Threshold models in time series analysis — 30 years on

Abstract

This paper is a selective review of the development of the threshold model in time series analysis over the past 30 years or so. First, it re-visits the motivation of the model. Next, it describes the various expressions of the model, highlighting the principle underlying them and the main probabilistic and statistical properties. Finally, after listing some of the recent offsprings of the threshold model, it finishes with some on-going research in the context of threshold volatility.