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\u4f5c\u8005\uff1a\u8001\u4f59\u635e\u9c7c<\/a><\/p>\n\n\n\n

\u539f\u521b\u4e0d\u6613\uff0c\u8f6c\u8f7d\u8bf7\u6807\u660e\u51fa\u5904\u53ca\u539f\u4f5c\u8005\u3002<\/mark><\/strong><\/p>\n\n\n\n

\u672c\u6587\u7ea6 3800 \u5b57 | \u9605\u8bfb\u9884\u8ba1\u9700\u00a015 \u5206\u949f\uff0c\u5efa\u8bae\u5148\u6536\u85cf<\/p>\n\n\n\n

\n\n\n\n
\n

\u5199\u5728\u524d\u9762\u7684\u8bdd\uff1a<\/strong>\u8bfb\u5b8c\u5168\u6587\u540e\uff0c\u4f60\u5c06\u641e\u6e05\u695a\uff1a\u65f6\u95f4\u5e8f\u5217\u5230\u5e95\u662f\u4e2a\u4ec0\u4e48\u4e1c\u897f\u3001\u4e3a\u4ec0\u4e48\u6a21\u578b\u7ed9\u51fa\u7684\u9884\u671f\u503c\u51e0\u4e4e\u603b\u662f\u9519\u7684\u3001\u9a71\u52a8\u65f6\u95f4\u5e8f\u5217\u5206\u6790\u7684\u4e09\u5927\u6838\u5fc3\u4efb\u52a1\u3001\u4ece\u539f\u59cb\u6570\u636e\u5230\u4ea4\u6613\u4fe1\u53f7\u7684\u5b8c\u6574\u5b9e\u73b0\u6d41\u7a0b\u3001\u4ee5\u53ca\u5bfc\u81f490%\u7684\u65f6\u95f4\u5e8f\u5217\u6a21\u578b\u5728\u78b0\u771f\u94b1\u4e4b\u524d\u5c31\u5931\u6548\u7684\u90a3\u4e2a\u5173\u952e\u9677\u9631\u3002<\/p>\n<\/blockquote>\n\n\n\n

\u4e00\u3001\u65f6\u95f4\u5e8f\u5217\u5230\u5e95\u662f\u4ec0\u4e48\uff1f<\/h2>\n\n\n\n

\u65f6\u95f4\u5e8f\u5217<\/strong>\uff0c\u8bf4\u767d\u4e86\u5c31\u662f\u6309\u56fa\u5b9a\u65f6\u95f4\u95f4\u9694\u8bb0\u5f55\u4e0b\u6765\u7684\u4e00\u4e32\u89c2\u5bdf\u503c\u3002\u80a1\u7968\u6bcf\u5929\u7684\u6536\u76d8\u4ef7\u3001\u6c14\u6e29\u6bcf\u5c0f\u65f6\u8bfb\u6570\u3001\u6bcf\u6708\u5931\u4e1a\u7387\u6570\u5b57\u3002\u8fd9\u4e9b\u90fd\u662f\u6309\u65f6\u95f4\u7d22\u5f15\u6392\u5217\u7684\u4e00\u7ec4\u6570\u503c\u3002<\/p>\n\n\n\n

\u8fd9\u4e2a\u5b9a\u4e49\u6280\u672f\u4e0a\u6ca1\u9519\uff0c\u4f46\u5b9e\u9645\u7528\u5904\u4e0d\u5927\u3002<\/p>\n\n\n\n

\u5927\u591a\u6570\u4eba\u5ffd\u7565\u7684\u5173\u952e\u70b9\u662f\uff1a\u6bcf\u4e00\u4e2a\u65f6\u95f4\u5e8f\u5217\u90fd\u662f\u7531\u67d0\u79cd\u4e1c\u897f\u751f\u6210\u7684\u3002<\/strong><\/p>\n\n\n\n

\u4e00\u53ea\u80a1\u7968\u7684\u4ef7\u683c\u8d70\u52bf\u4e0d\u662f\u51ed\u7a7a\u5192\u51fa\u6765\u7684\uff0c\u5b83\u662f\u6570\u4ee5\u767e\u4e07\u8ba1\u7684\u6295\u8d44\u4eba\u51b3\u7b56\u3001\u7b97\u6cd5\u6267\u884c\u3001\u5b8f\u89c2\u7ecf\u6d4e\u529b\u91cf\u5171\u540c\u4f5c\u7528\u7684\u7ed3\u679c\uff0c\u8fd9\u4e9b\u56e0\u7d20\u4f60\u65e0\u6cd5\u4ec5\u4ece\u4ef7\u683c\u5e8f\u5217\u4e0a\u76f4\u63a5\u89c2\u5bdf\u5230\u3002\u7ecf\u6d4e\u5b66\u5bb6\u628a\u4ef7\u683c\u53eb\u505a“\u5185\u751f\u53d8\u91cf”<\/strong>\uff0c\u771f\u6b63\u9a71\u52a8\u5b83\u7684\u662f\u90a3\u4e2a\u770b\u4e0d\u89c1\u7684\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u56fe\uff1a\u65f6\u95f4\u5e8f\u5217\u7531\u8d8b\u52bf\u3001\u5b63\u8282\u6027\u548c\u968f\u673a\u51b2\u51fb\u4e09\u90e8\u5206\u7ec4\u6210<\/p>\n\n\n\n

\u4efb\u4f55\u4e00\u4e2a\u65f6\u95f4\u5e8f\u5217\u90fd\u53ef\u4ee5\u62c6\u89e3\u6210\u4e09\u4e2a\u6210\u5206\uff1a<\/strong><\/p>\n\n\n\n

\u6210\u5206<\/th>\u542b\u4e49<\/th>\u5e02\u573a\u4e2d\u7684\u4f8b\u5b50<\/th><\/tr>
\u8d8b\u52bf (Trend)<\/strong><\/td>\u957f\u671f\u65b9\u5411\u6027\u8fd0\u52a8<\/td>\u6307\u6570\u957f\u671f\u4e0a\u884c\/\u4e0b\u884c\u8f68\u8ff9<\/td><\/tr>
\u5b63\u8282\u6027 (Seasonality)<\/strong><\/td>\u56fa\u5b9a\u95f4\u9694\u91cd\u590d\u51fa\u73b0\u7684\u6a21\u5f0f<\/td>\u6708\u5ea6\u9500\u552e\u5468\u671f\u3001\u5b63\u5ea6\u8d22\u62a5\u6548\u5e94\u3001\u5468\u5185\u6210\u4ea4\u91cf\u89c4\u5f8b<\/td><\/tr>
\u51b2\u51fb\/\u6b8b\u5dee (Shock)<\/strong><\/td>\u56f4\u7ed5\u8d8b\u52bf\u548c\u5b63\u8282\u6027\u7684\u968f\u673a\u6ce2\u52a8<\/td>\u7a81\u53d1\u4e8b\u4ef6\u3001\u65b0\u95fb\u3001\u610f\u5916\u6d88\u606f<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

\u5173\u4e8e\u8d8b\u52bf\u548c\u5b63\u8282\u6027\uff0c\u6709\u4e00\u4e2a\u975e\u5e38\u5173\u952e\u7684\u8ba4\u77e5\uff1a\u5b83\u4eec\u53ea\u6709\u5728\u7a33\u5b9a\u7684\u65f6\u5019\u624d\u6709\u610f\u4e49\u3002<\/strong><\/p>\n\n\n\n

