Wavelet linear density estimation for a GARCH model under various dependence structures

Christophe Chesneau*, Hassan Doosti

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalJournal of the Iranian Statistical Society
Volume11
Issue number1
Publication statusPublished - 2012
Externally publishedYes

Keywords

  • Dependent sequence
  • GARCH models
  • Linear estimator
  • Rate of convergence
  • Wavelets

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