Functional-coefficient models under unit root behaviour

We analyze the statistical properties of non-parametrically estimated functions in a functional-coefficient model if the data have a unit root. We show that the estimated function converges at a faster rate than under the stationary case. However, the estimator has a mixed normal distribution so that point-wise confidence intervals are calculated using the usual normal distribution theory rather than a Dickey-Fuller distribution. The results are used to show how one can discriminate between a unit root process and a non-linear functional-coefficient process. We illustrate the procedure using U.S. unemployment and interest rate data.