{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/nonlinear-spectral-analysis-a-local-gaussian","title":"Nonlinear spectral analysis: A local Gaussian approach","arxiv_id":"1708.02166","date":"2017-08-07","proceeding":null,"authors":["Lars Arne Jordanger","Dag Tjøstheim"],"abstract":"The spectral distribution $f(\\omega)$ of a stationary time series $\\{Y_t\\}_{t\\in\\mathbb{Z}}$ can be used to investigate whether or not periodic structures are present in $\\{Y_t\\}_{t\\in\\mathbb{Z}}$, but $f(\\omega)$ has some limitations due to its dependence on the autocovariances $\\gamma(h)$. For example, $f(\\omega)$ can not distinguish white i.i.d. noise from GARCH-type models (whose terms are dependent, but uncorrelated), which implies that $f(\\omega)$ can be an inadequate tool when $\\{Y_t\\}_{t\\in\\mathbb{Z}}$ 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 introduced in Tj{\\o}stheim and Hufthammer (2013), 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 periodic phenomena that remain undetected in an ordinary spectral analysis.","url_abs":"https://arxiv.org/abs/1708.02166v3","url_pdf":"https://arxiv.org/pdf/1708.02166v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"nonlinear-spectral-analysis-a-local-gaussian","repo_url":"https://github.com/LAJordanger/localgaussSpec","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}