\u5982\u679c\u4e00\u53ea\u80a1\u7968\u7684\u8d8b\u52bf\u6bcf\u51e0\u4e2a\u5c0f\u65f6\u5c31\u53cd\u8f6c\u4e00\u6b21\uff0c\u90a3\u8d8b\u52bf\u6210\u5206\u5bf9\u4f60\u6765\u8bf4\u6ca1\u6709\u4efb\u4f55\u53c2\u8003\u4ef7\u503c\u3002\u7a33\u5b9a\u6027\u662f\u4efb\u4f55\u65f6\u95f4\u5e8f\u5217\u6a21\u578b\u5177\u5907\u524d\u77bb\u4ef7\u503c\u7684\u524d\u63d0\u6761\u4ef6\u3002<\/strong><\/p>\n\n\n\n

\u6253\u4e2a\u6bd4\u65b9\uff1a\u5047\u8bbe\u73b0\u5728\u662f12\u6708\u7684\u7ebd\u7ea6\uff0c\u5f53\u524d\u6c14\u6e29\u96f6\u4e0b6\u6444\u6c0f\u5ea6\u3002\u5982\u679c\u8ba9\u4f60\u731c\u660e\u5929\u7684\u6e29\u5ea6\uff0c\u4f60\u5927\u6982\u4f1a\u8bf4\u8fd8\u662f\u5dee\u4e0d\u591a\u96f6\u4e0b\u51e0\u5ea6\u4e0a\u4e0b\u3002\u4f60\u4e0d\u662f\u5728\u505a\u7cbe\u786e\u9884\u6d4b\uff0c\u4f60\u662f\u57fa\u4e8e\u5f53\u524d\u72b6\u6001\u548c\u5df2\u77e5\u7684\u5b63\u8282\u6a21\u5f0f\u7ed9\u51fa\u4e00\u4e2a\u671f\u671b\u503c<\/strong>\u3002\u8fd9\u4e2a\u671f\u671b\u503c\u5728\u6b63\u5e38\u60c5\u51b5\u4e0b\u662f\u5bf9\u7684\u3002<\/p>\n\n\n\n

\u4f46\u5982\u679c\u51b0\u5c9b\u7a81\u7136\u706b\u5c71\u7206\u53d1\uff0c\u5168\u7403\u6c14\u6e29\u4e00\u5468\u5185\u98d9\u53478\u6444\u6c0f\u5ea6\u5462\uff1f\u4f60\u7684\u6e29\u5ea6\u9884\u6d4b\u4f1a\u4e25\u91cd\u504f\u79bb\u3002\u4e0d\u662f\u56e0\u4e3a\u6a21\u578b\u4e0d\u597d\u7528\u4e86\uff0c\u800c\u662f\u56e0\u4e3a\u751f\u6210\u6570\u636e\u7684\u5e95\u5c42\u8fc7\u7a0b\u53d1\u751f\u4e86\u53d8\u5316<\/strong>\uff0c\u800c\u8fd9\u79cd\u53d8\u5316\u5728\u6e29\u5ea6\u5e8f\u5217\u4e0a\u662f\u5b8c\u5168\u770b\u4e0d\u5230\u7684\u3002<\/p>\n\n\n\n

\u8fd9\u8ddf2008\u5e74\u62b5\u62bc\u8d37\u6b3e\u8bc1\u5238\u7684\u60c5\u51b5\u4e00\u6a21\u4e00\u6837\u3002\u4ef7\u683c\u5e8f\u5217\u770b\u8d77\u6765\u4e00\u5207\u6b63\u5e38\uff0c\u4f46\u5e95\u5c42\u7684\u771f\u5b9e\u4fe1\u7528\u72b6\u51b5\u5df2\u7ecf\u53d8\u4e86\u3002\u5173\u952e\u4fe1\u606f\u6839\u672c\u4e0d\u5728\u4ef7\u683c\u5e8f\u5217\u91cc\u9762\u3002<\/p>\n\n\n\n

\n

\u8001\u4f59\u63d0\u9192\uff1a<\/strong>\u62ff\u4f60\u73b0\u5728\u5173\u6ce8\u7684\u4efb\u610f\u4e00\u4e2a\u54c1\u79cd\uff0c\u7528\u4e00\u53e5\u8bdd\u5199\u4e0b\u4f60\u8ba4\u4e3a\u9a71\u52a8\u5b83\u4ef7\u683c\u53d8\u52a8\u7684\u6700\u4e3b\u8981\u56e0\u7d20\u662f\u4ec0\u4e48\u3002\u90a3\u4e2a\u56e0\u7d20\u5c31\u662f\u4f60\u4f7f\u7528\u4efb\u4f55\u65f6\u95f4\u5e8f\u5217\u6a21\u578b\u65f6\u5fc5\u987b\u540c\u65f6\u76d1\u63a7\u7684\u4e1c\u897f\u3002\u4e00\u65e6\u5b83\u53d8\u4e86\uff0c\u4f60\u7684\u6a21\u578b\u5c31\u5f97\u91cd\u5efa\u3002<\/p>\n<\/blockquote>\n\n\n\n

\u4e8c\u3001\u4e3a\u4ec0\u4e48\u9884\u671f\u503c\u603b\u662f”\u9519”\u7684\uff1f<\/h2>\n\n\n\n

\u6240\u6709\u65f6\u95f4\u5e8f\u5217\u5206\u6790\u7684\u5e94\u7528\u90fd\u9003\u4e0d\u51fa\u4e09\u4e2a\u7c7b\u522b\u3002\u641e\u6e05\u695a\u4f60\u5728\u505a\u54ea\u4e00\u7c7b\uff0c\u80fd\u5e2e\u4f60\u907f\u5f00\u91cf\u5316\u91d1\u878d\u91cc\u6700\u5e38\u89c1\u4e5f\u6700\u6602\u8d35\u7684\u4e00\u4e2a\u5751\u3002<\/p>\n\n\n\n

\u4efb\u52a1\u4e00\uff1a\u6ee4\u6ce2 (Filtering)<\/h3>\n\n\n\n

\u6ee4\u6ce2\u662f\u7528\u8fc7\u53bb\u548c\u73b0\u5728\u7684\u6570\u636e\u6765\u4f30\u8ba1\u7cfb\u7edf\u7684\u5f53\u524d\u72b6\u6001<\/strong>\u3002\u4f60\u8981\u505a\u7684\u662f\u5265\u79bb\u566a\u58f0\uff0c\u770b\u6e05\u73b0\u5728\u5230\u5e95\u5728\u53d1\u751f\u4ec0\u4e48\u3002<\/p>\n\n\n\n

\u79fb\u52a8\u5e73\u5747\u7ebf\u5c31\u662f\u4e00\u4e2a\u6ee4\u6ce2\u5668\u3002\u5b83\u4e0d\u9884\u6d4b\u672a\u6765\uff0c\u5b83\u53ea\u662f\u544a\u8bc9\u4f60\u8fc7\u53bb\u4e00\u6bb5\u65f6\u95f4\u7684\u5e73\u5747\u6c34\u5e73\u662f\u591a\u5c11\u3002\u4f60\u5728\u4ea4\u6613\u8f6f\u4ef6\u56fe\u8868\u4e0a\u653e\u7684\u6bcf\u4e00\u4e2a\u6307\u6807\uff0c\u672c\u8d28\u4e0a\u90fd\u5728\u505a\u67d0\u79cd\u5f62\u5f0f\u7684\u6ee4\u6ce2\u5de5\u4f5c\u3002\u5f53\u4f60\u653e\u4e0a\u4e00\u676120\u65e5\u5747\u7ebf\u65f6\uff0c\u4f60\u5b9e\u9645\u4e0a\u662f\u5728\u8bf4\uff1a”\u6211\u60f3\u770b\u770b\u8fd9\u4e2a\u8d44\u4ea7\u5265\u79bb\u4e86\u77ed\u671f\u566a\u58f0\u4e4b\u540e\u7684\u771f\u5b9e\u72b6\u6001\u3002”\u5c31\u8fd9\u4e48\u7b80\u5355\u3002<\/p>\n\n\n\n

