Bootstrap Inference for Garch Models by the Least Absolute Deviation Estimation

Abstract

This article considers the generalized bootstrap method to approximate the least absolute deviation estimation and portmanteau test for generalized autoregressive conditional heteroskedastic models. The generalized bootstrap approach is easy‐to‐implement, and includes many bootstrap methods as special cases, such as Efron's bootstrap, Bayesian bootstrap, and random‐weighting bootstrap. The proposed bootstrap procedure is shown to be asymptotically valid for both estimation and test. The finite‐sample performance is assessed by simulation studies, and its usefulness is illustrated by a real application to the Hang Seng Index.