Estimation and testing for unit root processes with GARCH (1, 1) errors: Theory and Monte Carlo evidence

Shiqing LING, Wai Keung LI, Michael MCALEER

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47 Citations (Scopus)

Abstract

Least squares (LS) and maximum likelihood (ML) estimation are considered for unit root processes with GARCH (1, 1) errors. The asymptotic distributions of LS and ML estimators are derived under the condition α + β < 1. The former has the usual unit root distribution and the latter is a functional of a bivariate Brownian motion, as in Ling and Li [Ling, S., Li, W. K. (1998). Limiting distributions of maximum likelihood estimators for unstable autoregressive moving‐average time series with GARCH errors. Ann. Statist.26:84–125]. Several unit root tests based on LS estimators, ML estimators, and mixing LS and ML estimators, are constructed. Simulation results show that tests based on mixing LS and ML estimators perform better than Dickey–Fuller tests which are based on LS estimators, and that tests based on the ML estimators perform better than the mixed estimators. Copyright © 2003 Taylor & Francis.
Original languageEnglish
Pages (from-to)179-202
JournalEconometric Reviews
Volume22
Issue number2
DOIs
Publication statusPublished - 2003

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Maximum likelihood estimator
Unit root
Generalized autoregressive conditional heteroscedasticity
Testing
Least squares
Least squares estimator
Dickey-Fuller test
Asymptotic distribution
Limiting distribution
Maximum likelihood estimation
Unit root tests
Estimator
Simulation
Brownian motion

Citation

Ling, S., Li, W. K., & McAleer, M. (2003). Estimation and testing for unit root processes with GARCH (1, 1) errors: Theory and Monte Carlo evidence. Econometric Reviews, 22(2), 179-202. doi: 10.1081/ETC-120020462

Keywords

  • Asymptotic distribution
  • Brownian motion
  • GARCH model
  • Least squares estimator
  • Maximum likelihood estimator
  • Unit root