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.
|Number of pages||21|
|Journal||Journal of the Iranian Statistical Society|
|Publication status||Published - 2012|
- Dependent sequence
- GARCH models
- Linear estimator
- Rate of convergence