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 à 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 ÿnite sample properties investigated.

In this paper we introduce threshold type nonlinearities within a single equation cointegrating regression model and propose a testing procedure for testing the null hypothesis of linear cointegration versus cointegration with threshold effects. Our framework allows the modelling of long run equilibrium relationships that may switch according to the magnitude of a threshold variable assumed to be stationary and ergodic and thus constitutes an attempt to deal econometrically with the potential presence of multiple equilibria. The framework is flexible enough to accomodate regressor endogeneity and serial correlation.

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 à 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 ÿnite sample properties investigated.

Abstract. We study the impact of the system dimension on commonly used model selection criteria (AIC, BIC, HQ) and LR based general to specific testing strategies for lag length estimation in VARs. We show that AIC's well known overparameterization feature becomes quickly irrelevant as we move away from univariate models, with the criterion leading to consistent estimates under sufficiently large system dimensions. Unless the sample size is unrealistically small, all model selection criteria will tend to point towards low orders as the system dimension increases, with the AIC remaining by far the best performing criterion. This latter point is also illustrated via the use of an analytical power function for model selection criteria. The comparison between the model selection and general to specific testing strategy is discussed within the context of a new penalty term leading to the same choice of lag length under both approaches.