Abstract
This paper focuses on time series with deterministic shifts, and specifically on common features shared by the equations in a VAR system where the shift is assumed to be smooth. We apply the three main test principles in econometrics and an F-approximation for likelihood-ratio based tests for detecting common nonlinear smooth changes in the time-varying intercept of a pair of economic time series co-shifting, and common nonlinear smooth seasonal pattern, co-seasonality. Monte Carlo simulations are used to evaluate the sample performance of the test statistics. Our tests are applied to two time series, Japanese income and Japanese consumption.