scholarly journals Testing for a unit root against ESTAR stationarity

2017 ◽  
Vol 22 (1) ◽  
Author(s):  
David I. Harvey ◽  
Stephen J. Leybourne ◽  
Emily J. Whitehouse
Keyword(s):  
Unit Root ◽  
Unit Root Tests ◽  
Smooth Transition ◽  
Local Power ◽  
Sources Of Uncertainty ◽  
Deterministic Trend ◽  
Smooth Transition Autoregressive

AbstractIn this paper we examine the local power of unit root tests against globally stationary exponential smooth transition autoregressive [ESTAR] alternatives under two sources of uncertainty: the degree of nonlinearity in the ESTAR model, and the presence of a linear deterministic trend. First, we show that the KSS test (Kapetanios, G., Y. Shin, and A. Snell. 2003. “Testing for a Unit Root in the Nonlinear STAR Framework.”

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.

scholarly journals UNEMPLOYMENT HYSTERESIS IN TURKEY: EVIDENCE FROM NONLINEAR UNIT ROOT TESTS WITH FOURIER FUNCTION

2019 ◽  
Vol 20 (3) ◽  
pp. 178-188
Author(s):  
Burak Güriş ◽  
Gülşah Sedefoğlu
Keyword(s):  
Time Series ◽  
Unit Root ◽  
Development Process ◽  
Structural Breaks ◽  
Unit Root Tests ◽  
Smooth Transition ◽  
Star Model ◽  
Fourier Function ◽  
Smooth Transition Autoregressive ◽  
Nonlinear Unit Root Tests

The purpose of the article is to give brief information about the development process of time series analysis and to test the validity of the unemployment hysteresis in Turkey for female and male graduates for the years from 1988 to 2013. For this purpose, Kapetanios et al. [2003], Sollis [2009] and Kruse [2011] nonlinear unit root tests are applied based on the smooth transition autoregressive (STAR) model. Besides, nonlinear unit root tests proposed by Christopoulos et al. [2010] and Guris [2018] are employed to model the structural breaks through Fourier approach and to model the nonlinearity through a STAR model.

scholarly journals Smooth Break Detection and De-Trending in Unit Root Testing

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 371
Author(s):  
Furkan Emirmahmutoglu ◽  
Tolga Omay ◽  
Syed Jawad Hussain Shahzad ◽  
Safwan Mohd Nor
Keyword(s):  
Unit Root ◽  
Structural Breaks ◽  
Structural Break ◽  
Unit Root Tests ◽  
Smooth Transition ◽  
Unit Root Testing ◽  
Augmented Dickey Fuller ◽  
Power Comparisons ◽  
Fourier Function ◽  
Unexpected Outcomes

This study explores the methods to de-trend the smooth structural break processes while conducting the unit root tests. The two most commonly applied approaches for modelling smooth structural breaks namely the smooth transition and the Fourier functions are considered. We perform a sequence of power comparisons among alternative unit root tests that accommodate smooth or sharp structural breaks. The power experiments demonstrate that the unit root tests utilizing the Fourier function lead to unexpected results. Furthermore, through simulation studies, we investigate the source of such unexpected outcomes. Moreover, we provide the asymptotic distribution of two recently proposed unit root tests, namely Fourier-Augmented Dickey–Fuller (FADF) and Fourier-Kapetanios, Shin and Shell (FKSS), which are not given in the original studies. Lastly, we find that the selection of de-trending function is pivotal for unit root testing with structural breaks.

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.

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