Threshold variable selection using nonparametric methods

Abstract

Selecting the threshold variable is a key step in building a generalized threshold autoregressive (TAR) model. This paper proposes a semi-parametric method for this purpose that is based on a single-index functional coefficient model. The asymptotic distribution of the estimator is obtained. A simple algorithm is given and its convergence is proved. Some simulations are reported. Two data sets are analyzed, one of which gives strong statistical support for ratio-dependent predation in Ecology.