Smooth Break Detection and De-Trending in Unit Root Testing

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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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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A revisit of the unemployment rate, interest rate, GDP growth and Inflation of Pakistan: Whether Structural break or unit root?

iRASD Journal of Economics ◽

10.52131/joe.2021.0302.0027 ◽

2021 ◽

Vol 3 (2) ◽

pp. 80-92

Author(s):

Sara Muhammadullah ◽

Amena Urooj ◽

Faridoon Khan

Keyword(s):

Interest Rate ◽

Unemployment Rate ◽

Unit Root ◽

Structural Breaks ◽

Inflation Rate ◽

Structural Break ◽

Unit Root Test ◽

Unit Root Tests ◽

Gdp Growth ◽

Macroeconomic Indicators

The study investigates the query of structural break or unit root considering four macroeconomic indicators; unemployment rate, interest rate, GDP growth, and inflation rate of Pakistan. The previous studies create ambiguity regarding the stationarity and non-stationarity of these variables. We employ Zivot & Andrews (1992) unit root test and Step Indicator Saturation (SIS) method for multiple break detection in mean. GDP growth and inflation rate are stationary at level whereas unit root tests fail to reject the null hypothesis of the unemployment rate and interest rate at level. However, Zivot and Andrew unit root test with a single endogenous break indicates that the unemployment rate and interest rate are stationary at level with a single endogenous break. On the other hand, the SIS method reveals that the series are stationary with multiple structural breaks. It is inferred that it is inappropriate to take the first difference of the unemployment rate and interest rate to attain stationarity. The results of this study confirmed that there exist multiple breaks in the macroeconomic variables considered in the context of Pakistan.

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The effects of shocks on Turkish tourism demand: Evidence using panel unit root test

Tourism Economics ◽

10.1177/1354816619899831 ◽

2020 ◽

pp. 135481661989983 ◽

Cited By ~ 1

Author(s):

Yagmur Saglam ◽

Apostolos Ampountolas

Keyword(s):

Empirical Study ◽

Unit Root ◽

Structural Breaks ◽

Structural Break ◽

Unit Root Test ◽

Transition Process ◽

Smooth Transition ◽

Tourism Demand ◽

Panel Unit Root Test ◽

Panel Unit Root

This empirical study examines the stationarity of tourism demand in Turkey in response to the effects of structural breaks, which indicate external or internal shocks based on tourist arrivals from 12 Slavic-speaking countries between 2000 and 2016. We employed a panel unit root test based on the Flexible Fourier approach, which Karul enhanced to allow gradual shifts and a smooth transition process; structural break dates come from the Carrion-i-Silvestre unit root test framework. The empirical findings indicate that there are differences in the effects of these structural breaks across the 12 countries in question.

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Testing the Unit Root Hypothesis When the Alternative is a Trend Break Stationary Process: An Application to Tourist Arrivals in Fiji

Tourism Economics ◽

10.5367/000000005774352971 ◽

2005 ◽

Vol 11 (3) ◽

pp. 351-364 ◽

Cited By ~ 26

Author(s):

Paresh Kumar Narayan

Keyword(s):

New Zealand ◽

Structural Change ◽

Unit Root ◽

Structural Breaks ◽

Stationary Process ◽

Structural Break ◽

Unit Root Tests ◽

Test Statistic ◽

Seminal Contribution ◽

The Usa

The unit root hypothesis owes much to the work of Dickey and Fuller and has gained momentum since the seminal contribution of Perron (1989), who introduced the idea of structural breaks in unit root tests. In a recent study Sen (2003), extending the work of Zivot and Andrews (1992), recommends the F-test statistic for a unit root in the presence of a structural change in the economy. The central aim of this paper is to apply the Sen test to tourist arrivals to Fiji. The idea behind this exercise is to identify the year of the structural break and, more importantly, to examine whether the break has had a permanent or temporary effect on tourist arrivals in Fiji. Among our key results, we find that visitor arrivals in Fiji from Australia, New Zealand and the USA are stationary, implying that shocks have a temporary effect.

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Is It the Natural Rate Hypothesis or the Hysteresis Hypothesis for Unemployment Rates in Newly Industrialized Economies?

