{"id":581,"date":"2023-07-29T10:41:04","date_gmt":"2023-07-29T10:41:04","guid":{"rendered":"https:\/\/statorials.org\/id\/tes-kotak-ljung\/"},"modified":"2023-07-29T10:41:04","modified_gmt":"2023-07-29T10:41:04","slug":"tes-kotak-ljung","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/tes-kotak-ljung\/","title":{"rendered":"Tes ljung-box: definisi + contoh"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Uji Ljung-Box<\/strong> , dinamai menurut ahli statistik <a href=\"https:\/\/en.wikipedia.org\/wiki\/Greta_M._Ljung\" target=\"_blank\" rel=\"noopener noreferrer\">Greta M. Ljung<\/a> dan <a href=\"https:\/\/en.wikipedia.org\/wiki\/George_E._P._Box\" target=\"_blank\" rel=\"noopener noreferrer\">George EP Box<\/a> , adalah uji statistik yang memeriksa apakah terdapat autokorelasi dalam suatu deret waktu.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tes Ljung-Box banyak digunakan dalam ekonometrika dan bidang lain yang umum menggunakan data deret waktu.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Dasar-dasar tes Ljung-Box<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Berikut dasar-dasar tes Ljung-Box:<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Hipotesis<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Uji Ljung-Box menggunakan asumsi sebagai berikut:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> Residunya terdistribusi secara mandiri.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>A<\/sub> :<\/strong> Sisanya tidak dibagikan secara mandiri; mereka menunjukkan korelasi serial.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Idealnya, kami tidak ingin menolak hipotesis nol. Artinya, kita ingin nilai p pengujian lebih besar dari 0,05, karena ini berarti residu model deret waktu kita bersifat independen, yang sering kali menjadi asumsi yang kita buat saat membuat model.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Statistik uji<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Statistik uji Ljung-Box adalah sebagai berikut:<\/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;\">Emas:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>n<\/strong> = ukuran sampel<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03a3 = simbol mewah yang berarti &#8220;jumlah&#8221; dan dianggap sebagai jumlah dari 1 sampai <em>h<\/em> , dimana <em>h<\/em> adalah jumlah offset yang diuji.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>p <sub>k<\/sub><\/strong> = sampel autokorelasi pada lag <em>k<\/em><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Wilayah penolakan<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Statistik uji <em>Q<\/em> mengikuti distribusi Chi-kuadrat dengan derajat kebebasan <em>h<\/em> ; yaitu Q~ <sup>X2<\/sup> (jam).<\/span><\/p>\n<p> <span style=\"color: #000000;\">Kami menolak hipotesis nol dan mengatakan bahwa residu model tidak terdistribusi secara independen jika Q &gt; X <sup>2<\/sup> <sub>1-\u03b1, h<\/sub><\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Contoh: Cara melakukan tes Ljung-Box di R<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Untuk melakukan pengujian Ljung-Box di R untuk rangkaian waktu tertentu, kita dapat menggunakan fungsi <strong>Box.test()<\/strong> , yang menggunakan notasi berikut:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Box.test<\/strong> (x, offset=1, type=c(\u201cBox-Pierce\u201d, \u201cLjung-Box\u201d), fitdf = 0)<\/span><\/p>\n<p> <span style=\"color: #000000;\">Emas:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>x:<\/strong> vektor numerik atau deret waktu univariat<\/span><\/li>\n<li> <strong>offset:<\/strong> jumlah offset yang ditentukan<\/li>\n<li> <strong>jenis:<\/strong> Tes yang akan dilakukan; pilihannya termasuk Box-Pierce dan Ljung-Box<\/li>\n<li> <strong>fitdf: derajat kebebasan bD<\/strong> untuk melakukan pengurangan jika x adalah rangkaian residu<\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Contoh berikut mengilustrasikan cara melakukan uji Ljung-Box untuk vektor sembarang dengan 100 nilai yang mengikuti distribusi normal dengan mean = 0 dan varians = 1:<\/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;\">Ini menghasilkan keluaran berikut:<\/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;\">Statistik uji dari tes ini adalah Q = <strong>6,0721<\/strong> dan nilai p dari tes tersebut adalah <strong>0,8092<\/strong> , yang jauh lebih tinggi dari 0,05. Dengan demikian, kami gagal menolak hipotesis nol dari pengujian tersebut dan menyimpulkan bahwa nilai data adalah independen.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Perhatikan bahwa kami menggunakan nilai offset 10 dalam contoh ini, namun Anda dapat memilih nilai apa pun yang ingin Anda gunakan untuk offset, bergantung pada situasi khusus Anda.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Terkait:<\/strong> <a href=\"https:\/\/statorials.org\/id\/python-uji-kotak-ljung\/\" target=\"_blank\" rel=\"noopener noreferrer\">Cara Melakukan Tes Ljung-Box dengan Python<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Uji Ljung-Box , dinamai menurut ahli statistik Greta M. Ljung dan George EP Box , adalah uji statistik yang memeriksa apakah terdapat autokorelasi dalam suatu deret waktu. Tes Ljung-Box banyak digunakan dalam ekonometrika dan bidang lain yang umum menggunakan data deret waktu. Dasar-dasar tes Ljung-Box Berikut dasar-dasar tes Ljung-Box: Hipotesis Uji Ljung-Box menggunakan asumsi sebagai [&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":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Tes Ljung-Box: Definisi + Contoh - Statorial<\/title>\n<meta name=\"description\" content=\"Penjelasan sederhana tentang tes Ljung-Box, termasuk definisi tes serta contoh cara menjalankannya di R.\" \/>\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\/id\/tes-kotak-ljung\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Tes Ljung-Box: Definisi + Contoh - Statorial\" \/>\n<meta property=\"og:description\" content=\"Penjelasan sederhana tentang tes Ljung-Box, termasuk definisi tes serta contoh cara menjalankannya di R.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/id\/tes-kotak-ljung\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-29T10:41:04+00:00\" \/>\n<meta name=\"author\" content=\"Benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/id\/tes-kotak-ljung\/\",\"url\":\"https:\/\/statorials.org\/id\/tes-kotak-ljung\/\",\"name\":\"Tes Ljung-Box: Definisi + Contoh - Statorial\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/id\/#website\"},\"datePublished\":\"2023-07-29T10:41:04+00:00\",\"dateModified\":\"2023-07-29T10:41:04+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\"},\"description\":\"Penjelasan sederhana tentang tes Ljung-Box, termasuk definisi tes serta contoh cara menjalankannya di R.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/id\/tes-kotak-ljung\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/id\/tes-kotak-ljung\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/id\/tes-kotak-ljung\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/statorials.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Tes ljung-box: definisi + contoh\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/id\/#website\",\"url\":\"https:\/\/statorials.org\/id\/\",\"name\":\"Statorials\",\"description\":\"Panduan anda untuk kompetensi statistik!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/id\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"id\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\",\"name\":\"Benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin anderson\"},\"description\":\"Halo, saya Benjamin, pensiunan profesor statistika yang menjadi guru Statorial yang berdedikasi. 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