root tests of Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238), inter alia. Our analysis is performed under the same conditions on the innovations as in Chang and Park (2002), thereby allowing for general linear processes driven by (possibly conditionally heteroskedastic) martingale difference innovations. We show that the limiting null distributions of the t-statistics for unit roots at the zero and Nyquist frequencies and joint F-type statistics are pivotal, whereas those of the t-statistics at the harmonic seasonal frequencies depend on nuisance parameters that derive from the lag parameters characterizing the linear process. Moreover, the rates on the lag truncation required for these results to hold are shown to coincide with the corresponding rates given in Chang and Park (2002); in particular, an o(T1/2) rate is shown to be sufficient.

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