{"id":"https://openalex.org/W4310232022","doi":"https://doi.org/10.3390/e24121730","title":"Mildly Explosive Autoregression with Strong Mixing Errors","display_name":"Mildly Explosive Autoregression with Strong Mixing Errors","publication_year":2022,"publication_date":"2022-11-26","ids":{"openalex":"https://openalex.org/W4310232022","doi":"https://doi.org/10.3390/e24121730","pmid":"https://pubmed.ncbi.nlm.nih.gov/36554135"},"language":"en","primary_location":{"id":"doi:10.3390/e24121730","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24121730","pdf_url":"https://www.mdpi.com/1099-4300/24/12/1730/pdf?version=1669736310","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/12/1730/pdf?version=1669736310","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100349374","display_name":"Xian Liu","orcid":"https://orcid.org/0000-0003-4788-175X"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xian Liu","raw_affiliation_strings":["School of Big Data and Statistics, Anhui University, Hefei 230039, China"],"affiliations":[{"raw_affiliation_string":"School of Big Data and Statistics, Anhui University, Hefei 230039, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100707520","display_name":"Xiaoqin Li","orcid":"https://orcid.org/0000-0003-3562-9389"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoqin Li","raw_affiliation_strings":["School of Big Data and Statistics, Anhui University, Hefei 230039, China"],"affiliations":[{"raw_affiliation_string":"School of Big Data and Statistics, Anhui University, Hefei 230039, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100678965","display_name":"Min Gao","orcid":"https://orcid.org/0000-0002-6888-2965"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Gao","raw_affiliation_strings":["School of Big Data and Statistics, Anhui University, Hefei 230039, China"],"affiliations":[{"raw_affiliation_string":"School of Big Data and Statistics, Anhui University, Hefei 230039, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030299364","display_name":"Wenzhi Yang","orcid":"https://orcid.org/0000-0003-0487-5974"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wenzhi Yang","raw_affiliation_strings":["School of Big Data and Statistics, Anhui University, Hefei 230039, China"],"affiliations":[{"raw_affiliation_string":"School of Big Data and Statistics, Anhui University, Hefei 230039, China","institution_ids":["https://openalex.org/I143868143"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5030299364"],"corresponding_institution_ids":["https://openalex.org/I143868143"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.2467,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.5994752,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"24","issue":"12","first_page":"1730","last_page":"1730"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.7876285314559937},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.74125075340271},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7341973185539246},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7144177556037903},{"id":"https://openalex.org/keywords/explosive-material","display_name":"Explosive material","score":0.5958070158958435},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.5101888179779053},{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.5079613327980042},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"Asymptotic distribution","score":0.48460492491722107},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.45812851190567017},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43639475107192993},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.41630297899246216},{"id":"https://openalex.org/keywords/confidence-interval","display_name":"Confidence interval","score":0.4116172790527344},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2833477854728699},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18368124961853027}],"concepts":[{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.7876285314559937},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.74125075340271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7341973185539246},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7144177556037903},{"id":"https://openalex.org/C154238967","wikidata":"https://www.wikidata.org/wiki/Q12870","display_name":"Explosive material","level":2,"score":0.5958070158958435},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.5101888179779053},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.5079613327980042},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.48460492491722107},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.45812851190567017},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43639475107192993},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.41630297899246216},{"id":"https://openalex.org/C44249647","wikidata":"https://www.wikidata.org/wiki/Q208498","display_name":"Confidence