A new approach for detecting gradual changes in non-stationary time series with seasonal effects

This paper proposes a new method of detecting the gradual changes of time series when the changes in time series are mixed with seasonality. The key of the proposed method is to express the desired time-varying feature while removing the unwanted time-varying feature of seasonal effects through two-stage procedures. Asymptotic properties of the proposed methods are studied, and simulation results are presented. In addition, models with multiple changes have been studied. Furthermore, to demonstrate the usefulness of the proposed method, real data analysis with the number of Korean traveling to Japan is presented.