{"ID":2846452,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.01151","arxiv_id":"2511.01151","title":"A structural equation formulation for general quasi-periodic Gaussian processes","abstract":"This paper introduces a structural equation formulation that gives rise to a new family of quasi-periodic Gaussian processes, useful to process a broad class of natural and physiological signals. The proposed formulation simplifies generation and forecasting, and provides hyperparameter estimates, which we exploit in a convergent and consistent iterative estimation algorithm. A bootstrap approach for standard error estimation and confidence intervals is also provided. We demonstrate the computational and scaling benefits of the proposed approach on a broad class of problems, including water level tidal analysis, CO$_{2}$ emission data, and sunspot numbers data. By leveraging the structural equations, our method reduces the cost of likelihood evaluations and predictions from $\\mathcal{O}(k^2 p^2)$ to $\\mathcal{O}(p^2)$, significantly improving scalability.","short_abstract":"This paper introduces a structural equation formulation that gives rise to a new family of quasi-periodic Gaussian processes, useful to process a broad class of natural and physiological signals. The proposed formulation simplifies generation and forecasting, and provides hyperparameter estimates, which we exploit in a...","url_abs":"https://arxiv.org/abs/2511.01151","url_pdf":"https://arxiv.org/pdf/2511.01151v1","authors":"[\"Unnati Nigam\",\"Radhendushka Srivastava\",\"Faezeh Marzbanrad\",\"Michael Burke\"]","published":"2025-11-03T02:02:30Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"math.ST\",\"stat.AP\"]","methods":"[]","has_code":false}