Smooth transition modelling: Empirical investigation of logistic and exponential transition functions

Abstract

This paper considers two families of non-linear auto-regressive model, namely the Logistic Smooth Transition Autoregressive Model (LSTAR) and the Exponential Smooth Transition Autoregressive Model (ESTAR). Non-linear models have gained much attention in recent times as alternative to linear modelling of economic variables. The methods adopted include specification, through simple statistical tests like testing linearity against smooth transition auto-regression, determination of the delay parameter d and identification of the optimum non-linear alternative between LSTAR and ESTAR Models. We propose a transition function from a linear combination of LSTAR and ESTAR models and show how to select the better one between the two of them for a data set. The technique is illustrated with examples using simulated and real data.