{"id":5491,"date":"2023-01-17T15:35:50","date_gmt":"2023-01-17T07:35:50","guid":{"rendered":"https:\/\/fanyuzhao.com\/?p=5491"},"modified":"2023-01-29T15:55:11","modified_gmt":"2023-01-29T07:55:11","slug":"%e5%9b%a0%e5%ad%90%e6%8a%95%e8%b5%84%e7%9a%84%e9%ab%98%e7%bb%b4%e6%95%b0%e6%97%b6%e4%bb%a3","status":"publish","type":"post","link":"https:\/\/fanyuzhao.com\/?p=5491","title":{"rendered":"\u56e0\u5b50\u6295\u8d44\u7684\u9ad8\u7ef4\u6570\u65f6\u4ee3"},"content":{"rendered":"\n<p><strong>\u6458\u8981\uff1a<\/strong>\u5b9e\u8bc1\u8d44\u4ea7\u5b9a\u4ef7\u5df2\u7136\u8fdb\u5165\u56e0\u5b50\uff08\u534f\u53d8\u91cf\uff09\u7684\u9ad8\u7ef4\u6570\u65f6\u4ee3\u3002\u672c\u6587\u629b\u7816\u5f15\u7389\uff0c\u9610\u8ff0\u6211\u5bf9\u6b64\u7684\u56db\u70b9\u601d\u8003\u3002\uff08DGP: Data Generating Process\uff09<\/p>\n\n\n\n<ul><li>Key Takeaway: over-parameterization \u7684\u65f6\u4ee3\u5df2\u7ecf\u5230\u6765\uff0c\u53d8\u91cf\u6570\u91cf k \u5927\u4e8e\u6837\u672c\u6570\u91cf t \u4f3c\u4e4e\u5e76\u6ca1\u6709\u5e26\u6765 interpolate\u7684\u95ee\u9898\uff0c\u53cd\u800c\u7ed9prediction\u5e26\u6765\u4e86\u5e2e\u52a9\u3002<\/li><\/ul>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h_589370949_0\"><strong>0 \u5f15\u5b50<\/strong><\/h4>\n\n\n\n<p>\u65f6\u81f3\u4eca\u65e5\uff0c\u5b9e\u8bc1\u8d44\u4ea7\u5b9a\u4ef7\uff08\u4ee5\u53ca\u56e0\u5b50\u6295\u8d44\uff09\u5df2\u7136\u6b65\u5165\u4e86\u56e0\u5b50\uff08\u534f\u53d8\u91cf\uff09\u7684\u9ad8\u7ef4\u6570\u65f6\u4ee3\u3002\u5927\u91cf\u53d1\u8868\u5728\u9876\u520a\u4e0a\u7684\u5b9e\u8bc1\u7ed3\u679c\u8868\u660e\uff0c\u591a\u56e0\u5b50\u6a21\u578b\u5177\u6709\u5f88\u5927\u7684\u4e0d\u786e\u5b9a\u6027\u4e14\u56e0\u5b50\u7684\u7a00\u758f\u6027\u5047\u8bbe\u4e0d\u6210\u7acb\u3002\u4eba\u4eec\u719f\u77e5\u7684 ad-hoc \u7b80\u7ea6\u6a21\u578b\u65e0\u6cd5\u6307\u5f15\u672a\u6765\u7684\u6295\u8d44\u3002<\/p>\n\n\n\n<p>\u5728\u9ad8\u7ef4\u6570\u65f6\u4ee3\uff0c\u5bfb\u627e\u771f\u6b63\u80fd\u591f\u9884\u6d4b\u9884\u671f\u6536\u76ca\u7387\u7684\u534f\u53d8\u91cf\u662f\u6838\u5fc3\u95ee\u9898\u4e4b\u4e00\u3002\u4e3a\u4e86\u5b9e\u73b0\u8fd9\u4e2a\u76ee\u6807\uff0c\u9700\u8981\u8003\u8651\u7684\u95ee\u9898\u5305\u62ec\uff1a\uff081\uff09\u591a\u91cd\u5047\u8bbe\u5047\u8bbe\u68c0\u9a8c\uff1b\uff082\uff09\u6295\u8d44\u8005\uff08\u9ad8\u7ef4\uff09\u5b66\u4e60\u95ee\u9898 &amp; \u53e6\u7c7b\u6570\u636e\uff1b\uff083\uff09\u6765\u81ea\u8d44\u4ea7\u5b9a\u4ef7\u7406\u8bba\u7684\u6307\u5f15\uff1a\u5373\u89e3\u91ca\u9884\u671f\u6536\u76ca\u7387\u7684\u56e0\u5b50\u5e94\u8be5\u4e5f\u80fd\u89e3\u91ca\u8d44\u4ea7\u7684\u5171\u540c\u6ce2\u52a8\u3002\u6700\u540e\uff0c\u4e00\u4e2a\u6700\u65b0\u7684\u8ba8\u8bba\u70ed\u70b9\u662f\u56e0\u5b50\u7684\u4e2a\u6570\u662f\u5426\u8d8a\u591a\u8d8a\u597d\uff08\u5373\u6a21\u578b\u590d\u6742\u5ea6\u662f\u5426\u8d8a\u9ad8\u8d8a\u597d\uff09\uff1a\u590d\u6742\u6a21\u578b\u80fd\u66f4\u597d\u5730\u903c\u8fd1\u771f\u5b9e DGP\uff0c\u4f46\u53c2\u6570\u4f30\u8ba1\u7684\u65b9\u5dee\u66f4\u5927\uff1b\u7b80\u7ea6\u6a21\u578b\u7684\u53c2\u6570\u4f30\u8ba1\u66f4\u51c6\u786e\uff0c\u4f46\u5374\u672a\u5fc5\u662f DGP \u7684\u5408\u7406\u8fd1\u4f3c\u3002\u4e8c\u8005\u76f8\u6bd4\uff0c\u5982\u4f55\u6743\u8861\u5462\uff1f<\/p>\n\n\n\n<p>\u8fd1\u65e5\uff0c\u6211\u5728\u67d0\u5238\u5546 2023 \u7684\u5e74\u5ea6\u7b56\u7565\u4f1a\u4e0a\u505a\u4e86\u9898\u4e3a\u300a\u56e0\u5b50\u6295\u8d44\u7684\u9ad8\u7ef4\u6570\u65f6\u4ee3\u300b\u7684\u62a5\u544a\uff0c\u9610\u8ff0\u4e86\u6211\u5bf9\u4e0a\u8ff0\u56db\u70b9\u7684\u601d\u8003\u3002\u672c\u6587\u501f\u7740\u62a5\u544a\u7684 slides \u505a\u7b80\u8981\u4ecb\u7ecd\u3002\u7531\u4e8e\u5bf9\u4e8e\u67d0\u4e9b\u95ee\u9898\u4e13\u680f\u5df2\u7ecf\u505a\u4e86\u5927\u91cf\u7684\u68b3\u7406\uff08\u6bd4\u5982\u591a\u91cd\u5047\u8bbe\u68c0\u9a8c\uff09\uff0c\u56e0\u6b64\u5728\u672c\u6587\u7684\u9610\u8ff0\u4e2d\uff0c\u5728\u5fc5\u8981\u7684\u5730\u65b9\u4f1a\u4f7f\u7528\u6700\u5c11\u7684\u6587\u5b57\uff08\u4f60\u9a6c\u4e0a\u5c31\u4f1a\u660e\u767d\u6211\u7684\u610f\u601d\uff09\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h_589370949_1\"><strong>1 \u591a\u91cd\u5047\u8bbe\u68c0\u9a8c<\/strong><\/h4>\n\n\n\n<p>\u8fd9\u90e8\u5206\uff0c\u4e00\u56fe\u80dc\u5343\u8a00\u3002\u9700\u8981\u76f8\u5173\u77e5\u8bc6\u7684\u5c0f\u4f19\u4f34\uff0c\u8bf7\u67e5\u770b\u516c\u4f17\u53f7\u7684<a href=\"https:\/\/zhuanlan.zhihu.com\/p\/571568798\">\u300a\u51fa\u8272\u4e0d\u5982\u8d70\u8fd0\u300b<\/a>\u7cfb\u5217\u3002<\/p>\n\n\n\n<p>Next.