# Stationary bootstrap for kernel density estimators under ψ-weak dependence

## Author

Listed:
• Hwang, Eunju
• Shin, Dong Wan

## Abstract

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, 313–342], 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.

## Suggested Citation

• Hwang, Eunju & Shin, Dong Wan, 2012. "Stationary bootstrap for kernel density estimators under ψ-weak dependence," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1581-1593.
• Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1581-1593 DOI: 10.1016/j.csda.2011.10.001
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## References listed on IDEAS

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## Citations

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Cited by:

1. Hwang, Eunju & Shin, Dong Wan, 2015. "Stationary bootstrapping for semiparametric panel unit root tests," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 14-25.
2. Barbeito, Inés & Cao, Ricardo, 2016. "Smoothed stationary bootstrap bandwidth selection for density estimation with dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 130-147.
3. Hwang, Eunju & Shin, Dong Wan, 2013. "Stationary bootstrapping realized volatility," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2045-2051.
4. Eunju Hwang & Dong Wan Shin, 2016. "Kernel estimators of mode under $$\psi$$ ψ -weak dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 301-327, April.

### Keywords

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

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