Stationary bootstrap for kernel density estimators under ψ-weak dependence

Eunju Hwang, Dong Wan Shin

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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

Bibliographical note

Funding Information:
The authors are very grateful for the constructive and valuable comments of two anonymous referees. This work was supported by the Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2009-0093827 ).


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


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