\u4efb\u52a1\u4e8c\uff1a\u5e73\u6ed1 (Smoothing)<\/h3>\n\n\n\n

\u5e73\u6ed1\u662f\u7528\u8fc7\u53bb\u548c\u672a\u6765<\/strong>\u7684\u6570\u636e\u6765\u4f30\u8ba1\u67d0\u4e2a\u5386\u53f2\u65f6\u523b\u7684\u72b6\u6001\u3002\u5b83\u9700\u8981\u7528\u5230”\u540e\u89c6\u4fe1\u606f”\uff0c\u4e5f\u5c31\u662f\u8bf4\u4f60\u9700\u8981\u77e5\u9053\u4e00\u4e2a\u65f6\u95f4\u70b9\u4e4b\u540e\u53d1\u751f\u4e86\u4ec0\u4e48\uff0c\u624d\u80fd\u6700\u597d\u5730\u523b\u753b\u90a3\u4e2a\u65f6\u95f4\u70b9\u5f53\u65f6\u7684\u72b6\u6001\u3002<\/p>\n\n\n\n

\u5e73\u6ed1\u5bf9\u5206\u6790\u5386\u53f2\u6570\u636e\u548c\u6784\u5efa\u7814\u7a76\u6570\u636e\u96c6\u5f88\u6709\u7528\uff0c\u4f46\u5b83\u4e0d\u80fd\u76f4\u63a5\u7528\u4e8e\u5b9e\u65f6\u4ea4\u6613\u51b3\u7b56<\/strong>\uff0c\u56e0\u4e3a\u5b83\u9700\u8981\u672a\u6765\u7684\u4fe1\u606f\u3002<\/p>\n\n\n\n

\u4efb\u52a1\u4e09\uff1a\u9884\u671f (Forecasting)<\/h3>\n\n\n\n

\u9884\u671f\u662f\u7528\u5f53\u524d\u548c\u8fc7\u53bb\u7684\u72b6\u6001\u6765\u4ea7\u751f\u4e00\u4e2a\u5173\u4e8e\u672a\u6765\u7684\u671f\u671b\u503c\u3002\u8fd9\u662f\u5927\u591a\u6570\u4eba\u6700\u5173\u6ce8\u7684\u5730\u65b9\uff0c\u4e5f\u662f\u8bef\u89e3\u6700\u96c6\u4e2d\u7684\u5730\u65b9\u3002<\/p>\n\n\n\n

\n

E[X\u209c\u208a\u2081 | X\u2081, X\u2082, \u2026, X\u209c]<\/strong><\/p>\n<\/blockquote>\n\n\n\n

\u4e0a\u9762\u8fd9\u4e2a\u516c\u5f0f\u5c31\u662f\u6761\u4ef6\u671f\u671b\uff0c\u7ed9\u5b9a\u5230\u76ee\u524d\u4e3a\u6b62\u6240\u6709\u89c2\u6d4b\u503c\u7684\u60c5\u51b5\u4e0b\uff0c\u4e0b\u4e00\u4e2a\u503c\u7684\u6570\u5b66\u671f\u671b\u3002<\/p>\n\n\n\n

\u8fd9\u91cc\u6709\u4e00\u4e2a\u7edd\u5927\u591a\u6570\u4ea4\u6613\u7c7b\u6559\u80b2\u90fd\u4e0d\u613f\u610f\u660e\u786e\u8bf4\u51fa\u6765\u7684\u771f\u76f8\uff1a<\/strong><\/p>\n\n\n\n

\n

\u9884\u671f \u2260 \u9884\u6d4b\u3002\u5b83\u4eec\u4e0d\u662f\u4e00\u56de\u4e8b\u3002<\/strong>\u671f\u671b\u503c\u662f\u5728\u6240\u6709\u53ef\u80fd\u672a\u6765\u7ed3\u679c\u4e2d\u4f7f\u5747\u65b9\u8bef\u5dee\u6700\u5c0f\u7684\u90a3\u4e2a\u5355\u4e00\u6570\u503c\u3002\u5f53\u4f60\u63b7\u4e00\u679a\u516c\u5e73\u9ab0\u5b50\u65f6\uff0c\u671f\u671b\u503c\u662f3.5\u3002\u9ab0\u5b50\u80fd\u63b7\u51fa3.5\u5417\uff1f\u4e0d\u80fd\u3002\u4f463.5\u4ecd\u7136\u662f\u4f60\u505a\u51b3\u7b56\u65f6\u6700\u6709\u7528\u7684\u6570\u5b57\uff0c\u56e0\u4e3a\u5b83\u662f\u957f\u671f\u6eda\u52a8\u4e2d\u4f7f\u4f60\u7684\u5e73\u5747\u8bef\u5dee\u6700\u5c0f\u5316\u7684\u503c\u3002<\/p>\n<\/blockquote>\n\n\n\n

\u5e02\u573a\u9884\u671f\u7684\u5de5\u4f5c\u65b9\u5f0f\u5b8c\u5168\u4e00\u6837\u3002\u4f60\u7684\u6a21\u578b\u6839\u636e\u5df2\u6709\u4fe1\u606f\u4ea7\u751f\u6700\u4f73\u671f\u671b\u503c\u3002\u8fd9\u4e2a\u671f\u671b\u503c\u57fa\u672c\u4e0a\u6c38\u8fdc\u4e0d\u4f1a\u7b49\u4e8e\u6700\u7ec8\u5b9e\u73b0\u7684\u4ef7\u683c\u3002\u4f46\u53ea\u8981\u5b83\u5728\u5e73\u5747\u610f\u4e49\u4e0a\u662f\u5bf9\u7684\uff0c\u800c\u4e14\u4f60\u80fd\u7cfb\u7edf\u5730\u5229\u7528\u8fd9\u4e00\u70b9\uff0c\u5c31\u80fd\u4ea7\u751f\u6301\u7eed\u6027\u7684\u6536\u76ca\u3002<\/p>\n\n\n\n

\u8fd9\u6b63\u662f\u505a\u5e02\u5546\u7684\u8fd0\u4f5c\u65b9\u5f0f\u3002\u4ed6\u4eec\u4e0d\u9700\u8981\u77e5\u9053\u4ef7\u683c\u786e\u5207\u4f1a\u53bb\u54ea\u3002\u4ed6\u4eec\u9700\u8981\u77e5\u9053\u671f\u671b\u4ef7\u683c\uff0c\u7136\u540e\u5728\u5468\u56f4\u62a5\u51fa\u4e70\u5356\u4ef7\u5dee\uff0c\u901a\u8fc7\u6570\u5343\u7b14\u4ea4\u6613\u7684\u79ef\u7d2f\u6765\u83b7\u5229\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u56fe\uff1a\u9884\u671f\u662f\u6761\u4ef6\u671f\u671b\uff0c\u662f\u4f7f\u8bef\u5dee\u6700\u5c0f\u5316\u7684\u5355\u4e00\u503c\uff0c\u5b83\u51e0\u4e4e\u6c38\u8fdc\u4e0d\u7b49\u4e8e\u5b9e\u9645\u503c<\/p>\n\n\n\n

