In this article we introduce a nonparametric estimator of the spectral density by smoothing the periodogram using beta kernel density. The estimator is proved to be bounded for short memory data and diverges at the origin for long memory data. The convergence in probability of the relative error and Monte Carlo simulations show that the proposed estimator automatically adapts to the long‐ and the short‐range dependency of the process. A cross‐validation procedure is studied in order to select the nuisance parameter of the estimator. Illustrations on historical as well as most recent returns and absolute returns of the S&P500 index show the performance of the beta kernel estimator. The Canadian Journal of Statistics 48: 582–595; 2020 © 2020 Statistical Society of Canada

中文翻译：

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长和短存储时间序列的非参数beta内核估计器

在本文中，我们通过使用β核密度对周期图进行平滑来介绍频谱密度的非参数估计器。证明了估计器对于短存储数据是有界的，并且在长存储数据的原点上是发散的。相对误差和蒙特卡洛模拟的概率收敛表明，所提出的估计器可以自动适应过程的长距离和短距离依赖性。为了选择估计器的讨厌参数，研究了交叉验证程序。S＆P500指数的历史以及最近的收益和绝对收益的图示说明了beta内核估计器的性能。《加拿大统计杂志》 48：582–595；加拿大 2020©2020加拿大统计学会