{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T07:17:04Z","timestamp":1762067824841,"version":"build-2065373602"},"reference-count":52,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T00:00:00Z","timestamp":1664409600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Humanity and Social Science Youth Foundation of Ministry of Education of China","award":["22YJC630109","YZ2019079","20KJB580012"],"award-info":[{"award-number":["22YJC630109","YZ2019079","20KJB580012"]}]},{"DOI":"10.13039\/100016798","name":"Yangzhou Natural Science Foundation","doi-asserted-by":"publisher","award":["22YJC630109","YZ2019079","20KJB580012"],"award-info":[{"award-number":["22YJC630109","YZ2019079","20KJB580012"]}],"id":[{"id":"10.13039\/100016798","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of the Jiangsu Higher Education Institutions of China","award":["22YJC630109","YZ2019079","20KJB580012"],"award-info":[{"award-number":["22YJC630109","YZ2019079","20KJB580012"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Traffic volatility modeling has been highly valued in recent years because of its advantages in describing the uncertainty of traffic flow during the short-term forecasting process. A few generalized autoregressive conditional heteroscedastic (GARCH) models have been developed to capture and hence forecast the volatility of traffic flow. Although these models have been confirmed to be capable of producing more reliable forecasts than traditional point forecasting models, the more or less imposed restrictions on parameter estimations may make the asymmetric property of traffic volatility be not or insufficiently considered. Furthermore, the performance of the models has not been fully evaluated and compared in the traffic forecasting context, rendering the choice of the models dilemmatic for traffic volatility modeling. In this study, an omnibus traffic volatility forecasting framework is proposed, where various traffic volatility models with symmetric and asymmetric properties can be developed in a unifying way by fixing or flexibly estimating three key parameters, namely the Box-Cox transformation coefficient \u03bb, the shift factor b, and the rotation factor c. Extensive traffic speed datasets collected from urban roads of Kunshan city, China, and from freeway segments of the San Diego Region, USA, were used to evaluate the proposed framework and develop traffic volatility forecasting models in a number of case studies. The models include the standard GARCH, the threshold GARCH (TGARCH), the nonlinear ARCH (NGARCH), the nonlinear-asymmetric GARCH (NAGARCH), the Glosten\u2013Jagannathan\u2013Runkle GARCH (GJR-GARCH), and the family GARCH (FGARCH). The mean forecasting performance of the models was measured with mean absolute error (MAE) and mean absolute percentage error (MAPE), while the volatility forecasting performance of the models was measured with volatility mean absolute error (VMAE), directional accuracy (DA), kickoff percentage (KP), and average confidence length (ACL). Experimental results demonstrate the effectiveness and flexibility of the proposed framework and provide insights into how to develop and select proper traffic volatility forecasting models in different situations.<\/jats:p>","DOI":"10.3390\/e24101392","type":"journal-article","created":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T21:03:10Z","timestamp":1664485390000},"page":"1392","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Traffic Volatility Forecasting Using an Omnibus Family GARCH Modeling Framework"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6251-9930","authenticated-orcid":false,"given":"Jishun","family":"Ou","sequence":"first","affiliation":[{"name":"College of Architectural Science and Engineering, Yangzhou University, Yangzhou 225127, China"},{"name":"State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangmei","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Architectural Science and Engineering, Yangzhou University, Yangzhou 225127, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Zhou","sequence":"additional","affiliation":[{"name":"Zachry Department of Civil and Environmental Engineering, Texas A&M University, College Station, TX 77840, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhigang","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Architectural Science and Engineering, Yangzhou University, Yangzhou 225127, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qinghui","family":"Nie","sequence":"additional","affiliation":[{"name":"College of Architectural Science and Engineering, Yangzhou University, Yangzhou 225127, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1061\/(ASCE)0733-947X(2002)128:6(490)","article-title":"Performance Evaluation of Short-Term Time-Series Traffic Prediction Model","volume":"128","author":"Ishak","year":"2002","journal-title":"J. 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