Powerful Unit Root Tests Free of Nuisance Parameters

2016 ◽  
Vol 37 (4) ◽  
pp. 533-554 ◽  
Author(s):  
Mehdi Hosseinkouchack ◽  
Uwe Hassler
Keyword(s):  
Unit Root ◽  
Unit Root Tests ◽  
Nuisance Parameters

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.

Unit Root Tests Based on M Estimators

1995 ◽  
Vol 11 (2) ◽  
pp. 331-346 ◽  
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.

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

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.

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.

scholarly journals TESTING FOR A UNIT ROOT IN A TIME SERIES WITH A LEVEL SHIFT AT UNKNOWN TIME

2002 ◽  
Vol 18 (2) ◽  
pp. 313-348 ◽  
Author(s):  
Pentti Saikkonen ◽  
Helmut Lütkepohl
Keyword(s):  
Time Series ◽  
Unit Root ◽  
Small Sample ◽  
Unit Root Tests ◽  
Nuisance Parameters ◽  
Level Shift ◽  
Generation Process ◽  
Data Generation ◽  
Level Shifts ◽  
Small Sample Properties

Unit root tests for time series with level shifts of general form are considered when the timing of the shift is unknown. It is proposed to estimate the nuisance parameters of the data generation process including the shift date in a first step and apply standard unit root tests to the residuals. The estimation of the nuisance parameters is done in such a way that the unit root tests on the residuals have the same limiting distributions as for the case of a known break date. Simulations are performed to investigate the small sample properties of the tests, and empirical examples are discussed to illustrate the procedure.

Survey on structural breaks and unit root tests

2020 ◽  
Vol 58 ◽  
pp. 96-141
Author(s):  
A. Skrobotov ◽  
◽  
Keyword(s):  
Unit Root ◽  
Structural Breaks ◽  
Unit Root Tests

scholarly journals UNIT ROOT TEST WITH HIGH-FREQUENCY DATA

2021 ◽  
pp. 1-59
Author(s):  
Sébastien Laurent ◽  
Shuping Shi
Keyword(s):  
Random Walk ◽  
Unit Root ◽  
High Frequency ◽  
Asset Prices ◽  
Composite Index ◽  
Mean Reversion ◽  
Unit Root Tests ◽  
High Frequency Data ◽  
Frequency Data ◽  
Intraday Data

Deviations of asset prices from the random walk dynamic imply the predictability of asset returns and thus have important implications for portfolio construction and risk management. This paper proposes a real-time monitoring device for such deviations using intraday high-frequency data. The proposed procedures are based on unit root tests with in-fill asymptotics but extended to take the empirical features of high-frequency financial data (particularly jumps) into consideration. We derive the limiting distributions of the tests under both the null hypothesis of a random walk with jumps and the alternative of mean reversion/explosiveness with jumps. The limiting results show that ignoring the presence of jumps could potentially lead to severe size distortions of both the standard left-sided (against mean reversion) and right-sided (against explosiveness) unit root tests. The simulation results reveal satisfactory performance of the proposed tests even with data from a relatively short time span. As an illustration, we apply the procedure to the Nasdaq composite index at the 10-minute frequency over two periods: around the peak of the dot-com bubble and during the 2015–2106 stock market sell-off. We find strong evidence of explosiveness in asset prices in late 1999 and mean reversion in late 2015. We also show that accounting for jumps when testing the random walk hypothesis on intraday data is empirically relevant and that ignoring jumps can lead to different conclusions.

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.

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