Working Papers 2002 – Abstracts
Influence Diagnostics in GARCH Processes
Xibin Zhang and Maxwell L. King
Influence diagnostics have become an important tool for statistical
analysis since the seminal work by Cook (1986). In this paper we present
a curvature-based diagnostic to access local influence of minor perturbations
on the modified likelihood displacement in a regression model. Using the
proposed diagnostic, we study the local influence in the GARCH model under
two perturbation schemes which involve, respectively, model perturbation
and data perturbation. We find that the curvature-based diagnostic often
provides more information on the local influence being examined than the
slope-based diagnostic, especially when the GARCH model is under investigation.
An empirical study involving GARCH modeling of the percentage daily returns
of the NYSE composite index illustrates the effectiveness of the proposed
diagnostic and shows that the curvature-based diagnostic may provide information
that cannot be uncovered by the slope-based diagnostic. We find that the
effect or influence of each observation is not invariant across different
perturbation schemes, thus it is advisable to study the local influence
under different perturbation schemes through curvature-based diagnostics.
Keywords: Normal curvature, modified likelihood displacement,
GARCH models.
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