Estimation and model selection based inference in single and multiple threshold models

Abstract

This paper evaluates the properties of a joint and sequential estimation procedure for estimating the parameters of single and multiple threshold models. We initially proceed under the assumption that the number of regimes is known a priori but subsequently relax this assumption via the introduction of a model selection based procedure that allows the estimation of both the unknown parameters and their number to be performed jointly. Theoretical properties of the resulting estimators are derived and their finite sample properties investigated.