{"id":579,"date":"2023-07-29T10:41:04","date_gmt":"2023-07-29T10:41:04","guid":{"rendered":"https:\/\/statorials.org\/my\/ljung-box-%e1%80%80%e1%80%ad%e1%80%af%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba\/"},"modified":"2023-07-29T10:41:04","modified_gmt":"2023-07-29T10:41:04","slug":"ljung-box-%e1%80%80%e1%80%ad%e1%80%af%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/ljung-box-%e1%80%80%e1%80%ad%e1%80%af%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba\/","title":{"rendered":"Ljung-box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f- \u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a + \u1025\u1015\u1019\u102c"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1015\u100a\u102c\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Greta_M._Ljung\" target=\"_blank\" rel=\"noopener noreferrer\">Greta M. Ljung<\/a> \u1014\u103e\u1004\u1037\u103a <a href=\"https:\/\/en.wikipedia.org\/wiki\/George_E._P._Box\" target=\"_blank\" rel=\"noopener noreferrer\">George EP Box \u1010\u102d\u102f\u1037\u1000\u102d\u102f<\/a> \u1021\u1005\u103d\u1032\u1015\u103c\u102f\u104d \u1021\u1019\u100a\u103a\u1015\u1031\u1038\u1011\u102c\u1038\u101e\u100a\u1037\u103a <strong>Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f<\/strong> \u101e\u100a\u103a \u1021\u1001\u103b\u102d\u1014\u103a\u1005\u102e\u1038\u101b\u102e\u1038\u1010\u1005\u103a\u1001\u102f\u1021\u1010\u103d\u1004\u103a\u1038 autocorrelation \u101b\u103e\u102d\u1019\u101b\u103e\u102d\u1005\u1005\u103a\u1006\u1031\u1038\u101e\u100a\u1037\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f econometrics \u1014\u103e\u1004\u1037\u103a time series data \u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1021\u101e\u102f\u1036\u1038\u1019\u103b\u102c\u1038\u101e\u100a\u1037\u103a \u1021\u1001\u103c\u102c\u1038\u1014\u101a\u103a\u1015\u101a\u103a\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1010\u103d\u1004\u103a\u1000\u103b\u101a\u103a\u1005\u103d\u102c \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f\u1021\u1001\u103c\u1031\u1001\u1036\u1019\u103b\u102c\u1038<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u1024\u101e\u100a\u103a\u1019\u103e\u102c Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u104f \u1021\u1001\u103c\u1031\u1001\u1036\u1021\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">\u101a\u1030\u1006\u1001\u103b\u1000\u103a<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a \u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1005\u103d\u102c \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>A<\/sub> :<\/strong> \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1001\u103d\u1032\u101d\u1031\u1001\u103c\u1004\u103a\u1038\u1019\u1015\u103c\u102f\u1015\u102b\u104b \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u1019\u103e\u1010\u103a\u1005\u1009\u103a\u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1015\u103c\u101e\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1000\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1036\u1038\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u101c\u102d\u102f\u1015\u102b\u101e\u100a\u103a\u104b \u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f p-value \u1000\u102d\u102f 0.05 \u1011\u1000\u103a \u1000\u103c\u102e\u1038\u1005\u1031\u101c\u102d\u102f\u101e\u100a\u103a\u104a \u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f time series model \u104f \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104a \u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1016\u1014\u103a\u1010\u102e\u1038\u101e\u100a\u1037\u103a\u1021\u1001\u102b\u1010\u103d\u1004\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u101a\u1030\u1006\u101c\u1031\u1037\u101b\u103e\u102d\u101e\u1031\u102c \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038\u1019\u103e\u102c \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1010\u102d\u102f\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/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;\">\u101b\u103d\u103e\u1031-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>n<\/strong> = \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u2211 = &#8220; \u1015\u1031\u102b\u1004\u103a\u1038&#8221;  \u101f\u102f \u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u101b\u101e\u1031\u102c \u1016\u1014\u103a\u1005\u102e\u101e\u1004\u103a\u1039\u1000\u1031\u1010\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 1 \u1019\u103e <em>h<\/em> \u1019\u103e \u1015\u1031\u102b\u1004\u103a\u1038\u101c\u1012\u103a\u1021\u1016\u103c\u1005\u103a \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u101e\u100a\u103a \u104a <em>h<\/em> \u101e\u100a\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1011\u102c\u1038\u101e\u1031\u102c \u1021\u1031\u102c\u1037\u1016\u103a\u1006\u1000\u103a\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>p <sub>k<\/sub><\/strong> = autocorrelation \u1014\u1019\u1030\u1014\u102c\u1019\u103e\u102c lag <em>k<\/em><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1015\u101a\u103a\u1001\u1036\u1012\u1031\u101e<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><em>Q<\/em> \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u101e\u100a\u103a \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f <em>h<\/em> \u1012\u102e\u1002\u101b\u102e\u1016\u103c\u1004\u1037\u103a