interval","level":2,"score":0.4116172790527344},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2833477854728699},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18368124961853027},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e24121730","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24121730","pdf_url":"https://www.mdpi.com/1099-4300/24/12/1730/pdf?version=1669736310","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:36554135","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36554135","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:2cef0f328bf645efa64550437a948b81","is_oa":true,"landing_page_url":"https://doaj.org/article/2cef0f328bf645efa64550437a948b81","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 24, Iss 12, p 1730 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/12/1730/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24121730","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 24; Issue 12; Pages: 1730","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:9778470","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9778470","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e24121730","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24121730","pdf_url":"https://www.mdpi.com/1099-4300/24/12/1730/pdf?version=1669736310","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4454302528","display_name":null,"funder_award_id":"2008085MA14","funder_id":"https://openalex.org/F4320334897","funder_display_name":"Natural Science Foundation of Anhui Province"},{"id":"https://openalex.org/G6620176974","display_name":null,"funder_award_id":"2108085MA06","funder_id":"https://openalex.org/F4320334897","funder_display_name":"Natural Science Foundation of Anhui Province"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334897","display_name":"Natural Science Foundation of Anhui Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4310232022.pdf","grobid_xml":"https://content.openalex.org/works/W4310232022.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W629979766","https://openalex.org/W1971141015","https://openalex.org/W1975994995","https://openalex.org/W2024267958","https://openalex.org/W2027568953","https://openalex.org/W2029910124","https://openalex.org/W2030080040","https://openalex.org/W2063764360","https://openalex.org/W2077979927","https://openalex.org/W2091369032","https://openalex.org/W2125979918","https://openalex.org/W2139238934","https://openalex.org/W2165321616","https://openalex.org/W2238061309","https://openalex.org/W2761798416","https://openalex.org/W2811486259","https://openalex.org/W3005960233","https://openalex.org/W3012658710","https://openalex.org/W3082244980","https://openalex.org/W3102488938","https://openalex.org/W3121874347","https://openalex.org/W3123499142","https://openalex.org/W3136209049","https://openalex.org/W4283700008","https://openalex.org/W4289745239","https://openalex.org/W4292963524","https://openalex.org/W6644390931"],"related_works":["https://openalex.org/W2287334727","https://openalex.org/W1488588773","https://openalex.org/W2048510477","https://openalex.org/W2762476777","https://openalex.org/W2328795663","https://openalex.org/W2600150541","https://openalex.org/W2347510524","https://openalex.org/W2130579679","https://openalex.org/W2005388848","https://openalex.org/W2109421145"],"abstract_inverted_index":{"In":[0,93],"this":[1],"paper,":[2],"we":[3,95],"consider":[4],"the":[5,36,43,53,68,72,76,83,97,102,111],"mildly":[6],"explosive":[7],"autoregression":[8],"yt=\u03c1nyt\u22121+ut,":[9],"1\u2264t\u2264n,":[10],"where":[11],"\u03c1n=1+c/n\u03bd,":[12],"c>0,":[13],"\u03bd\u2208(0,1),":[14],"and":[15,32,58,75],"u1,\u2026,un":[16],"are":[17,79],"arithmetically":[18],"\u03b1-mixing":[19,60],"errors.":[20,61],"Under":[21],"some":[22,30],"weak":[23],"conditions,":[24],"such":[25,66],"as":[26,67],"Eu1=0,":[27],"E|u1|4+\u03b4<\u221e":[28],"for":[29,42,64],"\u03b4>0":[31],"mixing":[33],"coefficients":[34],"\u03b1(n)=O(n\u2212(2+8/\u03b4)),":[35],"Cauchy":[37,84,98],"limiting":[38,85,99],"distribution":[39,100],"is":[40],"established":[41],"least":[44],"squares":[45],"(LS)":[46],"estimator":[47,104],"\u03c1^n":[48,105],"of":[49,55,71,101],"\u03c1n,":[50,65],"which":[51,87],"extends":[52],"cases":[54],"independent":[56],"errors":[57],"geometrically":[59],"Some":[62],"simulations":[63],"empirical":[69,77],"probability":[70],"confidence":[73],"interval":[74],"density,":[78],"presented":[80],"to":[81,106,118],"illustrate":[82,107],"distribution,":[86],"have":[88],"good":[89],"finite":[90],"sample":[91],"performances.":[92],"addition,":[94],"use":[96],"LS":[103],"real":[108],"data":[109],"from":[110,115],"NASDAQ":[112],"composite":[113],"index":[114],"April":[116,119],"2011":[117],"2021.":[120]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}