回火函数时间序列

IF 1.2 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Farzad Sabzikar, Piotr Kokoszka
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引用次数: 0

摘要

我们提出了一类广泛的曲线(函数)时间序列模型,可用于量化近长期依赖性或近单位根行为。我们建立了这些模型的基本性质以及样本均值函数和样本协方差算子的一致性率。后者的作用类似于多变量时间序列的样本交叉协方差,但在函数设置中要重要得多,因为它的本征函数用于主成分分析,这是函数数据分析的主要工具。它用于特征提取的降维。我们还根据我们的模型建立了函数的中心极限定理。中心极限定理(CLT)中的一致性率和归一化都是非标准的。它们反映了局部单位根行为和中等滞后的长记忆结构。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Tempered functional time series

We propose a broad class of models for time series of curves (functions) that can be used to quantify near long-range dependence or near unit root behavior. We establish fundamental properties of these models and rates of consistency for the sample mean function and the sample covariance operator. The latter plays a role analogous to sample cross-covariances for multivariate time series, but is far more important in the functional setting because its eigenfunctions are used in principal component analysis, which is a major tool in functional data analysis. It is used for dimension reduction of feature extraction. We also establish a central limit theorem for functions following our model. Both the consistency rates and the normalizations in the Central Limit Theorem (CLT) are nonstandard. They reflect the local unit root behavior and the long memory structure at moderate lags.

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来源期刊
Journal of Time Series Analysis
Journal of Time Series Analysis 数学-数学跨学科应用
CiteScore
2.00
自引率
0.00%
发文量
39
审稿时长
6-12 weeks
期刊介绍: During the last 30 years Time Series Analysis has become one of the most important and widely used branches of Mathematical Statistics. Its fields of application range from neurophysiology to astrophysics and it covers such well-known areas as economic forecasting, study of biological data, control systems, signal processing and communications and vibrations engineering. The Journal of Time Series Analysis started in 1980, has since become the leading journal in its field, publishing papers on both fundamental theory and applications, as well as review papers dealing with recent advances in major areas of the subject and short communications on theoretical developments. The editorial board consists of many of the world''s leading experts in Time Series Analysis.
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