scholarly journals BOOTSTRAP-ASSISTED UNIT ROOT TESTING WITH PIECEWISE LOCALLY STATIONARY ERRORS

2018 ◽  
Vol 35 (1) ◽  
pp. 142-166 ◽  
Author(s):  
Yeonwoo Rho ◽  
Xiaofeng Shao

In unit root testing, a piecewise locally stationary process is adopted to accommodate nonstationary errors that can have both smooth and abrupt changes in second- or higher-order properties. Under this framework, the limiting null distributions of the conventional unit root test statistics are derived and shown to contain a number of unknown parameters. To circumvent the difficulty of direct consistent estimation, we propose to use the dependent wild bootstrap to approximate the nonpivotal limiting null distributions and provide a rigorous theoretical justification for bootstrap consistency. The proposed method is compared through finite sample simulations with the recolored wild bootstrap procedure, which was developed for errors that follow a heteroscedastic linear process. Furthermore, a combination of autoregressive sieve recoloring with the dependent wild bootstrap is shown to perform well. The validity of the dependent wild bootstrap in a nonstationary setting is demonstrated for the first time, showing the possibility of extensions to other inference problems associated with locally stationary processes.

2011 ◽  
Vol 27 (5) ◽  
pp. 1026-1047 ◽  
Author(s):  
Patrick Marsh

This paper provides a (saddlepoint) tail probability approximation for the distribution of an optimal unit root test. Under restrictive assumptions, Gaussianity, and known covariance structure, the order of error of the approximation is given. More generally, when innovations are a linear process in martingale differences, the estimated saddlepoint is proved to yield valid asymptotic inference. Numerical evidence, considered over a range of models, demonstrates some finite-sample superiority over approximations for a directly comparable test based on simulation of its limiting stochastic representation.


2020 ◽  
Vol 8 (4) ◽  
pp. 409-423
Author(s):  
Sümeyra GAZEL

In this study, weak form efficiency of the Exchange Traded Funds (ETF) in the Morgan Stanley Capital International (MSCI) Index of developed and developing countries is tested. The Fourier Unit Root test, which does not lose its predictive power in terms of structural break date, number and form, is used on daily data. Also, conventional unit root tests are used for comparison between two different tests. Analysis results indicate common findings in some countries for both unit root testing. However, the Fourier unit root test results relatively more support the assumption of efficient market hypothesis that developed countries may be more efficient than developing countries.


1996 ◽  
Vol 12 (4) ◽  
pp. 724-731 ◽  
Author(s):  
Jon Faust

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.


2012 ◽  
Vol 28 (5) ◽  
pp. 1121-1143 ◽  
Author(s):  
Tomás del Barrio Castro ◽  
Denise R. Osborn ◽  
A.M. Robert Taylor

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.


Author(s):  
Sera Şanlı ◽  
Mehmet Özmen

Detecting the direction of inflation-growth relationship has been a controversial issue in terms of the theoretical framework, notedly since the rise of Mundell-Tobin effect which is based upon the assumption of substitutability between money and capital. In this study, it has been aimed to investigate the cointegrating relationship and its direction between inflation and economic growth covering the period 1998Q1:2014Q4 for Turkey as grounded on the testing sequence that is illustrated by Ilmakunnas (1990) in order to handle unit root testing in a seasonal context by testing the appropriate order of differencing and concerns with the case where SI(2,1) (seasonally integrated of order (2,1)) is the maximum order of seasonal integration. It has been also utilized from ADF unit root test and DHF, HEGY & OCSB seasonal unit root tests in seasonal integration analysis. In the study, five cointegration regressions have been considered in the level, seasonally averaged, quarterly differenced, first differenced and twice differenced forms and two series have been found to have the same degree of seasonal integration as SI(1,1). Applying various residual tests have revealed the presence of a cointegrating relationship between two variables. In addition, the inflation-growth relationship in Turkey has been concluded to perform in an opposite direction.


Author(s):  
Md. Rasel Hossain ◽  
Ahsanul Haque ◽  
Md. Abdullah Amir Hamja ◽  
M. Shohel Rana

It is important to know the future movement of economic variables for the planning and development of a country, Vector Error Correction (VEC) Model has been applied to disclose hidden long run as well as short-run patterns of the selected variables. ADF unit root testing procedure was applied to satisfy the conditions of applying the VEC Model. Using Johansen cointegration test long-run cointegration has been justified. But the VEC model reveals that long run significant causal relationship between the variables whereas there is no short-run causal relationship. The parameter was estimated using the OLS estimation technique. The validity of the model was confirmed by applying different quantitative approaches such as normality test, autocorrelation test, Portmanteau test, Unit root test, and various graphical approaches which suggested model selection and estimation were correct. The result of this present study may help Govt. agencies as well as planners to take an idea.


2019 ◽  
Vol 145 ◽  
pp. 74-80
Author(s):  
Nan Zou ◽  
Dimitris N. Politis

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