Hysteretic autoregressive time series models

Guodong LI, Bo GUAN, Wai Keung LI, Leung Ho Philip YU

Research output: Contribution to journalArticlespeer-review

32 Citations (Scopus)


This paper extends the classical two-regime threshold autoregressive model by introducing hysteresis to its regime-switching structure, which leads to a new model: the hysteretic autoregressive model. The proposed model enjoys the piecewise linear structure of a threshold model but has a more flexible regime switching mechanism. A sufficient condition is given for geometric ergodicity. Conditional least squares estimation is discussed, and the asymptotic distributions of its estimators and information criteria for model selection are derived. Simulation results and an example support the model. Copyright © 2015 Biometrika Trust.
Original languageEnglish
Pages (from-to)717-723
Issue number3
Early online dateJun 2015
Publication statusPublished - Sept 2015


Li, G., Guan, B., Li, W. K., & Yu, P. L. H. (2015). Hysteretic autoregressive time series models. Biometrika, 102(3), 717-723. doi: 10.1093/biomet/asv017


  • Autoregression
  • Conditional least squares
  • Geometric ergodicity
  • Hysteresis
  • Threshold model


Dive into the research topics of 'Hysteretic autoregressive time series models'. Together they form a unique fingerprint.