\n

\u6838\u5fc3\u7ed3\u8bba<\/strong>
\u7cfb\u7edf\u5316\u4ea4\u6613\u4f7f\u7528\u65f6\u95f4\u5e8f\u5217\u5206\u6790\u7684\u6838\u5fc3\u903b\u8f91\u662f\uff1a\u4f60\u4e0d\u9700\u8981\u5b8c\u7f8e\u7684\u9884\u671f\u503c\uff0c\u4f60\u53ea\u9700\u8981\u5728\u5e73\u5747\u610f\u4e49\u4e0a\u6b63\u786e<\/strong>\u7684\u9884\u671f\u503c\uff0c\u5e76\u4e14\u9891\u7387\u9ad8\u5230\u8db3\u4ee5\u8986\u76d6\u4ea4\u6613\u6210\u672c\u3002\u540c\u65f6\u4f60\u9700\u8981\u4e00\u5957\u4e25\u683c\u7684\u6846\u67b6\u6765\u5224\u65ad\u6a21\u578b\u4ec0\u4e48\u65f6\u5019\u4e0d\u518d”\u8fd1\u4f3c\u6b63\u786e”\u3002<\/p>\n<\/blockquote>\n\n\n\n

\u4e09\u3001\u5355\u4f4d\u6839\u9677\u9631\uff1a\u6bc1\u6389\u5927\u591a\u6570\u6a21\u578b\u7684\u9690\u5f62\u6740\u624b<\/h2>\n\n\n\n

\u8fd9\u4e00\u8282\u7684\u5185\u5bb9\u80fd\u5e2e\u4f60\u907f\u5f00\u91cf\u5316\u91d1\u878d\u4e2d\u6700\u5e38\u89c1\u3001\u4ee3\u4ef7\u6700\u9ad8\u7684\u9519\u8bef\uff1a\u5728\u975e\u5e73\u7a33\u6570\u636e\u4e0a\u8dd1\u56de\u5f52\u6a21\u578b<\/strong>\u3002<\/p>\n\n\n\n

\u5f88\u591a\u4eba\u60f3\u7ed9\u80a1\u4ef7\u5efa\u9884\u6d4b\u6a21\u578b\uff0c\u7b2c\u4e00\u6b65\u5c31\u662f\u62ff\u6628\u5929\u7684\u6536\u76d8\u4ef7\u53bb\u56de\u5f52\u4eca\u5929\u7684\u6536\u76d8\u4ef7\u3002\u8dd1\u5b8c\u4e4b\u540e\u53d1\u73b0R\u65b9\u8d85\u8fc70.99\uff0c\u89c9\u5f97\u81ea\u5df1\u53d1\u73b0\u4e86\u8fd1\u4e4e\u5b8c\u7f8e\u7684\u9884\u6d4b\u5173\u7cfb\u3002<\/p>\n\n\n\n

\u7136\u800c\uff0c<\/strong>\u4ed6\u4eec\u6389\u8fdb\u4e86\u7edf\u8ba1\u5b66\u91cc\u6700\u8457\u540d\u7684\u9677\u9631\u4e4b\u4e00\uff1a\u4f2a\u56de\u5f52\uff08Spurious Regression\uff09<\/strong>\u3002<\/p>\n\n\n\n

\u5b9e\u9645\u60c5\u51b5\u662f\u8fd9\u6837\u7684\uff1a\u628a\u540c\u6837\u7684\u56de\u5f52\u6362\u6210\u65e5\u6536\u76ca\u7387\u6765\u8dd1\uff0cR\u65b9\u4f1a\u4ece0.99\u9aa4\u964d\u5230\u5927\u7ea60.01\u3002\u4ece\u89e3\u91ca99%\u7684\u53d8\u5f02\u53d8\u6210\u53ea\u80fd\u89e3\u91ca1%\u3002\u540c\u6837\u7684\u6807\u7684\u3001\u540c\u6837\u7684\u6570\u636e\u3001\u540c\u6837\u7684\u6a21\u578b\u7ed3\u6784\uff0c\u7ed3\u679c\u5929\u5dee\u5730\u522b\u3002<\/p>\n\n\n\n

\u539f\u56e0\u5c31\u662f\u5355\u4f4d\u6839\uff08Unit Root\uff09<\/strong>\u3002<\/p>\n\n\n\n

\u5f53\u4e00\u4e2a\u65f6\u95f4\u5e8f\u5217\u7684\u5f53\u524d\u503c\u7b49\u4e8e\u524d\u4e00\u4e2a\u503c\u52a0\u4e0a\u4e00\u4e2a\u968f\u673a\u6270\u52a8\u65f6\uff0c\u5b83\u5c31\u5b58\u5728\u5355\u4f4d\u6839\uff1a<\/p>\n\n\n\n

\n

X\u209c = X\u209c\u208b\u2081 + \u03b5\u209c<\/strong><\/p>\n<\/blockquote>\n\n\n\n

\u8fd9\u5c31\u662f\u6240\u8c13\u7684\u968f\u673a\u6e38\u8d70\uff08Random Walk\uff09<\/strong>\u3002\u80a1\u4ef7\u5927\u81f4\u670d\u4ece\u8fd9\u4e2a\u8fc7\u7a0b\u3002\u5f53\u4f60\u62ff\u4e00\u4e2a\u968f\u673a\u6e38\u8d70\u53bb\u56de\u5f52\u53e6\u4e00\u4e2a\u968f\u673a\u6e38\u8d70\u65f6\uff0c\u5373\u4f7f\u4e24\u8005\u6beb\u65e0\u5173\u7cfb\uff0c\u4f60\u4e5f\u51e0\u4e4e\u603b\u80fd\u53d1\u73b0\u5f88\u5f3a\u7684\u7edf\u8ba1\u76f8\u5173\u6027\u3002\u8fd9\u5c31\u662f\u4f2a\u56de\u5f52\uff0c\u5b83\u662f\u65e0\u6570\u865a\u5047\u4ea4\u6613\u4fe1\u53f7\u7684\u6765\u6e90\u3002<\/strong><\/p>\n\n\n\n

\u68c0\u9a8c\u8fd9\u4e2a\u95ee\u9898\u7684\u5de5\u5177\u53ebADF\u68c0\u9a8c\uff08Augmented Dickey-Fuller Test\uff09<\/strong>\u3002\u5b83\u7684\u539f\u5047\u8bbe\u662f\u5e8f\u5217\u5b58\u5728\u5355\u4f4d\u6839\uff08\u975e\u5e73\u7a33\uff09\u3002\u5982\u679cp\u503c\u5c0f\u4e8e0.05\uff0c\u4f60\u53ef\u4ee5\u62d2\u7edd\u539f\u5047\u8bbe\uff0c\u8bf4\u660e\u5e8f\u5217\u5927\u6982\u7387\u662f\u5e73\u7a33\u7684\u3002\u5982\u679cp\u503c\u5927\u4e8e0.05\uff0c\u90a3\u8fd9\u4e2a\u5e8f\u5217\u5f88\u53ef\u80fd\u6709\u5355\u4f4d\u6839\uff0c\u76f4\u63a5\u5728\u4e0a\u9762\u8dd1\u56de\u5f52\u4f1a\u4ea7\u751f\u865a\u5047\u7ed3\u679c\u3002<\/p>\n\n\n\n

