{"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/model-agnostic-time-series-analysis-via","title":"Model Agnostic Time Series Analysis via Matrix Estimation","arxiv_id":"1802.09064","date":"2018-02-25","proceeding":null,"authors":["Anish Agarwal","Muhammad Jehangir Amjad","Devavrat Shah","Dennis Shen"],"abstract":"We propose an algorithm to impute and forecast a time series by transforming\nthe observed time series into a matrix, utilizing matrix estimation to recover\nmissing values and de-noise observed entries, and performing linear regression\nto make predictions. At the core of our analysis is a representation result,\nwhich states that for a large model class, the transformed time series matrix\nis (approximately) low-rank. In effect, this generalizes the widely used\nSingular Spectrum Analysis (SSA) in time series literature, and allows us to\nestablish a rigorous link between time series analysis and matrix estimation.\nThe key to establishing this link is constructing a Page matrix with\nnon-overlapping entries rather than a Hankel matrix as is commonly done in the\nliterature (e.g., SSA). This particular matrix structure allows us to provide\nfinite sample analysis for imputation and prediction, and prove the asymptotic\nconsistency of our method. Another salient feature of our algorithm is that it\nis model agnostic with respect to both the underlying time dynamics and the\nnoise distribution in the observations. The noise agnostic property of our\napproach allows us to recover the latent states when only given access to noisy\nand partial observations a la a Hidden Markov Model; e.g., recovering the\ntime-varying parameter of a Poisson process without knowing that the underlying\nprocess is Poisson. Furthermore, since our forecasting algorithm requires\nregression with noisy features, our approach suggests a matrix estimation based\nmethod - coupled with a novel, non-standard matrix estimation error metric - to\nsolve the error-in-variable regression problem, which could be of interest in\nits own right. Through synthetic and real-world datasets, we demonstrate that\nour algorithm outperforms standard software packages (including R libraries) in\nthe presence of missing data as well as high levels of noise.","url_abs":"http://arxiv.org/abs/1802.09064v6","url_pdf":"http://arxiv.org/pdf/1802.09064v6.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":"model-agnostic-time-series-analysis-via","repo_url":"https://github.com/jehangiramjad/tslib","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"imputation","task_name":"Imputation"},{"task_slug":"missing-values","task_name":"Missing Values"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1802.09064","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}