Combining fourier unit root tests based on linear and nonlinear models

Most of the economic time series is not stationary. However, in the time series analysis, it is generally assumed that the series is stationary. In this case, the time series regression may reveal some problems and the estimates made with the non-stationary series can be misleading. For this reason, stationarity analysis is of great importance. The stationarity analysis can be investigated by using the time series graph of the series, its correlogram and autocorrelation functions. However, in the later of twentieth century, stationarity analysis using unit root tests has became systematic and a large-scale unit root literature was formed. In this study, a new approach was developed by combining fourier unit root tests using Fisher method. The major advantage of this test is the combination of the properties of the unit root tests. Another advantage of this test, the use of Fourier approach regards as unneeded the assumption that the break form, break dates or number of breaks are known a priori. Simulation results show that the proposed combination test performs well. In this study, long-run validity of purchasing power parity is investigated by using proposed combining test for 18 OECD countries. The data used are the quarterly observations from 1995Q1 to 2018Q3. The results show that the purchasing power parity is valid for 8 countries (Australia, Iceland, Japan, Korea, New Zealand, Poland, Switzerland and Turkey). Key Words: Unit Root, Time Series, Fourier, Meta Analysis, Purchasing Power Parity