Testing for periodicity at an unknown frequency under cyclic long memory, with applications to respiratory muscle training

IF 1.4 4区 数学 Q2 STATISTICS & PROBABILITY
Jan Beran, Jeremy Näscher, Fabian Pietsch, Stephan Walterspacher
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引用次数: 0

Abstract

A frequent problem in applied time series analysis is the identification of dominating periodic components. A particularly difficult task is to distinguish deterministic periodic signals from periodic long memory. In this paper, a family of test statistics based on Whittle’s Gaussian log-likelihood approximation is proposed. Asymptotic critical regions and bounds for the asymptotic power are derived. In cases where a deterministic periodic signal and periodic long memory share the same frequency, consistency and rates of type II error probabilities depend on the long-memory parameter. Simulations and an application to respiratory muscle training data illustrate the results.

Abstract Image

在循环长记忆下测试未知频率的周期性,并应用于呼吸肌训练
在应用时间序列分析中,一个经常遇到的问题是如何识别占主导地位的周期成分。一个特别困难的任务是将确定性周期信号与周期性长记忆区分开来。本文提出了基于惠特尔高斯对数似然近似的检验统计量系列。推导出了渐近临界区和渐近功率的边界。在确定性周期信号和周期性长记忆共享相同频率的情况下,一致性和 II 型错误概率率取决于长记忆参数。模拟和呼吸肌训练数据的应用说明了这些结果。
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来源期刊
Asta-Advances in Statistical Analysis
Asta-Advances in Statistical Analysis 数学-统计学与概率论
CiteScore
2.20
自引率
14.30%
发文量
39
审稿时长
>12 weeks
期刊介绍: AStA - Advances in Statistical Analysis, a journal of the German Statistical Society, is published quarterly and presents original contributions on statistical methods and applications and review articles.
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