On mixture double autoregressive time series models

Guodong LI, Qianqian ZHU, Zhao LIU, Wai Keung LI

Research output: Contribution to journalArticle

2 Citations (Scopus)


This article proposes a mixture double autoregressive model by introducing the flexibility of mixture models to the double autoregressive model, a novel conditional heteroscedastic model recently proposed in the literature. To make it more flexible, the mixing proportions are further assumed to be time varying, and probabilistic properties including strict stationarity and higher order moments are derived. Inference tools including the maximum likelihood estimation, an expectation–maximization (EM) algorithm for searching the estimator and an information criterion for model selection are carefully studied for the logistic mixture double autoregressive model, which has two components and is encountered more frequently in practice. Monte Carlo experiments give further support to the new models, and the analysis of an empirical example is also reported. Copyright © 2017 American Statistical Association.
Original languageEnglish
Pages (from-to)306-317
JournalJournal of Business and Economic Statistics
Issue number2
Early online dateMar 2017
Publication statusPublished - 2017


Autoregressive Time Series
Time Series Models
Autoregressive Model
time series
Heteroscedastic Model
Higher Order Moments
Conditional Model
Information Criterion
Monte Carlo Experiment
Expectation-maximization Algorithm
Mixture Model
Maximum Likelihood Estimation
Model Selection
Time series models


Li, G., Zhu, Q., Liu, Z., & Li, W. K. (2017). On mixture double autoregressive time series models. Journal of Business & Economic Statistics, 35(2), 306-317. doi: 10.1080/07350015.2015.1102735


  • Double autoregressive model
  • EM algorithm
  • Mixture model
  • Stationarity