Moving average threshold heterogeneous autoregressive (MAT-HAR) models

Kaiji Motegi, Xiaojing Cai, Shigeyuki Hamori, Haifeng Xu

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We propose moving average threshold heterogeneous autoregressive (MAT-HAR) models as a novel combination of heterogeneous autoregression (HAR) and threshold autoregression (TAR). The MAT-HAR has multiple groups of lags of a target series, and a threshold term can appear in each group. The threshold is a moving average of lagged target series, which guarantees time-varying thresholds and simple estimation via least squares. We show via Monte Carlo simulations that the MAT-HAR has sharp in-sample and out-of-sample performance. An empirical application on the industrial production of Japan suggests that significant threshold effects exist, and the MAT-HAR has a higher forecast accuracy than the HAR.

Original languageEnglish
Pages (from-to)1035-1042
Number of pages8
JournalJournal of Forecasting
Issue number7
Publication statusPublished - Nov 1 2020


  • heterogeneous autoregression (HAR)
  • model selection
  • out-of-sample forecast
  • threshold autoregression (TAR)
  • time series analysis

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computer Science Applications
  • Strategy and Management
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research


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