{"id":280,"date":"2018-12-29T10:11:14","date_gmt":"2018-12-29T10:11:14","guid":{"rendered":"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=280"},"modified":"2018-12-29T10:11:45","modified_gmt":"2018-12-29T10:11:45","slug":"causality-invertibility-and-the-maand-ar-processes","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/statp10\/chapter\/causality-invertibility-and-the-maand-ar-processes\/","title":{"rendered":"Causality, Invertibility, and the MAand AR Processes"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/ktABhCXUSiE\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-281\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-03.jpg\" alt=\"\" width=\"799\" height=\"598\" \/> <img class=\"aligncenter size-full wp-image-282\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-05.jpg\" alt=\"\" width=\"881\" height=\"566\" \/> <img class=\"aligncenter size-full wp-image-283\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-06.jpg\" alt=\"\" width=\"815\" height=\"503\" \/> <img class=\"aligncenter size-full wp-image-284\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-10.jpg\" alt=\"\" width=\"842\" height=\"561\" \/> <img class=\"aligncenter size-full wp-image-285\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-12.jpg\" alt=\"\" width=\"836\" height=\"462\" \/> <img class=\"aligncenter size-full wp-image-286\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-15.jpg\" alt=\"\" width=\"855\" height=\"447\" \/> <img class=\"aligncenter size-full wp-image-287\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-16.jpg\" alt=\"\" width=\"845\" height=\"463\" \/> <img class=\"aligncenter size-full wp-image-288\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-19.jpg\" alt=\"\" width=\"860\" height=\"478\" \/> <img class=\"aligncenter size-full wp-image-289\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-20.jpg\" alt=\"\" width=\"884\" height=\"559\" \/> <img class=\"aligncenter size-full wp-image-290\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-26.jpg\" alt=\"\" width=\"873\" height=\"550\" \/> <img class=\"aligncenter size-full wp-image-291\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-29.jpg\" alt=\"\" width=\"878\" height=\"396\" \/> <img class=\"aligncenter size-full wp-image-292\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-30.jpg\" alt=\"\" width=\"921\" height=\"678\" \/> <img class=\"aligncenter size-full wp-image-293\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-35.jpg\" alt=\"\" width=\"865\" height=\"421\" \/> <img class=\"aligncenter size-full wp-image-294\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-41.jpg\" alt=\"\" width=\"856\" height=\"359\" \/> <img class=\"aligncenter size-full wp-image-295\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-42.jpg\" alt=\"\" width=\"841\" height=\"477\" \/> <img class=\"aligncenter size-full wp-image-296\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-43.jpg\" alt=\"\" width=\"883\" height=\"528\" \/> <img class=\"aligncenter size-full wp-image-297\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-51.jpg\" alt=\"\" width=\"741\" height=\"584\" \/> <img class=\"aligncenter size-full wp-image-298\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-56.jpg\" alt=\"\" width=\"860\" height=\"532\" \/> <img class=\"aligncenter size-full wp-image-299\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-57.jpg\" alt=\"\" width=\"863\" height=\"553\" \/> <img class=\"aligncenter size-full wp-image-300\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-60.jpg\" alt=\"\" width=\"791\" height=\"307\" \/>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Causality, Invertibility, and the MAand AR Processes <\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/ktABhCXUSiE\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<strong><em>References :<\/em><\/strong>\r\n\r\n<strong><em>\u00a0<\/em><\/strong>\r\n<ul>\r\n \t<li>S.Karlin&amp;H.M.Taylor : A First Course in Stochastic Process, Vol-1<\/li>\r\n \t<li>J Medhi : Stochastic Process<\/li>\r\n \t<li>D.R.Cox: : Renewal Theory<\/li>\r\n \t<li>S.Ross : Stochastic Process<\/li>\r\n \t<li>A.K.Basu : Stochastic Process<\/li>\r\n \t<li>P.G.Hoel, S.C.Port&amp;C.J.Stone : An Introduction to Stochastic Process<\/li>\r\n \t<li>R.N.Bhattacharyya&amp;E.Waymire : Stochastic Processes and Application<\/li>\r\n<\/ul>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/ktABhCXUSiE\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-281\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-03.jpg\" alt=\"\" width=\"799\" height=\"598\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-03.jpg 799w, https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-03-300x225.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-03-768x575.jpg 768w, 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decoding=\"async\" class=\"aligncenter size-full wp-image-298\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-56.jpg\" alt=\"\" width=\"860\" height=\"532\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-56.jpg 860w, https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-56-300x186.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-56-768x475.jpg 768w, 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srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-57.jpg 863w, https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-57-300x192.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-57-768x492.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-57-65x42.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-57-225x144.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-57-350x224.jpg 350w\" sizes=\"auto, (max-width: 863px) 100vw, 863px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-300\" src=\"http:\/\/statp10.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-60.jpg\" alt=\"\" width=\"791\" height=\"307\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-60.jpg 791w, https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-60-300x116.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-60-768x298.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-60-65x25.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-60-225x87.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-content\/uploads\/sites\/137\/2018\/12\/15325128099752_et_spts_causality_invertibility_and_the_ma_and_ar_processes-1-60-350x136.jpg 350w\" sizes=\"auto, (max-width: 791px) 100vw, 791px\" \/><\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Causality, Invertibility, and the MAand AR Processes <\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/ktABhCXUSiE\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p><strong><em>References :<\/em><\/strong><\/p>\n<p><strong><em>\u00a0<\/em><\/strong><\/p>\n<ul>\n<li>S.Karlin&amp;H.M.Taylor : A First Course in Stochastic Process, Vol-1<\/li>\n<li>J Medhi : Stochastic Process<\/li>\n<li>D.R.Cox: : Renewal Theory<\/li>\n<li>S.Ross : Stochastic Process<\/li>\n<li>A.K.Basu : Stochastic Process<\/li>\n<li>P.G.Hoel, S.C.Port&amp;C.J.Stone : An Introduction to Stochastic Process<\/li>\n<li>R.N.Bhattacharyya&amp;E.Waymire : Stochastic Processes and Application<\/li>\n<\/ul>\n","protected":false},"author":3,"menu_order":31,"template":"","meta":{"_acf_changed":false,"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["samopriya-basu","sugata-sen-roy"],"pb_section_license":""},"chapter-type":[],"contributor":[59,60],"license":[],"class_list":["post-280","chapter","type-chapter","status-publish","hentry","contributor-samopriya-basu","contributor-sugata-sen-roy"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-json\/pressbooks\/v2\/chapters\/280","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":1,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-json\/pressbooks\/v2\/chapters\/280\/revisions"}],"predecessor-version":[{"id":301,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-json\/pressbooks\/v2\/chapters\/280\/revisions\/301"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-json\/pressbooks\/v2\/chapters\/280\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-json\/wp\/v2\/media?parent=280"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-json\/pressbooks\/v2\/chapter-type?post=280"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-json\/wp\/v2\/contributor?post=280"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp10\/wp-json\/wp\/v2\/license?post=280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}