Authors

• Christophe Chesneau
• Hassan Doosti

Abstract

We consider n observations from the GARCH-type model:
S = σ2Z, where σ2 and Z are independent random variables. We develop
a new wavelet linear estimator of the unknown density of σ2 under
four different dependence structures: the strong mixing case, the β-
mixing case, the pairwise positive quadrant case and the ρ-mixing case.
Its asymptotic mean integrated squared error properties are explored.
In each case, we prove that it attains a fast rate of convergence.

Keywords

• Dependent sequence
• GARCH models
• linear estimator
• rate of convergence
• wavelets