Stationary bootstrap for kernel density estimators under ψ-weak dependence

Eunju Hwang, Dong Wan Shin

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Stationary bootstrap technique is applied for kernel-type estimators of densities and their derivatives of stationary ψ-weakly dependent processes. The ψ-weak dependence, introduced by Doukhan & Louhichi [Doukhan, P.; Louhichi, S.; 1999. A new weak dependence condition and applications to moment inequalities. Stochastic Processes and their Applications 84, 313342], unifies weak dependence conditions such as mixing, association, Gaussian sequences and Bernoulli shifts. The class of ψ-weakly dependent processes includes all weakly dependent processes of interest in statistics, containing such important processes as GARCH processes, threshold autoregressive processes, and bilinear processes. We obtain asymptotic validity for the stationary bootstrap in the density and derivatives estimation. A Monte-Carlo experiment compares the proposed method with other methods. Log returns of daily Dow Jones index are analyzed by the proposed method.

Original languageEnglish
Pages (from-to)1581-1593
Number of pages13
JournalComputational Statistics and Data Analysis
Issue number6
StatePublished - Jun 2012


  • Density
  • Derivative
  • Kernel estimator
  • Stationary bootstrap
  • Weak dependence


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