Testing nonlinearity: Decision rules for selecting between logistic and exponential STAR models

A new LM specification procedure to choose between Logistic and Exponential Smooth Transition Autoregressive (STAR) models is introduced. The new decision rule has better properties than those previously available in the literature when the model is ESTAR and similar properties when the model is LSTAR. A simple natural extension of the usual LM-test for linearity is introduced and evaluated in terms of power. Monte-Carlo simulations and empirical evidence are provided in support of our claims.