Some pitfalls in smooth transition models estimation : a Monte Carlo study

Abstract

Nonlinear regime switching models are becoming increasingly popular in recent applied literature, as they allow capturing state-dependent behaviors which would be otherwise impossible to model. However, despite their popularity, the specification and estimation of these type of models is computationally complex and it is far from being a univocally solved issue.This paper aims at contributing to this debate. In particular, we use Monte Carlo experiments to assess whether employing the standard trick of 'concentrating the sum of squares' by Leybourne et al. (Journal of Time Series Analysis, 19(1) : 83-97, 1998) in the application of nonlinear least squares to smooth transition models yields estimates with desirable asymptotic properties. Our results confirm that this procedure needs to be used with caution as it may yield biased and inconsistent estimates, especially when faced with small samples.