Statistics and Its Interface

Volume 4 (2011)

Number 2

Threshold models in time series analysis — 30 years on

Pages: 107 – 118



Howell Tong (London School of Economics and Political Science, London, United Kingdom)


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.


bi-modality, canadian lynx, chaos, conditional least squares, drift criterion, heteroscedasticity, ecology, ergodicity, indicator time series, invertibility, limit cycles, Markov chain, Markov switching, nonlinear oscillations, piecewise linearity, river-flow, Seiche record, skeleton, stability, test for linearity, threshold models, threshold principle, volatility, Yule’s pea-shooter

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