Least Absolute Deviation Based Unit Root Tests in Smooth Transition Type of Models

This paper considers a local least absolute deviation estimation for unit root processes with generalized autoregressive conditional heteroskedastic (GARCH) errors and derives its asymptotic properties under only finite second-order moment for both errors and innovations. When the innovations are symmetrically distributed, the asymptotic distribution of the estimated unit root is shown to be a functional of a bivariate Brownian motion, and then two unit root tests are derived. The simulation results demonstrate that the tests outperform those based on the Gaussian quasi maximum likelihood estimators with heavy-tailed innovations and those based on the simple least absolute deviation estimators.

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Testing for a unit root against ESTAR stationarity

Studies in Nonlinear Dynamics & Econometrics ◽

10.1515/snde-2016-0076 ◽

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.”

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Bootstrap unit root test based on least absolute deviation estimation under dependence assumptions

Journal of Applied Statistics ◽

10.1080/02664763.2014.999652 ◽

2015 ◽

Vol 42 (6) ◽

pp. 1332-1347

Author(s):

Xiaorong Yang

Keyword(s):

Unit Root ◽

Unit Root Test ◽

Least Absolute Deviation ◽

Absolute Deviation ◽

Least Absolute Deviation Estimation

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Smooth Break Detection and De-Trending in Unit Root Testing

Mathematics ◽

10.3390/math9040371 ◽

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.

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

The Stata Journal Promoting communications on statistics and Stata ◽

10.1177/1536867x1701700310 ◽

2017 ◽

Vol 17 (3) ◽

pp. 704-722 ◽

Cited By ~ 4

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

Metody Ilościowe w Badaniach Ekonomicznych ◽

10.22630/mibe.2019.20.3.17 ◽

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.

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