Estimation of GARCH models from the autocorrelations of the squares of a process

Richard T. Baillie, Huimin Chung

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


This paper shows how the parameters of a stable GARCH(1, 1) model can be estimated from the autocorrelations of the squared process. Specifically, the method applies a minimum distance estimator (MDE) to the sample autocorrelations of the squared realization. The asymptotic efficiency of the estimator is calculated from using the first g autocorrelations. The estimator can be surprisingly efficient for quite small numbers of autocorrelations and, in some cases, can be more efficient than the quasi maximum likelihood estimator (QMLE). Also, the estimated process can better fit the pattern of observed autocorrelations of squared returns than those from models estimated by maximum likelihood estimation (MLE). The estimator is applied to a series of hourly exchange rate returns, which are extremely non Gaussian.

Original languageEnglish
Pages (from-to)631-650
Number of pages20
JournalJournal of Time Series Analysis
Issue number6
StatePublished - 1 Jan 2001


  • Autocorrelations
  • Bartlett's formula
  • QMLE

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