{"id":581,"date":"2023-07-29T10:41:04","date_gmt":"2023-07-29T10:41:04","guid":{"rendered":"https:\/\/statorials.org\/tr\/ljung-kutu-testi\/"},"modified":"2023-07-29T10:41:04","modified_gmt":"2023-07-29T10:41:04","slug":"ljung-kutu-testi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ljung-kutu-testi\/","title":{"rendered":"Ljung-box testi: tan\u0131m + \u00f6rnek"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Ad\u0131n\u0131 istatistik\u00e7iler <a href=\"https:\/\/en.wikipedia.org\/wiki\/Greta_M._Ljung\" target=\"_blank\" rel=\"noopener noreferrer\">Greta M. Ljung<\/a> ve <a href=\"https:\/\/en.wikipedia.org\/wiki\/George_E._P._Box\" target=\"_blank\" rel=\"noopener noreferrer\">George EP Box&#8217;tan<\/a> alan <strong>Ljung-Box testi<\/strong> , bir zaman serisinde otokorelasyonun var olup olmad\u0131\u011f\u0131n\u0131 kontrol eden istatistiksel bir testtir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ljung-Box testi ekonometride ve zaman serisi verilerinin ortak oldu\u011fu di\u011fer alanlarda yayg\u0131n olarak kullan\u0131lmaktad\u0131r.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Ljung-Box testinin temelleri<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Ljung-Box testinin temelleri \u015funlard\u0131r:<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">hipotezler<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Ljung-Box testi a\u015fa\u011f\u0131daki varsay\u0131mlar\u0131 kullan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> Art\u0131klar ba\u011f\u0131ms\u0131z olarak da\u011f\u0131t\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>A<\/sub> :<\/strong> Art\u0131klar ba\u011f\u0131ms\u0131z olarak da\u011f\u0131t\u0131lmaz; seri korelasyon sergilerler.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130deal durumda s\u0131f\u0131r hipotezini reddetmemek isteriz. Yani testin p de\u011ferinin 0,05&#8217;ten b\u00fcy\u00fck olmas\u0131n\u0131 isteriz \u00e7\u00fcnk\u00fc bu, zaman serisi modelimizin art\u0131klar\u0131n\u0131n ba\u011f\u0131ms\u0131z oldu\u011fu anlam\u0131na gelir ki bu da genellikle bir model olu\u015ftururken yapt\u0131\u011f\u0131m\u0131z bir varsay\u0131md\u0131r.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Test istatisti\u011fi<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Ljung-Box test istatisti\u011fi a\u015fa\u011f\u0131daki gibidir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Q<\/strong> = n(n+2) \u03a3p <sub>k<\/sub> <sup>2<\/sup> \/ (nk)<\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>n<\/strong> = \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03a3 = &#8220;toplam&#8221; anlam\u0131na gelen s\u00fcsl\u00fc bir sembol ve 1&#8217;den <em>h&#8217;ye<\/em> kadar olan toplam olarak kabul edilir; burada <em>h<\/em> , test edilen ofsetlerin say\u0131s\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>p <sub>k<\/sub><\/strong> = <em>k<\/em> gecikmesindeki otokorelasyon \u00f6rne\u011fi<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Reddetme b\u00f6lgesi<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><em>Q<\/em> testi istatisti\u011fi, <em>h<\/em> serbestlik derecesine sahip bir Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131 takip eder; yani Q~ <sup>X2<\/sup> (h).<\/span><\/p>\n<p> <span style=\"color: #000000;\">S\u0131f\u0131r hipotezini reddediyoruz ve e\u011fer Q &gt; X <sup>2<\/sup> <sub>1-\u03b1, h<\/sub> ise model art\u0131klar\u0131n\u0131n ba\u011f\u0131ms\u0131z olarak da\u011f\u0131lmad\u0131\u011f\u0131n\u0131 s\u00f6yl\u00fcyoruz.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00d6rnek: R&#8217;de Ljung-Box testi nas\u0131l yap\u0131l\u0131r?