{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,3]],"date-time":"2026-01-03T06:46:07Z","timestamp":1767422767437,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,4]],"date-time":"2022-08-04T00:00:00Z","timestamp":1659571200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"NNSF of China","doi-asserted-by":"publisher","award":["11971208","11601197","21BTJ035","21&ZD152","2021112612345167"],"award-info":[{"award-number":["11971208","11601197","21BTJ035","21&ZD152","2021112612345167"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"NSSF of China","award":["11971208","11601197","21BTJ035","21&ZD152","2021112612345167"],"award-info":[{"award-number":["11971208","11601197","21BTJ035","21&ZD152","2021112612345167"]}]},{"name":"National Major Social Science Project of China","award":["11971208","11601197","21BTJ035","21&ZD152","2021112612345167"],"award-info":[{"award-number":["11971208","11601197","21BTJ035","21&ZD152","2021112612345167"]}]},{"name":"YM Training Project of Jiangxi University of Finance and Economics","award":["11971208","11601197","21BTJ035","21&ZD152","2021112612345167"],"award-info":[{"award-number":["11971208","11601197","21BTJ035","21&ZD152","2021112612345167"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Autoregressive exogenous, hereafter ARX, models are widely adopted in time series-related domains as they can be regarded as the combination of an autoregressive process and a predictive regression. Within a more complex structure, extant diagnostic checking methods face difficulties in remaining validity in many conditions existing in real applications, such as heteroscedasticity and error correlations exhibited between the ARX model itself and its exogenous processes. For these reasons, we propose a new serial correlation test method based on the profile empirical likelihood. Simulation results, as well as two real data examples, show that our method has a good performance in all mentioned conditions.<\/jats:p>","DOI":"10.3390\/e24081076","type":"journal-article","created":{"date-parts":[[2022,8,4]],"date-time":"2022-08-04T02:07:22Z","timestamp":1659578842000},"page":"1076","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Testing for Serial Correlation in Autoregressive Exogenous Models with Possible GARCH Errors"],"prefix":"10.3390","volume":"24","author":[{"given":"Hanqing","family":"Li","sequence":"first","affiliation":[{"name":"School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China"},{"name":"Key Laboratory of Data Science in Finance and Economics, Jiangxi University of Finance and Economics, Nanchang 330013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaohui","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China"},{"name":"Key Laboratory of Data Science in Finance and Economics, Jiangxi University of Finance and Economics, Nanchang 330013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuting","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Behavioral and Social Sciences, University of Maryland, College Park, MD 20742, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yawen","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China"},{"name":"Key Laboratory of Data Science in Finance and Economics, Jiangxi University of Finance and Economics, Nanchang 330013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,4]]},"reference":[{"key":"ref_1","unstructured":"Box, G.E., Jenkins, G.M., Reinsel, G.C., and Ljung, G.M. 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