Recursive generalized gamma kernel density estimation for nonnegative dependent data

Abstract

In this article, we consider the recursive generalized gamma (GG) kernel density estimator (KDE) for nonnegative dependent data from stationary α-mixing process. Asymptotic bias, variance and mean integrated squared error are provided. Simulation experiments from an autoregressive conditional duration model and a stochastic volatility model are conducted to compare the recursive GG KDE with non-recursive GG KDE. Two applications are provided for nonnegative time series data.

Keywords:

• Autoregressive conditional duration model
• Generalized gamma kernel
• Mixing process
• Recursive estimator
• Stochastic volatility model

Acknowledgments

This research has been supported by the Unit of Research LAMOS of University of Bejaia. We sincerely thank the editor, an associate editor, and anonymous referees for their valuable comments to improve the article. We are also grateful to Lydia Bouchal and Zahra Bouzeria for their valuable help in the improvement of the English writing quality of this article.

Disclosure statement

No potential conflict of interest was reported by the authors).