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.

Subject:
60: Probability theory and stochastic processes

Received: 2012/03/3 | Accepted: 2015/09/12

Received: 2012/03/3 | Accepted: 2015/09/12