# ADF\u5e73\u7a33\u6027\u68c0\u9a8c\u5b8c\u6574\u793a\u4f8b\nimport numpy as np\nimport pandas as pd\nimport yfinance as yf\nfrom statsmodels.tsa.stattools import adfuller\nimport warnings\nwarnings.filterwarnings('ignore')\n\n# 1. \u83b7\u53d6\u6570\u636e\nticker = yf.Ticker(\"SPY\")\ndf = ticker.history(period=\"5y\", interval=\"1d\")\n\n# 2. \u51c6\u5907\u5e8f\u5217\nprice = df['Close'].dropna()\n# \u666e\u901a\u6536\u76ca\u7387\uff08\u4e5f\u53ef\u4ee5\u7528\u5bf9\u6570\u6536\u76ca\u7387\uff0c\u7ed3\u8bba\u4e00\u81f4\uff09\nreturns = df['Close'].pct_change().dropna()\n# \u5bf9\u6570\u6536\u76ca\u7387\uff08\u66f4\u5e38\u7528\uff09\nlog_returns = np.log(df['Close'] \/ df['Close'].shift(1)).dropna()\n\n# 3. \u6267\u884cADF\u68c0\u9a8c\nprice_test = adfuller(price, autolag='AIC')\nreturns_test = adfuller(returns, autolag='AIC')\nlog_returns_test = adfuller(log_returns, autolag='AIC')\n\n# 4. \u8f93\u51fa\u7ed3\u679c\nprint(\"=\" * 50)\nprint(f\"Price ADF p-value: {price_test[1]:.6f}\")\nprint(f\"  \u2192 {'\u5e73\u7a33' if price_test[1] < 0.05 else '\u975e\u5e73\u7a33\uff08\u5b58\u5728\u5355\u4f4d\u6839\uff09'}\")\nprint(\"-\" * 50)\nprint(f\"Returns ADF p-value: {returns_test[1]:.6f}\")\nprint(f\"  \u2192 {'\u5e73\u7a33' if returns_test[1] < 0.05 else '\u975e\u5e73\u7a33\uff08\u5b58\u5728\u5355\u4f4d\u6839\uff09'}\")\nprint(\"-\" * 50)\nprint(f\"Log Returns ADF p-value: {log_returns_test[1]:.6f}\")\nprint(f\"  \u2192 {'\u5e73\u7a33' if log_returns_test[1] < 0.05 else '\u975e\u5e73\u7a33\uff08\u5b58\u5728\u5355\u4f4d\u6839\uff09'}\")\nprint(\"=\" * 50)<\/code><\/pre>\n\n\n\n
\u4f60\u4f1a\u53d1\u73b0\uff1a\u4ef7\u683c\u5e8f\u5217\u901a\u4e0d\u8fc7ADF\u68c0\u9a8c\uff0c\u6536\u76ca\u7387\u5e8f\u5217\u53ef\u4ee5\u901a\u8fc7\u3002\u8fd9\u8bf4\u660e\u6c38\u8fdc\u4e0d\u8981\u5728\u539f\u59cb\u4ef7\u683c\u6c34\u5e73\u4e0a\u6784\u5efa\u9884\u6d4b\u6a21\u578b<\/strong>\u3002\u4e00\u5b9a\u8981\u5148\u8f6c\u6362\u6210\u6536\u76ca\u7387\u3001\u5bf9\u6570\u6536\u76ca\u7387\u6216\u5176\u4ed6\u5e73\u7a33\u5f62\u5f0f\uff0c\u7136\u540e\u518d\u5e94\u7528\u65f6\u95f4\u5e8f\u5217\u6a21\u578b\u3002<\/p>\n\n\n\n
\u5c06\u4ef7\u683c\u5e8f\u5217\u8f6c\u6362\u4e3a\u5e73\u7a33\u5e8f\u5217\u7684\u65b9\u6cd5\u53eb\u505a\u4e00\u9636\u5dee\u5206<\/strong>\uff1a<\/p>\n\n\n\n
\n
r\u209c = ln(P\u209c) \u2014 ln(P\u209c\u208b\u2081)<\/strong><\/p>\n<\/blockquote>\n\n\n\n
\u5bf9\u6570\u6536\u76ca\u7387\u5927\u81f4\u662f\u5e73\u7a33\u7684\uff0c\u4e0d\u8fc7\u91d1\u878d\u6536\u76ca\u7387\u5e8f\u5217\u4ecd\u7136\u5b58\u5728\u4e00\u4e9b\u7eaf\u5e73\u7a33\u6027\u65e0\u6cd5\u5b8c\u5168\u6355\u6349\u7684\u7279\u5f81\uff0c\u6bd4\u5982\u539a\u5c3e\u6548\u5e94\uff0c\u6211\u4eec\u540e\u9762\u5728GARCH\u90e8\u5206\u4f1a\u8bb2\u5230\u3002<\/p>\n\n\n\n
\u5bf9\u6bd4\u7ef4\u5ea6<\/th>\u539f\u59cb\u4ef7\u683c\u5e8f\u5217<\/th>\u6536\u76ca\u7387\u5e8f\u5217<\/th><\/tr>
ADF\u68c0\u9a8cp\u503c<\/td>> 0.05\uff08\u901a\u5e38\uff09<\/td>< 0.05\uff08\u901a\u5e38\uff09<\/td><\/tr>
\u5e73\u7a33\u6027<\/td>\u975e\u5e73\u7a33\uff08\u5b58\u5728\u5355\u4f4d\u6839\uff09<\/td>\u8fd1\u4f3c\u5e73\u7a33<\/td><\/tr>
\u56de\u5f52R\u65b9<\/td>\u865a\u9ad8\uff080.99+\uff09<\/td>\u771f\u5b9e\u6c34\u5e73\uff08\u63a5\u8fd10\uff09<\/td><\/tr>
\u80fd\u5426\u7528\u4e8e\u5efa\u6a21<\/td>\u4e0d\u884c\uff01\u4f1a\u4ea7\u751f\u4f2a\u56de\u5f52<\/td>\u53ef\u4ee5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\u8001\u4f59\u63d0\u9192\uff1a<\/strong>\u68c0\u67e5\u4e00\u4e0b\u4f60\u73b0\u5728\u7528\u7684\u6216\u8005\u4ee5\u524d\u7528\u8fc7\u7684\u4efb\u4f55\u4ea4\u6613\u6a21\u578b\uff0c\u770b\u5b83\u662f\u5efa\u7acb\u5728\u4ef7\u683c\u6c34\u5e73\u4e0a\u8fd8\u662f\u6536\u76ca\u7387\u4e0a\u7684\u3002\u5982\u679c\u662f\u4ef7\u683c\u6c34\u5e73\uff0c\u5bf9\u5e95\u5c42\u6570\u636e\u8dd1\u4e00\u4e0bDickey-Fuller\u68c0\u9a8c\u3002\u5982\u679cp\u503c\u5927\u4e8e0.05\uff0c\u4f60\u7684\u56de\u6d4b\u7ed3\u679c\u5927\u6982\u7387\u88ab\u4f2a\u76f8\u5173 inflate \u4e86\u3002<\/code><\/pre>\n\n\n\n
\u56db\u3001\u771f\u6b63\u7ba1\u7528\u7684\u6a21\u578b\u5bb6\u65cf\uff1aAR \/ MA \/ ARMA \/ GARCH<\/strong><\/h2>\n\n\n\n
\u73b0\u5728\u4f60\u5df2\u7ecf\u7406\u89e3\u4e86\u65f6\u95f4\u5e8f\u5217\u7684\u672c\u8d28\u3001\u4e09\u5927\u6838\u5fc3\u4efb\u52a1\u548c\u5355\u4f4d\u6839\u95ee\u9898\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u6765\u770b\u90a3\u4e9b\u5728\u5b9e\u9645\u5e02\u573a\u4e2d\u771f\u6b63\u6709\u6548\u7684\u6a21\u578b\u3002<\/p>\n\n\n\n
\u6784\u6210\u7cfb\u7edf\u5316\u4ea4\u6613\u9aa8\u5e72\u7684\u6a21\u578b\u65cf\u662fARMA\u53ca\u5176\u6269\u5c55<\/strong>\u3002\u8fd9\u4e2a\u5bb6\u65cf\u4e2d\u7684\u6bcf\u4e2a\u6210\u5458\u6355\u6349\u7684\u662f\u91d1\u878d\u65f6\u95f4\u5e8f\u5217\u4e2d\u4e0d\u540c\u65b9\u9762\u7684\u5e8f\u5217\u4f9d\u8d56\u7ed3\u6784\u3002<\/p>\n\n\n\n
