Testing for Integer Integration in Functional Time Series

• 成果类型: Article; Early Access
• 署名作者: Seo, Won-Ki; Shang, Han Lin
• 署名单位: University of Sydney; Macquarie University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2649652
• 发表日期: 2026-05-28
• 关键词: Age-specific mortality rates; Functional Time Series; fractional integration; Maturity-specific yield curves; sequential testing; cointegrated linear-processes; mortality; lifetables; prediction; rates; NULL

摘要

We develop a statistical testing procedure to examine whether the curve-valued time series of interest is integrated of order d for a nonnegative integer d. The proposed procedure can distinguish between integer-integrated time series and fractionally-integrated ones, and it has broad applicability in practice. Monte Carlo simulation experiments show that the proposed testing procedure performs reasonably well. We apply our methodology to Canadian yield curve data and French sub-national age-specific mortality data. We find evidence that these time series are mostly integrated of order one, while some have fractional orders exceeding or falling below one. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.