Comparative Economic Research ◽

10.2478/cer-2019-0031 ◽

2019 ◽

Vol 22 (4) ◽

pp. 39-55

Author(s):

Dieu Nsenga ◽

Mirada Nach ◽

Hlalefang Khobai ◽

Clement Moyo ◽

Andrew Phiri

Keyword(s):

Unit Root ◽

Structural Breaks ◽

The Philippines ◽

Unit Root Tests ◽

Natural Rate ◽

Unemployment Rates ◽

Quarterly Data ◽

Testing Procedures ◽

Unit Root Testing ◽

Conventional Unit

The focus of our study is on determining whether unemployment rates in 8 New Industrialized Economies conform to the natural rate hypothesis or the hysteresis hypothesis. To this end, we employ a variety of unit of unit root testing procedures to quarterly data collected between 2002:q1 and 2017:q1. Summarizing of our findings, conventional unit root tests which account neither for asymmetries nor structural breaks produce the most inconclusive results. On the other hand, tests which incorporate structural breaks while ignoring asymmetries tends to favour the natural rate hypothesis for our panel of countries. However, simultaneously accounting for asymmetries and unobserved structural breaks seemingly produces the most robust findings and confirms hysteresis in all unemployment rates except for Asian economies/countries of Thailand and the Philippines.

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High Persistence and Nonlinear Behavior in Financial Variables: A More Powerful Unit Root Testing in the ESTAR Framework

Mathematics ◽

10.3390/math9202534 ◽

2021 ◽

Vol 9 (20) ◽

pp. 2534

Author(s):

Tolga Omay ◽

Aysegul Corakci ◽

Esra Hasdemir

Keyword(s):

Interest Rates ◽

Unit Root ◽

Nuisance Parameter ◽

Unit Root Test ◽

Information Loss ◽

Smooth Transition ◽

Unit Root Testing ◽

Fourier Function ◽

Near Unit Root ◽

Model Linearization

In this study, we consider the hybrid nonlinear features of the Exponential Smooth Transition Autoregressive-Fractional Fourier Function (ESTAR-FFF) form unit root test. As is well known, when developing a unit root test for the ESTAR model, linearization is performed by the Taylor approximation, and thereby the nuisance parameter problem is eliminated. Although this linearization process leads to a certain amount of information loss in the unit root testing equation, it also causes the resulting test to be more accessible and consistent. The method that we propose here contributes to the literature in three important ways. First, it reduces the information loss that arises due to the Taylor expansion. Second, the research to date has tended to misinterpret the Fourier function used with the Kapetanios, Shin and Snell (2003) (KSS) unit root test and considers it to capture multiple smooth transition structural breaks. The simulation studies that we carry out in this study clearly show that the Fourier function only restores the Taylor residuals of the ESTAR type function rather than accounting forthe smooth structural break. Third, the new nonlinear unit root test developed in this paper has very strong power in the highly persistent near unit root environment that the financial data exhibit. The application of the Kapetanios Shin Snell- Fractional Fourier (KSS-FF) test to ex-post real interest rates data of 11 OECD countries for country-specific sample periods shows that the new test catches nonlinear stationarity in many more countries than the KSS test itself.

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Do Asian Stock Markets Follow a Random Walk? Evidence from LM Unit Root Tests with One and Two Structural Breaks

Review of Pacific Basin Financial Markets and Policies ◽

10.1142/s0219091507000933 ◽

2007 ◽

Vol 10 (01) ◽

pp. 15-31 ◽

Cited By ~ 16

Author(s):

Hooi Hooi Lean ◽

Russell Smyth

Keyword(s):

Random Walk ◽

Lagrange Multiplier ◽

Unit Root ◽

Stock Prices ◽

Structural Breaks ◽

Structural Break ◽

Unit Root Test ◽

Unit Root Tests ◽

Asian Countries ◽

Random Walk Hypothesis

This paper applies univariate and panel Lagrange Multiplier (LM) unit root tests with one and two structural breaks to examine the random walk hypothesis for stock prices in eight Asian countries. The results from the univariate LM unit root tests and panel LM unit root test with one structural break suggest that stock prices in each country is characterized by a random walk, but the findings from the panel LM unit root test with two structural breaks suggest that stock prices in the eight countries are mean reverting.

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