5. Conclusion
This paper proposes a simple panel stationarity test with gradual/ smooth structural shifts, cross-section dependency, and cross-sectional heterogeneity. To account for structural shifts, we employ a Fourier approximation which does not require a priori knowledge on date, number, and form of breaks. The asymptotic distribution of the individual statistics under the null hypothesis only depends on the Fourier frequency and the panel statistic has a standard normal distribution after the standardization with the asymptotic moments. We investigate the small sample properties by Monte Carlo simulations for the different data generating processes. The findings for the size and power properties can be summarized as: (i) if the error terms are i.i.d. and the number of Fourier frequency is correctly specified then the Fourier panel statistic shows good size and power even when N is larger than T irrespective of the number of Fourier terms, (ii) if the error terms are i.i.d. but the number of Fourier frequency is wrongly specified in testing procedure, even though there is a size distortion and power reduction in the panel data sets where T is equal to or smaller than 50, fortunately the size distortions disappear as T increase and the power increases with larger T or N or both, (iii) if the error terms are serially correlated, the Fourier panel stationarity test has reasonable size and keeps its good power properties.
