Generalized autoregressive moving average models with GARCH errors

Tingguo Zheng, Han Xiao, Rong Chen

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


One of the important and widely used classes of models for non-Gaussian time series is the generalized autoregressive model average models (GARMA), which specifies an ARMA structure for the conditional mean process of the underlying time series. However, in many applications one often encounters conditional heteroskedasticity. In this article, we propose a new class of models, referred to as GARMA-GARCH models, that jointly specify both the conditional mean and conditional variance processes of a general non-Gaussian time series. Under the general modeling framework, we propose three specific models, as examples, for proportional time series, non-negative time series, and skewed and heavy-tailed financial time series. Maximum likelihood estimator (MLE) and quasi Gaussian MLE are used to estimate the parameters. Simulation studies and three applications are used to demonstrate the properties of the models and the estimation procedures.

Original languageEnglish (US)
Pages (from-to)125-146
Number of pages22
JournalJournal of Time Series Analysis
Issue number1
StatePublished - Jan 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


  • GARMA-GARCH model
  • Generalized ARMA model
  • non-negative time series
  • proportional time series
  • realized volatility
  • stock returns


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