{"id":122,"date":"2024-09-23T23:02:44","date_gmt":"2024-09-23T15:02:44","guid":{"rendered":"http:\/\/8.138.84.176\/?p=122"},"modified":"2024-09-23T23:02:44","modified_gmt":"2024-09-23T15:02:44","slug":"%e6%97%b6%e5%ba%8f%e5%88%86%e6%9e%90%e6%96%b9%e6%b3%95","status":"publish","type":"post","link":"https:\/\/blog.faspand.top\/index.php\/2024\/09\/23\/%e6%97%b6%e5%ba%8f%e5%88%86%e6%9e%90%e6%96%b9%e6%b3%95\/","title":{"rendered":"\u65f6\u5e8f\u5206\u6790\u65b9\u6cd5"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">1.\u76f8\u5173\u6982\u5ff5<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1.1\u6a21\u6001\uff08Modality\uff09<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">&#8220;\u6a21\u6001&#8221;\uff08Modality\uff09\u6307\u7684\u662f\u6570\u636e\u7684\u4e0d\u540c\u7c7b\u578b\u6216\u5f62\u5f0f<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1.2\u65f6\u5e8f\u6570\u636e\uff08Time Series Data)<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\"><em>1.2.1def.<\/em><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u65f6\u95f4\u5e8f\u5217<\/em>\u662f\u4ee5\u89c4\u5f8b\u7684\u65f6\u95f4\u95f4\u9694\u91c7\u96c6\u7684\u6d4b\u91cf\u503c\u7684\u6709\u5e8f\u96c6\u5408<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">1.2.2\u7279\u5f81<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u6570\u636e\u70b9\u4e4b\u95f4\u5b58\u5728\u65f6\u95f4\u987a\u5e8f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u65f6\u95f4\u5e8f\u5217\u7684\u987a\u5e8f\u548c\u65f6\u95f4\u95f4\u9694\u975e\u5e38\u91cd\u8981<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f9d\u8d56\u4e8e\u65f6\u95f4\uff0c\u4f46\u4e0d\u4e00\u5b9a\u662f\u65f6\u95f4\u7684\u4e25\u683c\u51fd\u6570<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">1.2.3\u5206\u7c7b<\/h4>\n\n\n\n<h5 class=\"wp-block-heading\">\u7814\u7a76\u5bf9\u8c61<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e00\u5143\u65f6\u95f4\u5e8f\u5217\u548c\u591a\u5143\u65f6\u95f4\u5e8f\u5217<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u65f6\u95f4\u53c2\u6570<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">\u79bb\u6563\u65f6\u95f4\u5e8f\u5217\u548c\u8fde\u7eed\u65f6\u95f4\u5e8f\u5217<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u7edf\u8ba1\u7279\u6027<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">\u5e73\u7a33\u65f6\u95f4\u5e8f\u5217\u548c\u975e\u5e73\u7a33\u65f6\u95f4\u5e8f\u5217<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u5206\u5e03\u89c4\u5f8b<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">\u9ad8\u65af\u578b\u65f6\u95f4\u5e8f\u5217\u548c\u975e\u9ad8\u65af\u578b\u65f6\u95f4\u5e8f\u5217<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u9ad8\u65af\u578b\u65f6\u95f4\u5e8f\u5217\u662f\u6307\u6570\u636e\u9075\u5faa\u6b63\u6001\u5206\u5e03\u7684\u65f6\u95f4\u5e8f\u5217<\/em><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1.3\u6587\u672c\u6570\u636e\uff08Textual Data\uff09<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">1.3.1def.