{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T18:57:40Z","timestamp":1779130660261,"version":"3.51.4"},"reference-count":49,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,12,22]],"date-time":"2021-12-22T00:00:00Z","timestamp":1640131200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002241","name":"Japan Science and Technology Agency","doi-asserted-by":"publisher","award":["JPMJCE1304"],"award-info":[{"award-number":["JPMJCE1304"]}],"id":[{"id":"10.13039\/501100002241","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Kanagawa Prefecture's &quot;Project to expand the use of metabolic syndrome risk index in municipalities&quot;","award":["N\/A"],"award-info":[{"award-number":["N\/A"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Physiological time series are affected by many factors, making them highly nonlinear and nonstationary. As a consequence, heart rate time series are often considered difficult to predict and handle. However, heart rate behavior can indicate underlying cardiovascular and respiratory diseases as well as mood disorders. Given the importance of accurate modeling and reliable predictions of heart rate fluctuations for the prevention and control of certain diseases, it is paramount to identify models with the best performance in such tasks. The objectives of this study were to compare the results of three different forecasting models (Autoregressive Model, Long Short-Term Memory Network, and Convolutional Long Short-Term Memory Network) trained and tested on heart rate beats per minute data obtained from twelve heterogeneous participants and to identify the architecture with the best performance in terms of modeling and forecasting heart rate behavior. Heart rate beats per minute data were collected using a wearable device over a period of 10 days from twelve different participants who were heterogeneous in age, sex, medical history, and lifestyle behaviors. The goodness of the results produced by the models was measured using both the mean absolute error and the root mean square error as error metrics. Despite the three models showing similar performance, the Autoregressive Model gave the best results in all settings examined. For example, considering one of the participants, the Autoregressive Model gave a mean absolute error of 2.069 (compared to 2.173 of the Long Short-Term Memory Network and 2.138 of the Convolutional Long Short-Term Memory Network), achieving an improvement of 5.027% and 3.335%, respectively. Similar results can be observed for the other participants. The findings of the study suggest that regardless of an individual\u2019s age, sex, and lifestyle behaviors, their heart rate largely depends on the pattern observed in the previous few minutes, suggesting that heart rate can be reasonably regarded as an autoregressive process. The findings also suggest that minute-by-minute heart rate prediction can be accurately performed using a linear model, at least in individuals without pathologies that cause heartbeat irregularities. The findings also suggest many possible applications for the Autoregressive Model, in principle in any context where minute-by-minute heart rate prediction is required (arrhythmia detection and analysis of the response to training, among others).<\/jats:p>","DOI":"10.3390\/s22010034","type":"journal-article","created":{"date-parts":[[2021,12,23]],"date-time":"2021-12-23T02:02:57Z","timestamp":1640224977000},"page":"34","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["Heart Rate Modeling and Prediction Using Autoregressive Models and Deep Learning"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5001-349X","authenticated-orcid":false,"given":"Alessio","family":"Staffini","sequence":"first","affiliation":[{"name":"Precision Health, Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan"},{"name":"Department of Economics and Finance, Catholic University of Milan, 20123 Milan, Italy"},{"name":"Business Promotion Division, ALBERT Inc., Tokyo 169-0074, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1283-358X","authenticated-orcid":false,"given":"Thomas","family":"Svensson","sequence":"additional","affiliation":[{"name":"Precision Health, Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan"},{"name":"School of Health Innovation, Kanagawa University of Human Services Graduate School, Yokosuka 210-0821, Japan"},{"name":"Department of Clinical Sciences, Lund University, Sk\u00e5ne University Hospital, 221 84 Malmo, Sweden"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4691-6394","authenticated-orcid":false,"given":"Ung-il","family":"Chung","sequence":"additional","affiliation":[{"name":"Precision Health, Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan"},{"name":"School of Health Innovation, Kanagawa University of Human Services Graduate School, Yokosuka 210-0821, Japan"},{"name":"Clinical Biotechnology, Center for Disease Biology and Integrative Medicine, Graduate School of Medicine, The University of Tokyo, Tokyo 113-0033, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2464-1932","authenticated-orcid":false,"given":"Akiko Kishi","family":"Svensson","sequence":"additional","affiliation":[{"name":"Precision Health, Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan"},{"name":"Department of Clinical Sciences, Lund University, Sk\u00e5ne University Hospital, 221 84 Malmo, Sweden"},{"name":"Department of Diabetes and Metabolic Diseases, The University of Tokyo, Tokyo 113-8655, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,22]]},"reference":[{"key":"ref_1","first-page":"6","article-title":"Heart rate as a risk factor for cardiovascular diseases","volume":"52","author":"Joly","year":"2010","journal-title":"Prog. 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