Critical values for linearity tests in time-varying smooth transition autoregressive models when data are highly persistent

In this paper, we derive asymptotic distributions for linearity tests in time-varying smooth transition autoregressive models in the presence of a unit root. The limiting distributions are non-standard because of the unit root assumption, and it is shown that the linearity hypothesis is rejected far too often (up to 30.9% of the times at a 5% significance level) when using critical values from a chi-square distribution. Copyright The Author(s). Journal compilation Royal Economic Society 2008