Chi-square \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1000\u102d\u102f \u101c\u102d\u102f\u1000\u103a\u1014\u102c\u101e\u100a\u103a\u104b \u1025\u1015\u1019\u102c Q~ <sup>X2<\/sup> (\u1007)\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">Q &gt; X <sup>2<\/sup> <sub>1-\u03b1, h<\/sub> \u1006\u102d\u102f\u101c\u103b\u103e\u1004\u103a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1001\u103d\u1032\u101d\u1031\u1019\u100a\u103a\u1019\u101f\u102f\u1010\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1015\u103c\u102e\u1038\u104a<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u1025\u1015\u1019\u102c- R \u1016\u103c\u1004\u1037\u103a Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1014\u100a\u103a\u1038<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u1015\u1031\u1038\u1011\u102c\u1038\u101e\u1031\u102c\u1021\u1001\u103b\u102d\u1014\u103a\u1005\u102e\u1038\u101b\u102e\u1038\u1010\u1005\u103a\u1001\u102f\u1021\u1010\u103d\u1000\u103a R \u1010\u103d\u1004\u103a Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u101b\u1014\u103a\u104a \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b\u1021\u1019\u103e\u1010\u103a\u1021\u101e\u102c\u1038\u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u1037\u103a <strong>Box.test()<\/strong> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Box.test<\/strong> (x\u104a offset=1\u104a type=c(\u201cBox-Pierce\u201d\u104a \u201cLjung-Box\u201d)\u104a fitdf = 0)<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101b\u103d\u103e\u1031-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>x-<\/strong> \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u102c\u1014\u103a\u1038 vector \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a univariate \u1021\u1001\u103b\u102d\u1014\u103a\u1005\u102e\u1038\u101b\u102e\u1038<\/span><\/li>\n<li> <strong>offset-<\/strong> \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1011\u102c\u1038\u101e\u1031\u102c \u1021\u1031\u102c\u1037\u1016\u103a\u1006\u1000\u103a\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a<\/li>\n<li> <strong>\u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038-<\/strong> \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101b\u1014\u103a\u104a \u101b\u103d\u1031\u1038\u1001\u103b\u101a\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a Box-Pierce \u1014\u103e\u1004\u1037\u103a Ljung-Box \u1010\u102d\u102f\u1037\u1015\u102b\u101d\u1004\u103a\u101e\u100a\u103a\u104b<\/li>\n<li> <strong>fitdf: x \u101e\u100a\u103a \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u104f \u1006\u1000\u103a\u1010\u102d\u102f\u1000\u103a\u1016\u103c\u1005\u103a\u101c\u103b\u103e\u1004\u103a \u1014\u102f\u1010\u103a\u101b\u1014\u103a \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f bD<\/strong> \u1012\u102e\u1002\u101b\u102e<\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1025\u1015\u1019\u102c\u101e\u100a\u103a \u101e\u102c\u1019\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u1001\u103b\u102e\u1019\u103e\u102f\u104f\u1014\u1031\u102c\u1000\u103a\u1010\u103d\u1004\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e = 0 \u1014\u103e\u1004\u1037\u103a \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f = 1 \u101b\u103e\u102d\u101e\u1031\u102c \u1010\u1014\u103a\u1018\u102d\u102f\u1038 100 \u104f \u1019\u1010\u101b\u102c\u1038\u101e\u1031\u102c vector \u1021\u1010\u103d\u1000\u103a Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u103a-<\/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;\">\u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b output \u1000\u102d\u102f\u1011\u102f\u1010\u103a\u1015\u1031\u1038\u101e\u100a\u103a-<\/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;\">\u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u104f \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u101e\u100a\u103a Q = <strong>6.0721<\/strong> \u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u104f p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a <strong>0.8092<\/strong> \u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 0.05 \u1011\u1000\u103a \u1019\u103b\u102c\u1038\u1005\u103d\u102c\u1019\u103c\u1004\u1037\u103a\u1019\u102c\u1038\u101e\u100a\u103a\u104b \u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1006\u102d\u102f\u101b\u1014\u103a \u1015\u103b\u1000\u103a\u1000\u103d\u1000\u103a\u1015\u103c\u102e\u1038 \u1012\u1031\u1010\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1016\u103c\u1005\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1000\u1031\u102c\u1000\u103a\u1001\u103b\u1000\u103a\u1001\u103b\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u1025\u1015\u1019\u102c\u1010\u103d\u1004\u103a 10 \u1021\u1031\u102c\u1037\u1016\u103a\u1006\u1000\u103a\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1011\u102c\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u101e\u1010\u102d\u1015\u103c\u102f\u1015\u102b\u104a \u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a \u101e\u1004\u1037\u103a\u1021\u1001\u103c\u1031\u1021\u1014\u1031\u1015\u1031\u102b\u103a\u1019\u1030\u1010\u100a\u103a\u104d \u1021\u1031\u102c\u1037\u1016\u103a\u1006\u1000\u103a\u1021\u1010\u103d\u1000\u103a \u101e\u1004\u103a\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101c\u102d\u102f\u101e\u100a\u1037\u103a\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u101e\u1004\u103a\u101b\u103d\u1031\u1038\u1001\u103b\u101a\u103a\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1006\u1000\u103a\u1005\u1015\u103a-<\/strong> <a href=\"https:\/\/statorials.org\/my\/ljung-box-\u1005\u1019\u103a\u1038\u101e\u1015\u103a-python\/\" target=\"_blank\" rel=\"noopener noreferrer\">Python \u1010\u103d\u1004\u103a Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1014\u100a\u103a\u1038<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1015\u100a\u102c\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038 Greta M. Ljung \u1014\u103e\u1004\u1037\u103a George EP Box \u1010\u102d\u102f\u1037\u1000\u102d\u102f \u1021\u1005\u103d\u1032\u1015\u103c\u102f\u104d \u1021\u1019\u100a\u103a\u1015\u1031\u1038\u1011\u102c\u1038\u101e\u100a\u1037\u103a Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f \u101e\u100a\u103a \u1021\u1001\u103b\u102d\u1014\u103a\u1005\u102e\u1038\u101b\u102e\u1038\u1010\u1005\u103a\u1001\u102f\u1021\u1010\u103d\u1004\u103a\u1038 autocorrelation \u101b\u103e\u102d\u1019\u101b\u103e\u102d\u1005\u1005\u103a\u1006\u1031\u1038\u101e\u100a\u1037\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f econometrics \u1014\u103e\u1004\u1037\u103a time series data \u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1021\u101e\u102f\u1036\u1038\u1019\u103b\u102c\u1038\u101e\u100a\u1037\u103a \u1021\u1001\u103c\u102c\u1038\u1014\u101a\u103a\u1015\u101a\u103a\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1010\u103d\u1004\u103a\u1000\u103b\u101a\u103a\u1005\u103d\u102c \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u101e\u100a\u103a\u104b Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f\u1021\u1001\u103c\u1031\u1001\u1036\u1019\u103b\u102c\u1038 \u1024\u101e\u100a\u103a\u1019\u103e\u102c Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u104f \u1021\u1001\u103c\u1031\u1001\u1036\u1021\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u101a\u1030\u1006\u1001\u103b\u1000\u103a Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a \u104b H 0 : \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1005\u103d\u102c \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u101e\u100a\u103a\u104b H A : \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1001\u103d\u1032\u101d\u1031\u1001\u103c\u1004\u103a\u1038\u1019\u1015\u103c\u102f\u1015\u102b\u104b \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u101e\u100a\u103a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f- \u1021\u1013\u102d\u1015\u1039\u1015\u102c\u101a\u103a\u1016\u103d\u1004\u1037\u103a\u1006\u102d\u102f\u1001\u103b\u1000\u103a + \u1025\u1015\u1019\u102c - Statorials<\/title>\n<meta name=\"description\" content=\"Ljung-Box test \u104f \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c \u101b\u103e\u1004\u103a\u1038\u101c\u1004\u103a\u1038\u1001\u103b\u1000\u103a\u104a \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u104f \u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u1016\u103d\u1004\u1037\u103a\u1006\u102d\u102f\u1001\u103b\u1000\u103a\u1014\u103e\u1004\u1037\u103a \u104e\u1004\u103a\u1038\u1000\u102d\u102f R \u1010\u103d\u1004\u103a \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u1025\u1015\u1019\u102c\u1010\u1005\u103a\u1001\u102f\u1021\u1015\u102b\u1021\u101d\u1004\u103a\u104a\" \/>\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\/my\/ljung-box-\u1000\u102d\u102f\u1005\u1019\u103a\u1038\u101e\u1015\u103a\/\" \/>\n<meta property=\"og:locale\" content=\"my_MM\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f- \u1021\u1013\u102d\u1015\u1039\u1015\u102c\u101a\u103a\u1016\u103d\u1004\u1037\u103a\u1006\u102d\u102f\u1001\u103b\u1000\u103a + \u1025\u1015\u1019\u102c - Statorials\" \/>\n<meta property=\"og:description\" content=\"Ljung-Box test \u104f \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c \u101b\u103e\u1004\u103a\u1038\u101c\u1004\u103a\u1038\u1001\u103b\u1000\u103a\u104a \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u104f \u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u1016\u103d\u1004\u1037\u103a\u1006\u102d\u102f\u1001\u103b\u1000\u103a\u1014\u103e\u1004\u1037\u103a \u104e\u1004\u103a\u1038\u1000\u102d\u102f R \u1010\u103d\u1004\u103a \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u1025\u1015\u1019\u102c\u1010\u1005\u103a\u1001\u102f\u1021\u1015\u102b\u1021\u101d\u1004\u103a\u104a\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/my\/ljung-box-\u1000\u102d\u102f\u1005\u1019\u103a\u1038\u101e\u1015\u103a\/\" \/>\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=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin Anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/my\/ljung-box-%e1%80%80%e1%80%ad%e1%80%af%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba\/\",\"url\":\"https:\/\/statorials.org\/my\/ljung-box-%e1%80%80%e1%80%ad%e1%80%af%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba\/\",\"name\":\"Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f- \u1021\u1013\u102d\u1015\u1039\u1015\u102c\u101a\u103a\u1016\u103d\u1004\u1037\u103a\u1006\u102d\u102f\u1001\u103b\u1000\u103a + \u1025\u1015\u1019\u102c - 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