A General Test For Time-dependence in Parameters

We propose a new test based on a Fourier series to approximate the unknown form of a nonlinear time-series model. The test has good size and power properties to detect structural breaks, seasonal parameters and random coefficients. Moreover, it has reasonable power to discriminate between nonlinearity in variables and nonlinearity in parameters. We use the test to show that U.S. inflation is appropriately estimated with a time-varying intercept that jumps in the late 1960’s, peaks in the early 1980’s and then begins to decline. German income and consumption data is used to illustrate the ability of the test to suggest the form of the nonlinearity.