Generalized autoregressive moving average models with GARCH errors

Tingguo Zheng, Han Xiao, Rong Chen

Research output: Contribution to journalArticlepeer-review

Abstract

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)
JournalJournal of Time Series Analysis
DOIs
StateAccepted/In press - 2021

All Science Journal Classification (ASJC) codes

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

Keywords

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

Fingerprint

Dive into the research topics of 'Generalized autoregressive moving average models with GARCH errors'. Together they form a unique fingerprint.

Cite this