<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Belirli bir zaman serisi i\u00e7in R&#8217;de Ljung-Box testi ger\u00e7ekle\u015ftirmek i\u00e7in a\u015fa\u011f\u0131daki g\u00f6sterimi kullanan <strong>Box.test()<\/strong> i\u015flevini kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Kutu.test<\/strong> (x, ofset=1, type=c(\u201cKutu Delme\u201d, \u201cLjung-Kutu\u201d), fitdf = 0)<\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>x:<\/strong> say\u0131sal bir vekt\u00f6r veya tek de\u011fi\u015fkenli zaman serisi<\/span><\/li>\n<li> <strong>ofset:<\/strong> belirtilen ofset say\u0131s\u0131<\/li>\n<li> <strong>tip:<\/strong> Ger\u00e7ekle\u015ftirilecek test; se\u00e7enekler aras\u0131nda Box-Pierce ve Ljung-Box bulunur<\/li>\n<li> <strong>fitdf: x&#8217;in bir dizi kal\u0131nt\u0131 olmas\u0131 durumunda \u00e7\u0131karma i\u015flemi i\u00e7in bD<\/strong> serbestlik derecesi<\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnek, ortalama = 0 ve varyans = 1 ile normal bir da\u011f\u0131l\u0131m izleyen 100 de\u011ferden olu\u015fan rastgele bir vekt\u00f6r i\u00e7in Ljung-Box testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6stermektedir:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#make this example reproducible\n<\/span>set.seed(1)\n\n<span style=\"color: #008080;\">#generate a list of 100 normally distributed random variables<\/span>\ndata &lt;- rnorm(100, 0, 1)\n\n<span style=\"color: #008080;\">#conduct Ljung-Box test<\/span>\nBox.test(data, lag = 10, type = \"Ljung\")\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Bu, a\u015fa\u011f\u0131daki \u00e7\u0131kt\u0131y\u0131 \u00fcretir:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong>Box-Ljung test\n\ndata:data\nX-squared = 6.0721, df = 10, p-value = 0.8092\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Testin test istatisti\u011fi Q = <strong>6,0721<\/strong> ve testin p de\u011feri <strong>0,8092<\/strong> olup, 0,05&#8217;ten \u00e7ok daha y\u00fcksektir. Dolay\u0131s\u0131yla testin s\u0131f\u0131r hipotezini reddedip veri de\u011ferlerinin ba\u011f\u0131ms\u0131z oldu\u011fu sonucuna varam\u0131yoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte 10&#8217;luk bir ofset de\u011feri kulland\u0131\u011f\u0131m\u0131z\u0131 unutmay\u0131n, ancak \u00f6zel durumunuza ba\u011fl\u0131 olarak ofset i\u00e7in kullanmak istedi\u011finiz herhangi bir de\u011feri se\u00e7ebilirsiniz.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u0130lgili:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/ljung-kutusu-testi-pitonu\/\" target=\"_blank\" rel=\"noopener noreferrer\">Python&#8217;da Ljung-Box Testi Nas\u0131l Yap\u0131l\u0131r<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ad\u0131n\u0131 istatistik\u00e7iler Greta M. Ljung ve George EP Box&#8217;tan alan Ljung-Box testi , bir zaman serisinde otokorelasyonun var olup olmad\u0131\u011f\u0131n\u0131 kontrol eden istatistiksel bir testtir. Ljung-Box testi ekonometride ve zaman serisi verilerinin ortak oldu\u011fu di\u011fer alanlarda yayg\u0131n olarak kullan\u0131lmaktad\u0131r. Ljung-Box testinin temelleri Ljung-Box testinin temelleri \u015funlard\u0131r: hipotezler Ljung-Box testi a\u015fa\u011f\u0131daki varsay\u0131mlar\u0131 kullan\u0131r: H 0 : [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-581","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Ljung-Box testi: Tan\u0131m + \u00d6rnek - Statoryaller<\/title>\n<meta name=\"description\" content=\"Ljung-Box testinin, testin tan\u0131m\u0131n\u0131n yan\u0131 s\u0131ra R&#039;de nas\u0131l \u00e7al\u0131\u015ft\u0131r\u0131laca\u011f\u0131na dair bir \u00f6rnek de dahil olmak \u00fczere basit bir a\u00e7\u0131klamas\u0131.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/ljung-kutu-testi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Ljung-Box testi: Tan\u0131m + \u00d6rnek - 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