Estimation of GARCH Models from the Autocorrelations of the Squares of a Process

Abstract

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.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 56 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.