×

zbMATH — the first resource for mathematics

Inference in ARCH and GARCH models with heavy-tailed errors. (English) Zbl 1136.62368
Summary: ARCH and GARCH models directly address the dependency of conditional second moments, and have proved particularly valuable in modelling processes where a relatively large degree of fluctuation is present. These include financial time series, which can be particularly heavy tailed. However, little is known about properties of ARCH or GARCH models in the heavy-tailed setting, and no methods are available for approximating the distributions of parameter estimators there. In this paper we show that, for heavy-tailed errors, the asymptotic distributions of quasi-maximum likelihood parameter estimators in ARCH and GARCH models are nonnormal, and are particularly difficult to estimate directly using standard parametric methods. Standard bootstrap methods also fail to produce consistent estimators. To overcome these problems we develop percentile-t, subsample bootstrap approximations to estimator distributions. Studentizing is employed to approximate scale, and the subsample bootstrap is used to estimate shape. The good performance of this approach is demonstrated both theoretically and numerically.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P05 Applications of statistics to actuarial sciences and financial mathematics
62E20 Asymptotic distribution theory in statistics
62G32 Statistics of extreme values; tail inference
PDF BibTeX XML Cite
Full Text: DOI