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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, the review re-visits the motivation of the model. Next, it describes the various expressions of the model, highlighting the underlying principle and the main probabilistic and statistical properties. Finally, after listing some of the recent offsprings of the threshold model, the review finishes with some on-going research in the context of threshold volatility.

Rejoinder from Howell Tong to the discussions on “Threshold models in time series analysis — 30 years on”