Estimating and Testing Threshold Regression Models with Multiple Threshold Variables

Conventional threshold models contain only one threshold variable. This paper provides the theoretical foundation for threshold models with multiple threshold variables. The new model is very different from a model with a single threshold variable as several novel problems arisefrom having an additional threshold variable. First, the model is not analogous to a change-point model. Second, the asymptotic joint distribution of the threshold estimators is difficult to obtain. Third, the estimation time increases exponentially with the number of threshold variables. This paper derives the consistency and the asymptotic joint distribution of the threshold estimators. A fast estimation algorithm to estimate the threshold values is proposed. We also develop tests for the number of threshold variables. The theoretical results are supported by simulation experiments. Our model is applied to the study of currency crises.