<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0d\u80fd\u53c2\u4e0e\u7b97\u672f\u8fd0\u7b97\u7684\u4efb\u4f55\u5b57\u7b26\uff0c\u4e5f\u79f0\u4e3a\u5b57\u7b26\u578b\u6570\u636e\u3002\u5982\u82f1\u6587\u5b57\u6bcd\u3001\u6c49\u5b57\u3001\u4e0d\u4f5c\u4e3a\u6570\u503c\u4f7f\u7528\u7684\u6570\u5b57(\u4ee5\u5355\u5f15\u53f7\u5f00\u5934)\u548c\u5176\u4ed6\u53ef\u8f93\u5165\u7684\u5b57\u7b26<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">1.3.2\u7279\u5f81<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">1\u3001\u534a\u7ed3\u6784\u5316<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6587\u672c\u6570\u636e\u65e2\u4e0d\u662f\u5b8c\u5168\u65e0\u7ed3\u6784\u7684\u4e5f\u4e0d\u662f\u5b8c\u5168\u7ed3\u6784\u5316\u7684\u3002\u4f8b\u5982\u6587\u672c\u53ef\u80fd\u5305\u542b\u7ed3\u6784\u5b57\u6bb5\uff0c\u5982\u6807\u9898\u3001\u4f5c\u8005\u3001\u51fa\u7248\u65e5\u671f\u3001\u957f\u5ea6\u3001\u5206\u7c7b\u7b49\uff0c\u4e5f\u53ef\u80fd\u5305\u542b\u5927\u91cf\u7684\u975e\u7ed3\u6784\u5316\u7684\u6570\u636e\uff0c\u5982\u6458\u8981\u548c\u5185\u5bb9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2\u3001\u9ad8\u7ef4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6587\u672c\u5411\u91cf\u7684\u7ef4\u6570\u4e00\u822c\u90fd\u53ef\u4ee5\u9ad8\u8fbe\u4e0a\u4e07\u7ef4\uff0c\u4e00\u822c\u7684\u6570\u636e\u6316\u6398\u3001\u6570\u636e\u68c0\u7d22\u7684\u65b9\u6cd5\u7531\u4e8e\u8ba1\u7b97\u91cf\u8fc7\u5927\u6216\u4ee3\u4ef7\u9ad8\u6602\u800c\u4e0d\u5177\u6709\u53ef\u884c\u6027\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3\u3001\u9ad8\u6570\u636e\u91cf<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e00\u822c\u7684\u6587\u672c\u5e93\u4e2d\u90fd\u4f1a\u5b58\u5728\u6700\u5c11\u6570\u5343\u4e2a\u6587\u672c\u6837\u672c\uff0c\u5bf9\u8fd9\u4e9b\u6587\u672c\u8fdb\u884c\u9884\u5904\u7406\u3001\u7f16\u7801\u3001\u6316\u6398\u7b49\u5904\u7406\u7684\u5de5\u4f5c\u91cf\u662f\u975e\u5e38\u5e9e\u5927\u7684\uff0c\u56e0\u800c\u624b\u5de5\u65b9\u6cd5\u4e00\u822c\u662f\u4e0d\u53ef\u884c\u7684\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">4\u3001\u8bed\u4e49\u6027<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6587\u672c\u6570\u636e\u4e2d\u5b58\u5728\u7740\u4e00\u8bcd\u591a\u4e49\u3001\u591a\u8bcd\u4e00\u4e49\uff0c\u5728\u65f6\u95f4\u548c\u7a7a\u95f4\u4e0a\u7684\u4e0a\u4e0b\u6587\u76f8\u5173\u7b49\u60c5\u51b5\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">2\u65f6\u5e8f\u5206\u6790\u5e38\u7528\u65b9\u6cd5<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">2.1\u63cf\u8ff0\u6027\u65f6\u5e8f\u5206\u6790<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u63cf\u8ff0\u6027\u65f6\u5e8f\u5206\u6790\u53c8\u88ab\u79f0\u4e4b\u4e3a\u786e\u5b9a\u578b\u65f6\u5e8f\u5206\u6790\uff0c\u5b83\u4e3b\u8981\u662f\u901a\u8fc7\u76f4\u89c2\u7684\u6570\u636e\u6bd4\u8f83\u6216\u7ed8\u56fe\u89c2\u6d4b\uff0c\u5bfb\u627e\u5e8f\u5217\u4e2d\u8574\u542b\u7684\u53d1\u5c55\u89c4\u5f8b\u3002\u8be5\u65b9\u6cd5\u7b80\u5355\u76f4\u63a5\uff0c\u6240\u4ee5\u4e00\u822c\u4e5f\u662f\u65f6\u5e8f\u5206\u6790\u7684\u7b2c\u4e00\u6b65\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b\u5982\uff0c1844 \u5e74\uff0c\u5fb7\u56fd\u5929\u6587\u5b66\u5bb6\u6d77\u56e0\u5229\u5e0c\u00b7\u53f2\u74e6\u8d1d\u5728 Astronomische Nachrichten \u62a5\u544a\u4e86\u592a\u9633\u9ed1\u5b50\u6570\u91cf\u7684\u5468\u671f\u6027\u53d8\u5316\u89c4\u5f8b\u3002\u5176\u901a\u8fc7\u7cfb\u7edf\u6027\u7684\u8fde\u7eed\u89c2\u6d4b\uff0c\u53d1\u73b0\u592a\u9633\u9ed1\u5b50\u7684\u7206\u53d1\u5448\u73b0\u51fa 11 \u5e74\u4f5c\u7528\u7684\u5468\u671f\u53d8\u5316\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"http:\/\/img.nozomicloud.top\/blog\/2024\/09\/20240923133129462.png\" alt=\"\" class=\"wp-image-133\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u76f4\u89c2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bf9\u6570\u636e\u7684\u8981\u6c42\u5f88\u9ad8\uff0c\u9700\u8981\u4fdd\u8bc1\u6570\u636e\u5206\u5e03\u5448\u73b0\u51fa\u4e00\u5b9a\u7684\u89c4\u5f8b\u6027<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.2 \u7edf\u8ba1\u65f6\u5e8f\u5206\u6790<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5229\u7528\u6570\u7406\u7edf\u8ba1\u5b66\u76f8\u5173\u7684\u539f\u7406\u548c\u65b9\u6cd5\u6765\u5206\u6790\u65f6\u95f4\u5e8f\u5217<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">2.2.1 \u9891\u57df\u5206\u6790<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u5047\u8bbe\u4efb\u4f55\u4e00\u79cd\u65e0\u8d8b\u52bf\u7684\u65f6\u95f4\u5e8f\u5217\u90fd\u53ef\u4ee5\u5206\u89e3\u6210\u82e5\u5e72\u4e0d\u540c\u9891\u7387\u7684\u5468\u671f\u6ce2\u52a8<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">2.2.2 \u65f6\u57df\u5206\u6790<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u53c2\u7167\u4e8b\u4ef6\u53d1\u5c55\u8fc7\u7a0b\u4e2d\u7684\u60ef\u6027\uff0c\u4ece\u800c\u901a\u8fc7\u60ef\u6027\u7528\u7edf\u8ba1\u6765\u63cf\u8ff0\u5c31\u662f\u65f6\u95f4\u5e8f\u5217\u503c\u4e4b\u95f4\u5b58\u5728\u7684\u76f8\u5173\u5173\u7cfb,\u62df\u5408\u51fa\u9002\u5f53\u7684\u6570\u5b66\u6a21\u578b\u6765\u63cf\u8ff0\u8fd9\u79cd\u89c4\u5f8b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u81ea\u56de\u5f52 AR \u6a21\u578b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">ARMA \u6a21\u578b:\u5e73\u7a33\u65f6\u95f4\u5e8f\u5217\u5206\u6790\u8fc7\u7a0b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">ARIMA \u6a21\u578b:\u975e\u5e73\u7a33\u5e8f\u5217\u968f\u673a\u5206\u6790\u8fc7\u7a0b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.3 \u5e73\u7a33\u65f6\u95f4\u5e8f\u5217\u68c0\u9a8c<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">2.3.1 \u4e25\u5e73\u7a33\u65f6\u95f4\u5e8f\u5217<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u5e8f\u5217\u6240\u6709\u7684\u7edf\u8ba1\u6027\u8d28\u90fd\u4e0d\u4f1a\u968f\u7740\u65f6\u95f4\u7684\u63a8\u79fb\u800c\u53d1\u751f\u53d8\u5316<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">2.3.2 \u5bbd\u5e73\u7a33\u65f6\u95f4\u5e8f\u5217<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u53ea\u8981\u4fdd\u8bc1\u5e8f\u5217&nbsp;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Moment_mathematics\">\u4e8c\u9636\u77e9<\/a>&nbsp;\u5e73\u7a33\uff0c\u5c31\u4ee3\u8868\u5e8f\u5217\u7a33\u5b9a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.4 \u81ea\u76f8\u5173(Autocorrelation)\u56fe<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u53c8\u79f0\u4e4b\u4e3a\u5e8f\u5217\u76f8\u5173\u3002\u5728\u65f6\u95f4\u5e8f\u5217\u4e2d\uff0c\u5f53\u6211\u4eec\u4f7f\u7528\u4ee5\u524d\u7684\u65f6\u95f4\u6b65\u957f\u6765\u8ba1\u7b97\u65f6\u95f4\u5e8f\u5217\u89c2\u6d4b\u7684\u76f8\u5173\u6027\u65f6\u3002\u7531\u4e8e\u65f6\u95f4\u5e8f\u5217\u7684\u76f8\u5173\u6027\u4e0e\u4e4b\u524d\u7684\u76f8\u540c\u7cfb\u5217\u7684\u503c\u8fdb\u884c\u4e86\u8ba1\u7b97\uff0c\u5c31\u88ab\u79f0\u4e4b\u4e3a\u81ea\u76f8\u5173<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.5 \u7eaf\u968f\u673a\u6027\u68c0\u9a8c<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u7528\u6765\u5224\u65ad\u4e00\u4e2a\u5e73\u7a33\u5e8f\u5217\u662f\u5426\u968f\u673a=&gt;\u7eaf\u968f\u673a\u5e8f\u5217\u662f\u6ca1\u6709\u4efb\u4f55\u5206\u6790\u4ef7\u503c\u7684<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6d89\u53ca\u4e24\u4e2a\u7edf\u8ba1\u91cf\uff1aQ \u7edf\u8ba1\u91cf\u548c LB \u7edf\u8ba1\u91cf\uff08Ljung-Box\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f46\u7531\u4e8e LB \u7edf\u8ba1\u91cf\u662f Q \u7edf\u8ba1\u91cf\u7684\u4fee\u6b63\uff0c\u6240\u4ee5\u4e1a\u754c\u901a\u5e38\u6240\u79f0\u7684 Q \u7edf\u8ba1\u91cf\u4e5f\u5c31\u662f LB \u7edf\u8ba1\u91cf\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8ba1\u7b97\uff1aPython \u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528&nbsp;<code>statsmodels<\/code>&nbsp;\u7edf\u8ba1\u8ba1\u7b97\u5e93\u4e2d\u7684&nbsp;<code>acorr_ljungbox()<\/code>&nbsp;\u51fd\u6570\u8ba1\u7b97 LB \u7edf\u8ba1\u91cf\uff0c\u8be5\u51fd\u6570\u9ed8\u8ba4\u4f1a\u8fd4\u56de LB \u7edf\u8ba1\u91cf\u548c LB \u7edf\u8ba1\u91cf\u7684 P \u503c\u3002\u5982\u679c LB \u7edf\u8ba1\u91cf\u7684 P \u503c\u5c0f\u4e8e&nbsp;<code>0.05<\/code>\uff0c\u6211\u4eec\u5219\u8ba4\u4e3a\u8be5\u5e8f\u5217\u4e3a\u975e\u968f\u673a\u5e8f\u5217\uff0c\u5426\u5219\u5c31\u4e3a\u968f\u673a\u5e8f\u5217\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.6 &nbsp;ARMA\uff08<strong>A<\/strong>uto<strong>r<\/strong>egressive&nbsp;<strong>m<\/strong>oving&nbsp;<strong>a<\/strong>verage\uff09\u81ea\u56de\u5f52\u79fb\u52a8\u5e73\u5747\u6a21\u578b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u9002\u7528\u4e8e\u5e73\u7a33\u5e8f\u5217<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">2.6.1 \u5206\u7c7b<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">AR \u81ea\u56de\u5f52\u6a21\u578b\uff0cMA \u79fb\u52a8\u5e73\u5747\u6a21\u578b\u548c ARMA&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">AR\u6a21\u578b<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u5047\u8bbe\u5e8f\u5217\u5305\u542b\u7ebf\u6027\u5173\u7cfb\uff0c\u7136\u540e\u4f7f\u7528&nbsp;$x_{1}$&nbsp;\u81f3&nbsp;$x_{t\u22121}$&nbsp;\u5e8f\u5217\u6765\u9884\u6d4b&nbsp;$x_{t}$\u3002\u5176\u4e2d\uff0c$p$&nbsp;\u9636 AR \u6a21\u578b\u7684\u516c\u5f0f\u4e3a\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$X_{t}=c+\\sum _{{i=1}}^{p}\\varphi _{i}X_{{t-i}}+\\varepsilon_{t}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5176\u4e2d\uff0c$c$&nbsp;\u4e3a\u5e38\u6570\u9879\u3002$\u03b5_{t}$&nbsp;\u88ab\u5047\u8bbe\u4e3a\u5e73\u5747\u6570\u7b49\u4e8e 0\uff0c\u6807\u51c6\u5dee\u7b49\u4e8e&nbsp;$\u03c3$\u7684\u968f\u673a\u8bef\u5dee\u503c\u3002$\u03c3$&nbsp;\u88ab\u5047\u8bbe\u4e3a\u5bf9\u4e8e\u4efb\u4f55\u7684&nbsp;$t$&nbsp;\u90fd\u4e0d\u53d8\u3002$p$&nbsp;\u5219\u4ee3\u8868\u843d\u540e\u671f\u6570\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">MA\u6a21\u578b<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u82e5\u968f\u673a\u8fc7\u7a0b\u00a0$x_{t}$\u00a0\u4e3a\u73b0\u5728\u4e0e\u8fc7\u53bb\u00a0$q$\u00a0\u671f\u968f\u673a\u8fc7\u7a0b\u00a0$\u03b5_{t},\u03b5_{t\u22121},&#8230;,\u03b5_{t\u2212q}$\u00a0\u4e4b\u52a0\u6743\u5e73\u5747\uff0c\u5219\u00a0$q$\u00a0\u9636 MA \u6a21\u578b\u7684\u516c\u5f0f\u4e3a\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">${x_{t}=\\varepsilon _{t} + \\theta _{1}\\varepsilon _{t-1} +<br>                    \\theta _{2}\\varepsilon _{t-2} + \\cdots + \\theta<br>                    _{q}\\varepsilon _{t-q}}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5176\u4e2d\uff0c$\u03b8_{1},&#8230;,\u03b8_{q}$&nbsp;\u662f\u53c2\u6570\uff0c$\u03b5_{t},\u03b5_{t\u22121},&#8230;,\u03b5_{t\u2212q}$&nbsp;\u90fd\u662f\u767d\u566a\u58f0\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">ARMA<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">ARMA \u6a21\u578b\u4e00\u822c\u8bb0\u4f5c\uff1a$ARMA(p,q)$\uff0c\u5373\u4e3a&nbsp;$p$&nbsp;\u9636 AR \u548c&nbsp;$q$&nbsp;\u9636 MA \u6a21\u578b\u7684\u7ec4\u5408\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u5efa\u6a21\u8fc7\u7a0b<\/h5>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u83b7\u53d6\u5e8f\u5217<\/li>\n\n\n\n<li>\u901a\u8fc7\u5e73\u7a33\u6027\u68c0\u9a8c<\/li>\n\n\n\n<li>\u901a\u8fc7\u7eaf\u968f\u673a\u6027\u68c0\u9a8c&nbsp;<\/li>\n\n\n\n<li>\u9700\u8981\u786e\u5b9a&nbsp;$p$&nbsp;\u548c&nbsp;$q$&nbsp;\u7684\u53d6\u503c\u3002\u4e00\u822c\u6765\u8bb2\uff0c\u786e\u5b9a\u4e8c\u8005\u7684\u53d6\u503c\u6709 3 \u79cd\u65b9\u6cd5\uff0c\u5206\u522b\u662f AIC\uff08Akaike Information Criterion \uff09\uff0cBIC\uff08Bayesian Information Criterion \uff09 \u548c HQIC\uff08Hannan-Quinn Criterion \uff09\u3002<\/li>\n\n\n\n<li>\u642d\u5efa ARMA \u6a21\u578b<\/li>\n\n\n\n<li>\u6a21\u578b\u8bc4\u4f30<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">2.7 \u5dee\u5206\u8fd0\u7b97<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u76ee\u7684\uff1a\u5e8f\u5217\u5e73\u7a33\u7684\u65b9\u6cd5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5dee\u5206\u8fd0\u7b97\u5b9e\u9645\u4e0a\u662f\u4e00\u79cd\u4ece\u5e8f\u5217\u4e2d\u63d0\u53d6\u786e\u5b9a\u6027\u4fe1\u606f\u7684\u65b9\u6cd5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1\u9636\u5dee\u5206\uff1a\u5bf9\u4e24\u4e2a\u5e8f\u5217\u76f8\u90bb\u503c\uff08\u5ef6\u8fdf 1 \u671f <code>\u65f6\u95f4\u95f4\u9694<\/code>\uff09\u4f5c\u51cf\u6cd5\u8fd0\u7b97<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\nabla x_t = x_t &#8211; x_{t-1}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b64\u65f6\uff0c\u5982\u679c\u5bf9\u00a0$1$\u00a0\u9636\u5dee\u5206\u540e\u7684\u5e8f\u5217\u518d\u8fdb\u884c\u4e00\u6b21\u00a0$1$\u00a0\u9636\u5dee\u5206\u8fd0\u7b97\uff0c\u5c31\u53ef\u4ee5\u8bb0\u00a0$\u2207^{2}x_{t}$\u00a0\u4e3a\u00a0$x_{t}$\u00a0\u7684\u00a0$2$\u00a0\u9636\u5dee\u5206\uff0c\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\nabla^2 x_t = \\nabla x_t &#8211; \\nabla x_{t-1}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u90a3\u4e48\uff0c\u4f9d\u6b21\u7c7b\u63a8\uff0c\u5bf9\u00a0$p\u22121$\u00a0\u9636\u5dee\u5206\u540e\u5e8f\u5217\u518d\u8fdb\u884c\u4e00\u6b21\u00a0$1$\u00a0\u9636\u5dee\u5206\u8fd0\u7b97\uff0c\u5c31\u53ef\u4ee5\u8bb0\u00a0$\u2207^{p}x_{t}$\u00a0\u4e3a\u00a0$x_{t}$\u00a0\u7684\u00a0$p$\u00a0\u9636\u5dee\u5206\uff0c\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\nabla^p x_t = \\nabla^{p-1} x_t &#8211; \\nabla^{p-1} x_{t-1}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9664\u6b64\u4e4b\u5916\uff0c\u5982\u679c\u4e24\u4e2a\u5e8f\u5217\u503c\u4e4b\u95f4\u5ef6\u8fdf\u00a0$k$\u00a0\u671f\u518d\u505a\u51cf\u6cd5\u8fd0\u7b97\u79f0\u4e3a\u00a0$k$\u00a0\u6b65\u5dee\u5206\u8fd0\u7b97\uff0c\u8bb0\u00a0$\u2207_kx^t$\u00a0\u4e3a\u00a0$x_t$\u00a0\u7684\u00a0$k$\u00a0\u9636\u6b65\u5dee\u5206\uff0c\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\nabla_k x_t = x_t &#8211; x_{t-k}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e00\u822c\u5728\u5dee\u5206\u65f6\u9636\u6570\u4e0d\u5b9c\u8fc7\u5927\u3002\u539f\u56e0\u5728\u4e8e\u5dee\u5206\u5176\u5b9e\u662f\u5bf9\u4fe1\u606f\u63d0\u53d6\u52a0\u5de5\u7684\u8fc7\u7a0b\uff0c\u6bcf\u6b21\u5dee\u5206\u90fd\u4f1a\u5e26\u6765\u4fe1\u606f\u635f\u5931\uff0c\u8fc7\u5ea6\u5dee\u5206\u4f1a\u5bfc\u81f4\u6709\u6548\u4fe1\u606f\u635f\u5931\u800c\u964d\u4f4e\u7cbe\u5ea6\u3002\u4e00\u822c\u60c5\u51b5\u4e0b\uff0c\u7ebf\u6027\u53d8\u5316\u901a\u8fc7 1 \u6b21\u5dee\u5206\u5373\u53ef\u5e73\u7a33\uff0c\u975e\u7ebf\u6027\u8d8b\u52bf 2\uff0c3 \u6b21\u5dee\u5206\u4e5f\u80fd\u53d8\u5f97\u5e73\u7a33\uff0c\u4e00\u822c\u5dee\u5206\u6b21\u6570\u4e0d\u8d85\u8fc7 2 \u6b21\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.8 &nbsp;ARIMA \u4ecb\u7ecd\u53ca\u5efa\u6a21<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u975e\u5e73\u7a33<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u76f8\u6bd4\u4e8e ARMA \u6a21\u578b\u4e2d\u5b58\u5728\u7684&nbsp;$p$,&nbsp;$q$&nbsp;\u53c2\u6570\uff0cARIMA \u591a\u4e86\u4e00\u4e2a\u53c2\u6570\uff0c\u90a3\u5c31\u662f\u4f7f\u975e\u5e73\u7a33\u5e8f\u5217\u6210\u4e3a\u5e73\u7a33\u5e8f\u5217\u6240\u505a\u7684\u5dee\u5206\u9636\u6570&nbsp;$d$\u3002\u6240\u4ee5\uff0cARIMA \u6a21\u578b\u901a\u5e38\u8bb0\u4f5c\uff1a$ARIMA(p,d,q)$\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"http:\/\/img.nozomicloud.top\/blog\/2024\/09\/20240923133129153.png\" alt=\"\" class=\"wp-image-134\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>1.\u76f8\u5173\u6982\u5ff5 1.1\u6a21\u6001\uff08Modality\uff09 &#8220;\u6a21\u6001&#8221;\uff08Modality\uff09\u6307\u7684\u662f\u6570\u636e\u7684 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":200,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[15,19,21],"class_list":["post-122","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-notes","tag-15","tag-19","tag-21"],"_links":{"self":[{"href":"https:\/\/blog.faspand.top\/index.php\/wp-json\/wp\/v2\/posts\/122","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.faspand.top\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.faspand.top\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.faspand.top\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.faspand.top\/index.php\/wp-json\/wp\/v2\/comments?post=122"}],"version-history":[{"count":0,"href":"https:\/\/blog.faspand.top\/index.php\/wp-json\/wp\/v2\/posts\/122\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.faspand.top\/index.php\/wp-json\/wp\/v2\/media\/200"}],"wp:attachment":[{"href":"https:\/\/blog.faspand.top\/index.php\/wp-json\/wp\/v2\/media?parent=122"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.faspand.top\/index.php\/wp-json\/wp\/v2\/categories?post=122"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.faspand.top\/index.php\/wp-json\/wp\/v2\/tags?post=122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}