Estimating the Spectral Density at Frequencies Near Zero

• 成果类型: Article
• 署名作者: McElroy, Tucker; Politis, Dimitris N.
• 署名单位: University of California System; University of California San Diego; University of California System; University of California San Diego
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2133719
• 发表日期: 2024
• 页码: 612-624
• 关键词: time-series; heteroskedasticity; inference; kernel

摘要

Estimating the spectral density function f(w) for some w is an element of[-pi,pi] has been traditionally performed by kernel smoothing the periodogram and related techniques. Kernel smoothing is tantamount to local averaging, that is, approximating f(w) by a constant over a window of small width. Although f(w) is uniformly continuous and periodic with period 2 pi, in this article we recognize the fact that w = 0 effectively acts as a boundary point in the underlying kernel smoothing problem, and the same is true for w=+/-pi. It is well-known that local averaging may be suboptimal in kernel regression at (or near) a boundary point. As an alternative, we propose a local polynomial regression of the periodogram or log-periodogram when w is at (or near) the points 0 or +/-pi. The case w = 0 is of particular importance since f(0) is the large-sample variance of the sample mean; hence, estimating f(0) is crucial in order to conduct any sort of inference on the mean. for this article are available online.