Abstract

The threshold autoregressive (TAR) model and the smooth threshold autoregressive (STAR) model have been among the most popular parametric nonlinear time series models for the past three decades or so. However, as yet there is no formal statistical test in the literature for one against the other. The two models are fundamentally different in their autoregressive functions, the TAR model being generally discontinuous while the STAR model being smooth (except in the limit of infinitely fast switching). The talk will adopt the approach initiated by Cox (1961, 1962) and develop tests of TAR models vs STAR models, treating the models as separate families of hypotheses, thus filling a serious gap in the literature.