Long-Range Dependent Curve Time Series

• 成果类型: Article
• 署名作者: Li, Degui; Robinson, Peter M.; Shang, Han Lin
• 署名单位: University of York - UK; University of London; London School Economics & Political Science; Australian National University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2019.1604362
• 发表日期: 2020
• 页码: 957-971
• 关键词: functional data; finite dimensionality; principal-components; mortality; models; inference; variance; memory; number; rates

摘要

We introduce methods and theory for functional or curve time series with long-range dependence. The temporal sum of the curve process is shown to be asymptotically normally distributed, the conditions for this covering a functional version of fractionally integrated autoregressive moving averages. We also construct an estimate of the long-run covariance function, which we use, via functional principal component analysis, in estimating the orthonormal functions spanning the dominant subspace of the curves. In a semiparametric context, we propose an estimate of the memory parameter and establish its consistency. A Monte Carlo study of finite-sample performance is included, along with two empirical applications. The first of these finds a degree of stability and persistence in intraday stock returns. The second finds similarity in the extent of long memory in incremental age-specific fertility rates across some developed nations. for this article are available online.