{"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/estimating-activity-cycles-with-probabilistic","title":"Estimating activity cycles with probabilistic methods I. Bayesian Generalised Lomb-Scargle Periodogram with Trend","arxiv_id":"1712.08235","date":"2017-12-21","proceeding":null,"authors":["N. Olspert","J. Pelt","M. J. Käpylä","J. Lehtinen"],"abstract":"Period estimation is one of the central topics in astronomical time series\nanalysis, where data is often unevenly sampled. Especially challenging are\nstudies of stellar magnetic cycles, as there the periods looked for are of the\norder of the same length than the datasets themselves. The datasets often\ncontain trends, the origin of which is either a real long-term cycle or an\ninstrumental effect, but these effects cannot be reliably separated, while they\ncan lead to erroneous period determinations if not properly handled. In this\nstudy we aim at developing a method that can handle the trends properly, and by\nperforming extensive set of testing, we show that this is the optimal procedure\nwhen contrasted with methods that do not include the trend directly to the\nmodel. The effect of the form of the noise (whether constant or\nheteroscedastic) on the results is also investigated. We introduce a Bayesian\nGeneralised Lomb-Scargle Periodogram with Trend (BGLST), which is a\nprobabilistic linear regression model using Gaussian priors for the\ncoefficients and uniform prior for the frequency parameter. We show, using\nsynthetic data, that when there is no prior information on whether and to what\nextent the true model of the data contains a linear trend, the introduced BGLST\nmethod is preferable to the methods which either detrend the data or leave the\ndata untrended before fitting the periodic model. Whether to use noise with\ndifferent than constant variance in the model depends on the density of the\ndata sampling as well as on the true noise type of the process.","url_abs":"http://arxiv.org/abs/1712.08235v2","url_pdf":"http://arxiv.org/pdf/1712.08235v2.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":"abstracts"},"code_links":[{"paper_slug":"estimating-activity-cycles-with-probabilistic","repo_url":"https://github.com/olspert/BGLST","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"period-estimation","task_name":"Period Estimation"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[{"method_slug":"linear-regression","method_name":"Linear Regression"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}