Smooth Transition Nonlinear Models

Abstract

The application of random walk models to some economic time series can be inappropriate, as when there are natural bounds or limits to the values that the series can take. For example, there are a number of studies that have tested for unit root nonstationarities in unemployment rates and (nominal) interest rate data; however, the former are bounded by zero and one, and negative nominal interest rates are not observed. In practice, the boundedness of these variables may be recognised by referring to ‘local’ nonstationarity in the observed series. A way of modelling this is to allow unit root behaviour, for example persistence and the absence of mean reversion, over a range of possible values, but reversion at other values.