Nonlinear Spectral Analysis: A Local Gaussian Approach

• 成果类型: Article
• 署名作者: Jordanger, Lars Arne; Tjostheim, Dag
• 署名单位: Western Norway University of Applied Sciences; University of Bergen
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1840991
• 发表日期: 2022
• 页码: 1010-1027
• 关键词: time-series; Periodogram; INDEPENDENCE; quantilogram; tests

摘要

The spectral distribution f(omega) of a stationary time series {Y-t}(t is an element of Z) can be used to investigate whether or not periodic structures are present in {Y-t}(t is an element of Z), but f(omega) has some limitations due to its dependence on the autocovariances gamma(h). For example, f(omega) can not distinguish white iid noise from GARCH-type models (whose terms are dependent, but uncorrelated), which implies that f(omega) can be an inadequate tool when {Y-t}(t is an element of Z) contains asymmetries and nonlinear dependencies. Asymmetries between the upper and lower tails of a time series can be investigated by means of the local Gaussian autocorrelations, and these local measures of dependence can be used to construct the local Gaussian spectral density presented in this paper. A key feature of the new local spectral density is that it coincides with f(omega) for Gaussian time series, which implies that it can be used to detect non-Gaussian traits in the time series under investigation. In particular, if f(omega) is flat, then peaks and troughs of the new local spectral density can indicate nonlinear traits, which potentially might discover local periodicphenomena that remain undetected in an ordinary spectral analysis.