4.1 AR\u6a21\u578b\uff1a\u81ea\u56de\u5f52\u6a21\u578b<\/strong><\/h3>\n\n\n\n
p\u9636\u81ea\u56de\u5f52\u6a21\u578b\u5199\u4f5cAR(p)\uff0c\u8bf4\u7684\u662f\u5f53\u524d\u503c\u662f\u5176\u81ea\u8eab\u8fc7\u53bbp\u4e2a\u503c\u7684\u7ebf\u6027\u7ec4\u5408\u52a0\u4e0a\u4e00\u4e2a\u968f\u673a\u51b2\u51fb\uff1a<\/p>\n\n\n\n
\n
X\u209c = \u03c6\u2081X\u209c\u208b\u2081 + \u03c6\u2082X\u209c\u208b\u2082 + \u2026 + \u03c6\u209aX\u209c\u208b\u209a + \u03b5\u209c<\/strong><\/p>\n<\/blockquote>\n\n\n\n
\u03c6\u7cfb\u6570\u5c31\u662f\u81ea\u56de\u5f52\u53c2\u6570\u3002\u5b83\u4eec\u6355\u6349\u7684\u662f\u5f53\u524d\u503c\u6709\u591a\u5c11\u6210\u5206\u6765\u81ea\u8fc7\u53bb\u7684\u503c\u3002<\/p>\n\n\n\n
\u5728\u4ea4\u6613\u4e2d\uff0cAR\u6a21\u578b\u9002\u5408\u6355\u6349\u77ed\u671f\u52a8\u91cf\u548c\u5747\u503c\u56de\u590d\u52a8\u6001\u3002\u03c6\u2081\u4e3a\u6b63\u7684AR(1)\u6a21\u578b\u6355\u6349\u7684\u662f\u52a8\u91cf\uff1b\u03c6\u2081\u4e3a\u8d1f\u7684AR(1)\u6a21\u578b\u6355\u6349\u7684\u662f\u5747\u503c\u56de\u590d\u3002<\/p>\n\n\n\n
4.2 MA\u6a21\u578b\uff1a\u6ed1\u52a8\u5e73\u5747\u6a21\u578b<\/strong><\/h3>\n\n\n\n
q\u9636\u6ed1\u52a8\u5e73\u5747\u6a21\u578b\u5199\u4f5cMA(q)\uff0c\u8bf4\u7684\u662f\u5f53\u524d\u503c\u662f\u8fc7\u53bbq\u4e2a\u968f\u673a\u51b2\u51fb\u7684\u7ebf\u6027\u51fd\u6570\uff1a<\/p>\n\n\n\n
\n
X\u209c = \u03b5\u209c + \u03b8\u2081\u03b5\u209c\u208b\u2081 + \u03b8\u2082\u03b5\u209c\u208b\u2082 + \u2026 + \u03b8q\u03b5\u209c\u208bq<\/strong><\/p>\n<\/blockquote>\n\n\n\n
MA\u6a21\u578b\u6355\u6349\u7684\u662f\u8fc7\u53bb\u7684”\u610f\u5916”\u5bf9\u5f53\u524d\u503c\u7684\u5f71\u54cd\u3002\u5b83\u7279\u522b\u9002\u5408\u5efa\u6a21\u5e02\u573a\u5bf9\u65b0\u95fb\u4e8b\u4ef6\u7684\u53cd\u5e94\u6a21\u5f0f\u3002<\/p>\n\n\n\n
4.3 ARMA\u6a21\u578b\uff1a\u4e24\u8005\u7ed3\u5408<\/strong><\/h3>\n\n\n\n
ARMA(p,q)\u6a21\u578b\u628a\u4e24\u4e2a\u6210\u5206\u7ec4\u5408\u5728\u4e00\u8d77\uff1a<\/p>\n\n\n\n
\n
X\u209c = \u03c6\u2081X\u209c\u208b\u2081 + \u2026 + \u03c6\u209aX\u209c\u208b\u209a + \u03b5\u209c + \u03b8\u2081\u03b5\u209c\u208b\u2081 + \u2026 + \u03b8q\u03b5\u209c\u208bq<\/strong><\/p>\n<\/blockquote>\n\n\n\n
\u5bf9\u4e8e\u975e\u5e73\u7a33\u5e8f\u5217\uff0c\u5148\u505a\u5dee\u5206\u4f7f\u5176\u5e73\u7a33\uff0c\u518d\u5957\u7528ARMA\uff0c\u5c31\u5f97\u5230\u4e86ARIMA(p,d,q)<\/strong>\uff0c\u5176\u4e2dd\u662f\u5dee\u5206\u7684\u9636\u6570\u3002<\/p>\n\n\n\n
4.4 GARCH\u6a21\u578b\uff1a\u7ed9\u6ce2\u52a8\u7387\u5efa\u6a21<\/strong><\/h3>\n\n\n\n
ARMA\u6a21\u578b\u7528\u5728\u91d1\u878d\u6570\u636e\u4e0a\u6709\u4e00\u4e2a\u5927\u95ee\u9898\uff1a\u5b83\u5047\u8bbe\u6ce2\u52a8\u7387\u662f\u6052\u5b9a\u7684\u3002\u4f46\u91d1\u878d\u5e02\u573a\u6709\u4e00\u4e2a\u975e\u5e38\u660e\u663e\u7684\u7279\u5f81\uff1a\u6ce2\u52a8\u7387\u805a\u96c6\uff08Volatility Clustering\uff09<\/strong>\uff1a\u5927\u7684\u6ce2\u52a8\u540e\u9762\u5f80\u5f80\u8ddf\u7740\u5927\u7684\u6ce2\u52a8\uff0c\u5c0f\u7684\u6ce2\u52a8\u540e\u9762\u8ddf\u7740\u5c0f\u7684\u6ce2\u52a8\u3002\u8fd9\u53eb\u505aARCH\u6548\u5e94<\/strong>\uff0c\u662f\u6574\u4e2a\u91d1\u878d\u9886\u57df\u6700 documented \u7684\u7279\u5f81\u4e4b\u4e00\u3002<\/p>\n\n\n\n
GARCH(1,1)\u6a21\u578b\u901a\u8fc7\u5c06\u8bef\u5dee\u9879\u7684\u65b9\u5dee\u5efa\u6a21\u4e3a\u4e00\u4e2a\u968f\u65f6\u95f4\u53d8\u5316\u7684\u91cf\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff1a<\/p>\n\n\n\n
\n
\u03c3\u209c\u00b2 = \u03c9 + \u03b1\u2081\u03b5\u209c\u208b\u2081\u00b2 + \u03b2\u2081\u03c3\u209c\u208b\u2081\u00b2<\/strong><\/p>\n<\/blockquote>\n\n\n\n
\u5176\u4e2d\u03c3\u209c\u00b2\u662ft\u65f6\u523b\u7684\u6761\u4ef6\u65b9\u5dee\uff0c\u03b5\u209c\u208b\u2081\u00b2\u662f\u4e0a\u4e00\u671f\u7684\u5e73\u65b9\u51b2\u51fb\uff0c\u03c3\u209c\u208b\u2081\u00b2\u662f\u4e0a\u4e00\u671f\u7684\u65b9\u5dee\u3002\u8fd9\u4e2a\u6a21\u578b\u7cbe\u786e\u5730\u6355\u6349\u5230\u4e86\u4f60\u5728\u5e02\u573a\u4e2d\u89c2\u5bdf\u5230\u7684\u6ce2\u52a8\u7387\u805a\u96c6\u73b0\u8c61\uff1a\u4eca\u5929\u7684\u5927\u6ce2\u52a8\u610f\u5473\u7740\u660e\u5929\u4e5f\u5f88\u53ef\u80fd\u6709\u9ad8\u6ce2\u52a8\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u56fe\uff1a GARCH\u6a21\u578b\u6355\u6349\u91d1\u878d\u6536\u76ca\u7684\u5173\u952e\u7279\u5f81\uff1a\u5927\u6ce2\u52a8\u540e\u8ddf\u5927\u6ce2\u52a8\uff0c\u5c0f\u6ce2\u52a8\u540e\u8ddf\u5c0f\u6ce2\u52a8<\/p>\n\n\n\n
