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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.

Research background: Studying the dynamic characteristics of unemployment rate is crucial for both economic theory and macroeconomic policies. Despite numerous research, the empirical evidence about stochastic behaviour of the unemployment rate remains disputable. It has been widely agreed that most economic variables, including unemployment rates, are characterized by both structural breaks and nonlinearities. However, a little work is done to examine both features simultaneously. Purpose of the article: In this paper, we analyse the stationarity properties of unemployment rates of Euro area member countries. Also, we aim to test stochastic convergence of unemployment rates among member countries. Our empirical procedures explicitly allow for simultaneous gradual breaks and nonlinearities in the series. Methods: This paper develops a new unit root test procedure for panel data, allowing for both gradual structural breaks and asymmetric adjustment towards equilibrium. We carry out Monte Carlo simulations to examine small sample performance of the proposed test procedure and compare it to the existing test procedures. We apply the newly proposed test to examine the stochastic properties of the unemployment rates of Euro-member countries as well as relative unemployment rates vis-?-vis the Eurozone unemployment rate. Findings & value added: We find that the newly developed test procedure outperforms existing tests in highly nonlinear settings. Also, these tests reject the null hypothesis of unit root in more cases when compared to the existing tests. We find stationarity in the series only after allowing for structural breaks in the data generating process. Allowing for nonlinear and asymmetric adjustment in addition to gradual breaks provides evidence of stationarity in more cases. Furthermore, our results suggest that relative unemployment rate series are stationary, providing evidence in favour of stochastic convergence in unemployment rates. Overall, our results imply a limited room for coordinated economic policy to fight unemployment in the Eurozone.

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