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Under some mild regularity conditions, we obtain a complete classification of the parameter space of an invertible first\u2010order TARMA model into parametric regions over which the model is either transient or recurrent, and the recurrence region is further subdivided into regions of null recurrence or positive recurrence, or even geometric recurrence. We derive a set of necessary and sufficient conditions for the ergodicity of invertible first\u2010order TARMA processes.<\/jats:p>","DOI":"10.1111\/jtsa.12440","type":"journal-article","created":{"date-parts":[[2018,12,5]],"date-time":"2018-12-05T05:34:44Z","timestamp":1543988084000},"page":"256-264","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["On the Ergodicity of First\u2010Order Threshold Autoregressive Moving\u2010Average Processes"],"prefix":"10.1111","volume":"40","author":[{"given":"Kung\u2010Sik","family":"Chan","sequence":"first","affiliation":[{"name":"Department of Statistics and Actuarial Science University of Iowa Iowa City IA USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Greta","family":"Goracci","sequence":"additional","affiliation":[{"name":"Department of Statistical Sciences University of Bologna Bologna Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2018,12,4]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02479833"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.1992.tb00096.x"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(93)90097-N"},{"issue":"2","key":"e_1_2_8_5_1","doi-asserted-by":"crossref","first-page":"267","DOI":"10.2307\/3213771","article-title":"A multiple\u2010threshold AR(1) model","volume":"22","author":"Chan KS","year":"1985","journal-title":"Journal of Applied Probability"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.2307\/1427125"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2010.04.036"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.2307\/3214493"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9892.2005.00412.x"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1032374627"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.3150\/07-BEJ5147"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.2307\/3214573"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1137\/0327073"},{"key":"e_1_2_8_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0043789"},{"key":"e_1_2_8_15_1","volume-title":"Markov Chains and Stochastic Stability","author":"Meyn SP","year":"2012"},{"key":"e_1_2_8_16_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466608090026"},{"key":"e_1_2_8_17_1","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198522249.001.0001","volume-title":"Non\u2010linear Time Series: A Dynamical System Approach","author":"Tong H","year":"1990"},{"key":"e_1_2_8_18_1","doi-asserted-by":"publisher","DOI":"10.2307\/3213735"},{"key":"e_1_2_8_19_1","doi-asserted-by":"publisher","DOI":"10.2307\/1425932"}],"container-title":["Journal of Time Series Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fjtsa.12440","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/jtsa.12440","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/jtsa.12440","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/jtsa.12440","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,13]],"date-time":"2024-07-13T00:58:08Z","timestamp":1720832288000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/jtsa.12440"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,4]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["10.1111\/jtsa.12440"],"URL":"https:\/\/doi.org\/10.1111\/jtsa.12440","archive":["Portico"],"relation":{},"ISSN":["0143-9782","1467-9892"],"issn-type":[{"value":"0143-9782","type":"print"},{"value":"1467-9892","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,4]]},"assertion":[{"value":"2017-10-12","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-10-31","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-12-04","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}