\u5bf9\u4e8e\u4ea4\u6613\u6765\u8bf4\uff0cGARCH\u7684\u6838\u5fc3\u4ef7\u503c\u5728\u4e8e\u4ed3\u4f4d\u7ba1\u7406<\/strong>\u3002\u5f53\u03c3\u209c\u00b2\u8f83\u9ad8\u65f6\uff0c\u4f60\u5e94\u8be5\u964d\u4f4e\u4ed3\u4f4d\u89c4\u6a21\u3002\u5f53\u03c3\u209c\u00b2\u8f83\u4f4e\u65f6\uff0c\u4f60\u53ef\u4ee5\u627f\u62c5\u66f4\u591a\u98ce\u9669\u3002\u4ec5\u9760\u8fd9\u4e00\u4e2a\u6d1e\u5bdf\uff0c\u6839\u636e\u9884\u4f30\u6ce2\u52a8\u7387\u52a8\u6001\u8c03\u6574\u4ed3\u4f4d\u5927\u5c0f\uff0c\u5c31\u8d21\u732e\u4e86\u7cfb\u7edf\u6027\u57fa\u91d1\u4ea7\u751f\u7684\u76f8\u5f53\u5927\u6bd4\u4f8b\u7684\u98ce\u9669\u8c03\u6574\u540e\u6536\u76ca\u3002<\/p>\n\n\n\n
\u6a21\u578b<\/th>\u5168\u79f0<\/th>\u6838\u5fc3\u529f\u80fd<\/th>\u5178\u578b\u5e94\u7528\u573a\u666f<\/th><\/tr>
AR(p)<\/strong><\/td>\u81ea\u56de\u5f52\u6a21\u578b<\/td>\u6355\u6349\u5386\u53f2\u503c\u7684\u7ebf\u6027\u4f9d\u8d56<\/td>\u77ed\u671f\u52a8\u91cf\/\u5747\u503c\u56de\u590d\u4fe1\u53f7<\/td><\/tr>
MA(q)<\/strong><\/td>\u6ed1\u52a8\u5e73\u5747\u6a21\u578b<\/td>\u6355\u6349\u5386\u53f2\u51b2\u51fb\u7684\u5f71\u54cd<\/td>\u65b0\u95fb\u4e8b\u4ef6\u540e\u7684\u53cd\u5e94\u5efa\u6a21<\/td><\/tr>
ARMA(p,q)<\/strong><\/td>\u81ea\u56de\u5f52\u6ed1\u52a8\u5e73\u5747<\/td>\u7ed3\u5408\u4e24\u8005<\/td>\u5e73\u7a33\u5e8f\u5217\u7684\u65b9\u5411\u6027\u4fe1\u53f7<\/td><\/tr>
ARIMA(p,d,q)<\/strong><\/td>\u5dee\u5206ARMA<\/td>\u5148\u5dee\u5206\u518dARMA<\/td>\u975e\u5e73\u7a33\u5e8f\u5217\u5efa\u6a21<\/td><\/tr>
GARCH(1,1)<\/strong><\/td>\u5e7f\u4e49\u81ea\u56de\u5f52\u6761\u4ef6\u5f02\u65b9\u5dee<\/td>\u52a8\u6001\u6ce2\u52a8\u7387\u5efa\u6a21<\/td>\u4ed3\u4f4d\u7ba1\u7406\/\u98ce\u9669\u63a7\u5236<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n
\u5173\u952e\u8ba4\u77e5\uff1a<\/strong>\u5373\u4f7f\u65b9\u5411\u65e0\u6cd5\u51c6\u786e\u9884\u5224\uff0c\u6ce2\u52a8\u7387\u4e5f\u662f\u53ef\u9884\u6d4b\u7684\u3002\u8fd9\u662fGARCH\u6a21\u578b\u6700\u91cd\u8981\u7684\u6d1e\u89c1\uff0c\u4e5f\u662f\u5b83\u5728\u5b9e\u9645\u4ea4\u6613\u7cfb\u7edf\u4e2d\u4e0d\u53ef\u66ff\u4ee3\u7684\u539f\u56e0\u3002<\/p>\n<\/blockquote>\n\n\n\n
\u4e94\u3001\u5b8c\u6574\u5b9e\u73b0\u6d41\u7a0b\uff1a\u4ece\u6570\u636e\u5230\u4fe1\u53f7\u7684\u843d\u5730\u4ee3\u7801<\/strong><\/h2>\n\n\n\n
\u8fd9\u4e00\u8282\u628a\u524d\u9762\u6240\u6709\u5185\u5bb9\u7ec4\u88c5\u6210\u4e00\u4e2a\u4f60\u4eca\u5929\u5c31\u80fd\u5728\u771f\u5b9e\u6570\u636e\u4e0a\u8fd0\u884c\u7684\u5b8c\u6574\u7cfb\u7edf\u3002<\/p>\n\n\n\n
import numpy as np\nimport pandas as pd\nimport yfinance as yf\nfrom statsmodels.tsa.arima.model import ARIMA\nfrom arch import arch_model\nfrom statsmodels.tsa.stattools import adfuller\nimport warnings\n\nwarnings.filterwarnings('ignore')\n\n\nclass TimeSeriesTradingSystem:\n    \"\"\"\u65f6\u95f4\u5e8f\u5217\u4ea4\u6613\u7cfb\u7edf \u2014 \u5b8c\u6574\u5b9e\u73b0\"\"\"\n\n    def __init__(self, ticker, period=\"5y\"):\n        self.ticker = ticker\n        self.period = period\n\n    def fetch_and_prepare(self):\n        \"\"\"\u7b2c\u4e00\u6b65\uff1a\u83b7\u53d6\u6570\u636e\u5e76\u8ba1\u7b97\u5bf9\u6570\u6536\u76ca\u7387\"\"\"\n        data = yf.Ticker(self.ticker).history(period=self.period)\n        self.prices = data['Close']\n        # \u8ba1\u7b97\u5bf9\u6570\u6536\u76ca\u7387\uff08\u767e\u5206\u6bd4\u5f62\u5f0f\uff09\n        self.returns = np.log(\n            self.prices \/ self.prices.shift(1)\n        ).dropna() * 100\n        return self.returns\n\n    def check_stationarity(self, series):\n        \"\"\"\u7b2c\u4e8c\u6b65\uff1aADF\u5e73\u7a33\u6027\u68c0\u9a8c\"\"\"\n        result = adfuller(series.dropna())\n        print(f\"ADF Statistic: {result[0]:.4f}\")\n        print(f\"P-value: {result[1]:.4f}\")\n        print(f\"Stationary: {result[1] < 0.05}\")\n        return result[1] < 0.05\n\n    def fit_arima_garch(self, returns,\n                        arima_order=(1, 0, 1),\n                        garch_order=(1, 1)):\n        \"\"\"\u7b2c\u4e09\u6b65\uff1a\u62df\u5408ARIMA + GARCH\u6a21\u578b\"\"\"\n        arima = ARIMA(returns, order=arima_order)\n        arima_result = arima.fit()\n        residuals = arima_result.resid\n\n        garch = arch_model(\n            residuals, vol='Garch',\n            p=garch_order[0], q=garch_order[1]\n        )\n        garch_result = garch.fit(disp='off')\n        return arima_result, garch_result\n\n    def generate_signals(self, returns, lookback=252):\n        \"\"\"\n        \u7b2c\u56db\u6b65\uff1a\u6eda\u52a8\u7a97\u53e3\u751f\u6210\u4ea4\u6613\u4fe1\u53f7\n        \u6838\u5fc3\u601d\u8def\uff1a\n        - \u7528ARIMA\u9884\u6d4b\u4e0b\u4e00\u671f\u65b9\u5411\n        - \u7528GARCH\u9884\u4f30\u4e0b\u4e00\u671f\u6ce2\u52a8\u7387\n        - \u6839\u636e\u6ce2\u52a8\u7387\u53cd\u5411\u8c03\u6574\u4ed3\u4f4d\u5927\u5c0f\n        \"\"\"\n        signals = []\n        for i in range(lookback, len(returns)):\n            window = returns.iloc[i-lookback:i]\n            try:\n                arima = ARIMA(window, order=(1, 0, 1)).fit()\n                forecast = arima.forecast(steps=1)[0]\n\n                garch = arch_model(\n                    arima.resid, vol='Garch',\n                    p=1, q=1\n                ).fit(disp='off')\n                vol_forecast = np.sqrt(\n                    garch.forecast(horizon=1)\n                    .variance.values[-1][0]\n                )\n\n                # \u65b9\u5411\u4fe1\u53f7\uff1a\u6b63\u9884\u671f\u2192+1\uff0c\u8d1f\u9884\u671f\u2192-1\n                signal = 1 if forecast > 0 else -1\n                # \u6ce2\u52a8\u7387\u5012\u6570\u4ed3\u4f4d\u7f29\u653e\n                position_size = min(\n                    1.0, 1.0 \/ max(vol_forecast, 0.1)\n                )\n                scaled_signal = signal * position_size\n            except:\n                scaled_signal = 0\n\n            signals.append({\n                'date': returns.index[i],\n                'signal': scaled_signal\n            })\n        return pd.DataFrame(signals).set_index('date')\n\n\n# ========== \u8fd0\u884c\u5b8c\u6574\u6d41\u7a0b ==========\nif __name__ == \"__main__\":\n    system = TimeSeriesTradingSystem(\"SPY\")\n    returns = system.fetch_and_prepare()\n\n    print(\"Checking stationarity of returns:\")\n    system.check_stationarity(returns)\n\n    arima_result, garch_result = system.fit_arima_garch(returns)\n    print(f\"\\nARIMA AIC: {arima_result.aic:.2f}\")\n    print(f\"GARCH Log-Likelihood: {garch_result.loglikelihood:.2f}\")\n\n    # \u751f\u6210\u4fe1\u53f7\u5e76\u8bc4\u4f30\u7b56\u7565\u8868\u73b0\n    signals = system.generate_signals(returns)\n    strategy_returns = (\n        signals['signal'].shift(1)\n        * returns.loc[signals.index]\n    )\n    sharpe = (\n        strategy_returns.mean()\n        \/ strategy_returns.std() * np.sqrt(252)\n    )\n    cumulative = (1 + strategy_returns \/ 100).cumprod()\n    max_dd = (\n        (cumulative - cumulative.cummax())\n        \/ cumulative.cummax()\n    ).min()\n\n    print(f\"\\n=== System Performance ===\")\n    print(f\"Annualized Sharpe: {sharpe:.4f}\")\n    print(f\"Maximum Drawdown: {max_dd:.4f}\")<\/code><\/pre>\n\n\n\n
\u90e8\u7f72\u4e4b\u524d\u4f60\u5fc5\u987b\u7406\u89e3\u7684\u4e09\u4ef6\u4e8b<\/strong><\/h3>\n\n\n\n
    \n
  1. GARCH\u4ed3\u4f4d\u7ba1\u7406\u6bd4ARIMA\u65b9\u5411\u9884\u6d4b\u505a\u5f97\u66f4\u591a<\/strong>\u5728\u9ad8\u6ce2\u52a8\u65f6\u671f\u964d\u4f4e\u4ed3\u4f4d\u66b4\u9732\uff0c\u662f\u6574\u4e2a\u7cfb\u7edf\u4e2d\u6700\u53ef\u9760\u7684\u8fb9\u9645\u4f18\u52bf\u6765\u6e90\u300260%\u51c6\u786e\u7387\u7684\u65b9\u5411\u4fe1\u53f7\u914d\u5408\u6ce2\u52a8\u7387\u7f29\u653e\u4ed3\u4f4d\uff0c\u6bd490%\u51c6\u786e\u7387\u7684\u56fa\u5b9a\u4ed3\u4f4d\u4ea7\u751f\u66f4\u597d\u7684\u98ce\u9669\u8c03\u6574\u540e\u6536\u76ca\u3002<\/li>\n\n\n\n
  2. \u6eda\u52a8\u7a97\u53e3\u7ed3\u6784\u662f\u4e0d\u53ef\u59a5\u534f\u7684<\/strong>\u6bcf\u4e00\u6b65\u4f60\u90fd\u5728\u5386\u53f2\u6570\u636e\u4e0a\u62df\u5408\u6a21\u578b\uff0c\u5f80\u524d\u63a8\u4e00\u6b65\u505a\u9884\u671f\u3002\u7edd\u5bf9\u4e0d\u8981\u5728\u5168\u91cf\u6570\u636e\u4e0a\u62df\u5408\u7136\u540e\u751f\u6210\u6837\u672c\u5185\u9884\u6d4b\u8fd8\u628a\u5b83\u5f53\u6210\u56de\u6d4b\u7ed3\u679c\u3002\u90a3\u4e0d\u662f\u56de\u6d4b\uff0c\u90a3\u662f\u8d34\u6807\u7b7e\u3002<\/li>\n\n\n\n
  3. \u66ff\u4ee3\u6570\u636e\u662f\u65f6\u95f4\u5e8f\u5217\u5206\u6790\u7684\u5929\u82b1\u677f<\/strong>\u672c\u6587\u4ecb\u7ecd\u7684\u6846\u67b6\u53ea\u6355\u6349\u4ef7\u683c\u5e8f\u5217\u5185\u90e8\u7684\u6a21\u5f0f\u3002\u6301\u7eed\u8dd1\u8d62\u5e02\u573a\u7684\u4ea4\u6613\u8005\u4f7f\u7528\u7684\u989d\u5916\u4fe1\u606f\u662f\u4ef7\u683c\u5e8f\u5217\u4e0d\u53ef\u80fd\u5305\u542b\u7684\u4e1c\u897f\uff1a\u8d22\u62a5\u7535\u8bdd\u4f1a\u8bae\u60c5\u7eea\u3001\u8ba2\u5355\u7c3f\u91cc\u7684\u6d41\u91cf\u5931\u8861\u3001\u4f9b\u5e94\u94fe\u6570\u636e\u3001\u8de8\u8d44\u4ea7\u72b6\u6001\u4fe1\u606f\u7b49\u3002\u8fd9\u4e9b\u4e0d\u662f\u6a21\u578b\u7684\u6539\u8fdb\uff0c\u5b83\u4eec\u6765\u81ea\u4e00\u4e2a\u5b8c\u5168\u4e0d\u540c\u7684\u4fe1\u606f\u96c6\u5408\u3002<\/li>\n<\/ol>\n\n\n\n
    \"\"<\/figure>\n\n\n\n
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    \n
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    \n\n\n\n
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