Testing for time dependence in parameters

This paper proposes a new test based on a Fourier series expansion to approximate the unknown functional form of a nonlinear time-series model. The test speci...cally allows for structural breaks, seasonal parameters and time-varying parameters. The test is shown to have very good size and power properties. However, it is not especially good in detecting nonlinearity in variables. As such, the test can help determine whether an observed rejection of the joint null hypothesis of linearity and time invariant parameters is due to time-varying coe¢cients or a nonlinearity in variables.