Finite sample performance of Schmidt–Philips unit root tests

1997 ◽  
Vol 4 (2) ◽  
pp. 129-132 ◽  
Author(s):  
Junsoo Lee
Keyword(s):  
Unit Root ◽  
Unit Root Tests ◽  
Finite Sample

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.

A family of nonparametric unit root tests for processes driven by infinite variance innovations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kemal Caglar Gogebakan
Keyword(s):  
Unit Root ◽  
Unit Root Tests ◽  
Tuning Parameter ◽  
Infinite Variance ◽  
Finite Sample ◽  
Power Performance ◽  
Finite Sample Size ◽  
Heavy Tailed ◽  
The Impact ◽  
Adf Test

Abstract This paper presents extensions to the family of nonparametric fractional variance ratio (FVR) unit root tests of Nielsen (2009. “A Powerful Test of the Autoregressive Unit Root Hypothesis Based on a Tuning Parameter Free Statistic.” Econometric Theory 25: 1515–44) under heavy tailed (infinite variance) innovations. In this regard, we first develop the asymptotic theory for these FVR tests under this setup. We show that the limiting distributions of the tests are free of serial correlation nuisance parameters, but depend on the tail index of the infinite variance process. Then, we compare the finite sample size and power performance of our FVR unit root tests with the well-known parametric ADF test under the impact of the heavy tailed shocks. Simulations demonstrate that under heavy tailed innovations, the nonparametric FVR tests have desirable size and power properties.

The finite-sample performance of robust unit root tests

2003 ◽  
Vol 44 (4) ◽  
pp. 469-482 ◽  
Author(s):  
Kai Carstensen
Keyword(s):  
Unit Root ◽  
Unit Root Tests ◽  
Finite Sample

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 UNIT ROOT TESTING IN PRACTICE: DEALING WITH UNCERTAINTY OVER THE TREND AND INITIAL CONDITION

2009 ◽  
Vol 25 (3) ◽  
pp. 587-636 ◽  
Author(s):  
David I. Harvey ◽  
Stephen J. Leybourne ◽  
A.M. Robert Taylor
Keyword(s):  
Decision Rule ◽  
Unit Root ◽  
Ordinary Least Squares ◽  
Unit Root Tests ◽  
Trend Detection ◽  
Initial Condition ◽  
Finite Sample ◽  
Testing Procedures ◽  
Unit Root Testing ◽  
Deterministic Trend

In this paper we focus on two major issues that surround testing for a unit root in practice, namely, (i) uncertainty as to whether or not a linear deterministic trend is present in the data and (ii) uncertainty as to whether the initial condition of the process is (asymptotically) negligible or not. In each case simple testing procedures are proposed with the aim of maintaining good power properties across such uncertainties. For the first issue, if the initial condition is negligible, quasi-differenced (QD) detrended (demeaned) Dickey–Fuller-type unit root tests are near asymptotically efficient when a deterministic trend is (is not) present in the data generating process. Consequently, we compare a variety of strategies that aim to select the detrended variant when a trend is present, and the demeaned variant otherwise. Based on asymptotic and finite-sample evidence, we recommend a simple union of rejections-based decision rule whereby the unit root null hypothesis is rejected whenever either of the detrended or demeaned unit root tests yields a rejection. Our results show that this approach generally outperforms more sophisticated strategies based on auxiliary methods of trend detection. For the second issue, we again recommend a union of rejections decision rule, rejecting the unit root null if either of the QD or ordinary least squares (OLS) detrended/demeaned Dickey–Fuller-type tests rejects. This procedure is also shown to perform well in practice, simultaneously exploiting the superior power of the QD (OLS) detrended/demeaned test for small (large) initial conditions.

scholarly journals Response Surface Models for OLS and GLS Detrending-based Unit-root Tests in Nonlinear ESTAR Models

2017 ◽  
Vol 17 (3) ◽  
pp. 704-722 ◽  
Author(s):  
Jesús Otero ◽  
Jeremy Smith
Keyword(s):  
Response Surface ◽  
Unit Root ◽  
Large Range ◽  
Autoregressive Process ◽  
Unit Root Tests ◽  
Smooth Transition ◽  
Finite Sample ◽  
Response Surface Models ◽  
Surface Models ◽  
Smooth Transition Autoregressive

In this article, we calculate response surface models for a large range of quantiles of the Kapetanios, Shin, and Snell (2003, Journal of Econometrics 112: 359–379) and Kapetanios and Shin (2008, Economics Letters 100: 377–380) tests for the null hypothesis of a unit root against the alternative—that the series of interest follows a globally stationary exponential smooth transition autoregressive process. The response surface models allow estimation of finite-sample critical values and approximate p-values for different combinations of the number of observations, T, and the lag order in the test regression, p. The latter can be either specified by the user or optimally selected using a data-dependent procedure. We present the new commands kssur and ksur and illustrate their use with an empirical example.

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