Testing nonlinearity: decision rules for selecting between logistic and exponential star models

Abstract

This paper analyzes Lagrange Multiplier (LM) type tests of STR and STAR type nonlinearity, as well as their use to specify the model to be estimated. Building from work by Luukkonen, Saikkonen and Tedisvirta (Biometrika, 1988) and Terasvirta (J.A.S.A., 1994), we propose the use of second order Tay)or series expansions for exponential models. This results in specifying a nonlinearity test with up to fourth order terms that serves two purposes. The first is a better approximation of the two inflexion points of the exponential transition function and asymmetric models in general. The second is to provide the basis of a more robust decision rule to decide between an ESTAR or a LSTAR model with which to start the estimation process. The test also provides information on non zero thresholds. Monte Carlo simulations show how the proposed test performs comparably well in small samples and has better power properties in larger samples. The decision rules are noticeably more robust in all cases.