{"id":581,"date":"2023-07-29T10:41:04","date_gmt":"2023-07-29T10:41:04","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e8%8d%a3%e6%a0%bc%e7%9b%92%e6%b5%8b%e8%af%95\/"},"modified":"2023-07-29T10:41:04","modified_gmt":"2023-07-29T10:41:04","slug":"%e8%8d%a3%e6%a0%bc%e7%9b%92%e6%b5%8b%e8%af%95","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e8%8d%a3%e6%a0%bc%e7%9b%92%e6%b5%8b%e8%af%95\/","title":{"rendered":"Ljung-box \u6d4b\u8bd5\uff1a\u5b9a\u4e49 + \u793a\u4f8b"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Ljung-Box \u68c0\u9a8c<\/strong>\u4ee5\u7edf\u8ba1\u5b66\u5bb6<a href=\"https:\/\/en.wikipedia.org\/wiki\/Greta_M._Ljung\" target=\"_blank\" rel=\"noopener noreferrer\">Greta M. Ljung<\/a>\u548c<a href=\"https:\/\/en.wikipedia.org\/wiki\/George_E._P._Box\" target=\"_blank\" rel=\"noopener noreferrer\">George EP Box<\/a>\u547d\u540d\uff0c\u662f\u4e00\u79cd\u68c0\u67e5\u65f6\u95f4\u5e8f\u5217\u4e2d\u662f\u5426\u5b58\u5728\u81ea\u76f8\u5173\u7684\u7edf\u8ba1\u68c0\u9a8c\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ljung-Box \u68c0\u9a8c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u8ba1\u91cf\u7ecf\u6d4e\u5b66\u548c\u5176\u4ed6\u5e38\u89c1\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u7684\u9886\u57df\u3002<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Ljung-Box \u6d4b\u8bd5\u7684\u57fa\u7840\u77e5\u8bc6<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u662f Ljung-Box \u6d4b\u8bd5\u7684\u57fa\u7840\u77e5\u8bc6\uff1a<\/span><\/p>\n<h3><strong><span style=\"color: #000000;\">\u5047\u8bbe<\/span><\/strong><\/h3>\n<p><span style=\"color: #000000;\">Ljung-Box \u68c0\u9a8c\u4f7f\u7528\u4ee5\u4e0b\u5047\u8bbe\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> \uff1a<\/strong>\u6b8b\u5dee\u72ec\u7acb\u5206\u5e03\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>A<\/sub> \uff1a<\/strong>\u6b8b\u5dee\u4e0d\u72ec\u7acb\u5206\u5e03\uff1b\u5b83\u4eec\u8868\u73b0\u51fa\u5e8f\u5217\u76f8\u5173\u6027\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u4e0d\u5e0c\u671b\u62d2\u7edd\u539f\u5047\u8bbe\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u5e0c\u671b\u68c0\u9a8c\u7684 p \u503c\u5927\u4e8e 0.05\uff0c\u56e0\u4e3a\u8fd9\u610f\u5473\u7740\u65f6\u95f4\u5e8f\u5217\u6a21\u578b\u7684\u6b8b\u5dee\u662f\u72ec\u7acb\u7684\uff0c\u8fd9\u901a\u5e38\u662f\u6211\u4eec\u5728\u521b\u5efa\u6a21\u578b\u65f6\u505a\u51fa\u7684\u5047\u8bbe\u3002<\/span><\/p>\n<h3><strong><span style=\"color: #000000;\">\u68c0\u9a8c\u7edf\u8ba1\u91cf<\/span><\/strong><\/h3>\n<p><span style=\"color: #000000;\">Ljung-Box \u68c0\u9a8c\u7edf\u8ba1\u91cf\u5982\u4e0b\uff1a<\/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;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>n<\/strong> = \u6837\u672c\u91cf<\/span><\/p>\n<p><span style=\"color: #000000;\">\u03a3 = \u4e00\u4e2a\u5947\u7279\u7684\u7b26\u53f7\uff0c\u8868\u793a\u201c\u603b\u548c\u201d\uff0c\u88ab\u89c6\u4e3a\u4ece 1 \u5230<em>h<\/em>\u7684\u603b\u548c\uff0c\u5176\u4e2d<em>h<\/em>\u662f\u6d4b\u8bd5\u7684\u504f\u79fb\u91cf\u6570\u91cf\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>p <sub>k<\/sub><\/strong> = \u6ede\u540e<em>k<\/em>\u5904\u7684\u81ea\u76f8\u5173\u6837\u672c<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u62d2\u7edd\u533a\u57df<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\"><em>Q<\/em>\u68c0\u9a8c\u7edf\u8ba1\u91cf\u9075\u5faa\u5177\u6709<em>h \u4e2a<\/em>\u81ea\u7531\u5ea6\u7684\u5361\u65b9\u5206\u5e03\uff1b\u5373Q~ <sup>X2<\/sup> (h)\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u62d2\u7edd\u96f6\u5047\u8bbe\u5e76\u8bf4\u5982\u679c Q &gt; X <sup>2<\/sup> <sub>1-\u03b1, h<\/sub>\u5219\u6a21\u578b\u6b8b\u5dee\u4e0d\u662f\u72ec\u7acb\u5206\u5e03\u7684<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u793a\u4f8b\uff1a\u5982\u4f55\u5728 R \u4e2d\u6267\u884c Ljung-Box \u6d4b\u8bd5<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u8981\u5728 R \u4e2d\u5bf9\u7ed9\u5b9a\u65f6\u95f4\u5e8f\u5217\u6267\u884c Ljung-Box \u6d4b\u8bd5\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528<strong>Box.test()<\/strong>\u51fd\u6570\uff0c\u8be5\u51fd\u6570\u4f7f\u7528\u4ee5\u4e0b\u7b26\u53f7\uff1a<\/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;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>x\uff1a<\/strong>\u6570\u503c\u5411\u91cf\u6216\u5355\u53d8\u91cf\u65f6\u95f4\u5e8f\u5217<\/span><\/li>\n<li><strong>offset\uff1a<\/strong>\u6307\u5b9a\u7684\u504f\u79fb\u91cf<\/li>\n<li><strong>type\uff1a<\/strong>\u8981\u6267\u884c\u7684\u6d4b\u8bd5\uff1b\u9009\u9879\u5305\u62ec Box-Pierce \u548c Ljung-Box<\/li>\n<li> <strong>fitdf\uff1a\u5982\u679c x \u662f\u4e00\u7cfb\u5217\u6b8b\u6570\uff0c\u5219\u8981\u51cf\u53bb\u7684 bD<\/strong>\u81ea\u7531\u5ea6<\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u793a\u4f8b\u8bf4\u660e\u5982\u4f55\u5bf9\u9075\u5faa\u5747\u503c = 0 \u4e14\u65b9\u5dee = 1 \u7684\u6b63\u6001\u5206\u5e03\u7684 100 \u4e2a\u503c\u7684\u4efb\u610f\u5411\u91cf\u6267\u884c Ljung-Box \u68c0\u9a8c\uff1a<\/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;\">\u8fd9\u4f1a\u751f\u6210\u4ee5\u4e0b\u8f93\u51fa\uff1a<\/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;\">\u8be5\u68c0\u9a8c\u7684\u68c0\u9a8c\u7edf\u8ba1\u91cf\u4e3a Q = <strong>6.0721<\/strong> \uff0c\u68c0\u9a8c\u7684 p \u503c\u4e3a<strong>0.8092<\/strong> \uff0c\u8fdc\u9ad8\u4e8e 0.05\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u672a\u80fd\u62d2\u7edd\u68c0\u9a8c\u7684\u539f\u5047\u8bbe\u5e76\u5f97\u51fa\u6570\u636e\u503c\u662f\u72ec\u7acb\u7684\u7ed3\u8bba\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8bf7\u6ce8\u610f\uff0c\u6211\u4eec\u5728\u6b64\u793a\u4f8b\u4e2d\u4f7f\u7528\u7684\u504f\u79fb\u503c\u662f 10\uff0c\u4f46\u60a8\u53ef\u4ee5\u6839\u636e\u60a8\u7684\u5177\u4f53\u60c5\u51b5\u9009\u62e9\u8981\u7528\u4e8e\u504f\u79fb\u7684\u4efb\u4f55\u503c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u76f8\u5173\uff1a<\/strong> <a href=\"https:\/\/statorials.org\/cn\/ljung-\u76d2\u6d4b\u8bd5-python\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u5982\u4f55\u5728 Python \u4e2d\u6267\u884c Ljung-Box \u6d4b\u8bd5<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ljung-Box \u68c0\u9a8c\u4ee5\u7edf\u8ba1\u5b66\u5bb6Greta M. Ljung\u548cGeorge EP Box\u547d\u540d\uff0c\u662f\u4e00\u79cd\u68c0\u67e5\u65f6\u95f4 [&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-11"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Ljung-Box \u6d4b\u8bd5\uff1a\u5b9a\u4e49 + \u793a\u4f8b - \u7edf\u8ba1<\/title>\n<meta name=\"description\" content=\"Ljung-Box \u6d4b\u8bd5\u7684\u7b80\u5355\u8bf4\u660e\uff0c\u5305\u62ec\u6d4b\u8bd5\u7684\u5b9a\u4e49\u4ee5\u53ca\u5982\u4f55\u5728 R \u4e2d\u8fd0\u884c\u8be5\u6d4b\u8bd5\u7684\u793a\u4f8b\u3002\" \/>\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\/cn\/\u8363\u683c\u76d2\u6d4b\u8bd5\/\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Ljung-Box \u6d4b\u8bd5\uff1a\u5b9a\u4e49 + \u793a\u4f8b - 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