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h_589370949_2\"><strong>2 \u6295\u8d44\u8005\u5b66\u4e60\u95ee\u9898 &amp; \u53e6\u7c7b\u6570\u636e<\/strong><\/h4>\n\n\n\n<p>\u7406\u6027\u9884\u671f\u5047\u8bbe\u6295\u8d44\u8005\u77e5\u9053\u771f\u5b9e\u7684\u4f30\u503c\u6a21\u578b\u3002<\/p>\n\n\n\n<p>\u7136\u800c\uff0c\u548c\u8fdb\u884c\u4e8b\u540e\uff08ex post\uff09\u56e0\u5b50\u5206\u6790\u7684\u4f60\u6211\u4e00\u6837\uff0c\u6295\u8d44\u8005\u5728\u6295\u8d44\u65f6\u540c\u6837\u9762\u4e34\u534f\u53d8\u91cf\u7684\u9ad8\u7ef4\u6570\u95ee\u9898\uff0c\u56e0\u6b64\u4e0d\u53ef\u80fd\u77e5\u9053\u771f\u5b9e\u7684\u4f30\u503c\u6a21\u578b\uff0c\u6240\u4ee5\u7406\u6027\u9884\u671f\u5047\u8bbe\u5e76\u4e0d\u6210\u7acb\u3002\u8fd9\u9020\u6210\u7684\u7ed3\u679c\u662f\uff0c\u5747\u8861\u72b6\u6001\u4e0b\u8d44\u4ea7\u4ef7\u683c\u548c\u7406\u6027\u9884\u671f\u60c5\u51b5\u4e0b\u76f8\u6bd4\u51fa\u73b0\u504f\u5dee\u3002\u5728\u4e8b\u540e\u5206\u6790\u4e2d\uff0c\u5df2\u5b9e\u73b0\u6536\u76ca\u7387\u4e2d\u5305\u542b\u4e00\u90e8\u5206\u56e0\u4f30\u8ba1\u8bef\u5dee\u5bfc\u81f4\u7684\u53ef\u9884\u6d4b\u6210\u5206\u3002\u4f46\u5bf9\u6295\u8d44\u8005\u6765\u8bf4\uff0c\u4e8b\u524d\uff08ex ante\uff09\u65e0\u6cd5\u5229\u7528\u4e0a\u8ff0\u53ef\u9884\u6d4b\u6027\u3002<\/p>\n\n\n\n<p>\u56e0\u8bef\u5dee\u5bfc\u81f4\u7684\u53ef\u9884\u6d4b\u6027\u80fd\u591f\u5728\u6837\u672c\u5185\uff08IS\uff09\u4ea7\u751f\u865a\u5047\u7684\u53ef\u9884\u6d4b\u6027\uff08\u65e0\u8bba\u6295\u8d44\u8005\u662f\u5426\u4f7f\u7528\u4e86\u5148\u9a8c\u4ee5\u53ca\u65e0\u8bba\u5148\u9a8c\u662f\u5426\u6b63\u786e\uff09\uff0c\u800c\u5728\u6837\u672c\u5916\uff08OOS\uff09\u5374\u65e0\u6cd5\u9884\u6d4b\u6536\u76ca\u7387\u3002\u8fd9\u5c31\u662f\u6295\u8d44\u8005\uff08\u9ad8\u7ef4\uff09\u5b66\u4e60\u95ee\u9898\u5bfc\u81f4\u7684\u865a\u5047\u7684\u53ef\u9884\u6d4b\u6027\uff08Martin and Nagel 2022\uff09\u3002\u5177\u4f53\u9610\u8ff0\u89c1<a href=\"https:\/\/zhuanlan.zhihu.com\/p\/382885396\">\u300aFalse In-Sample Predictability ?\u300b<\/a>\u3002\u9762\u5bf9\u8fd9\u4e2a\u95ee\u9898\uff0c\u9700\u8981\u901a\u8fc7 OOS \u68c0\u9a8c\u624d\u80fd\u89c4\u907f\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/pic3.zhimg.com\/80\/v2-7975fb2a1935eb4141474661eff0e66a_1440w.webp\" alt=\"\"\/><\/figure>\n\n\n\n<p>\u6295\u8d44\u8005\u65e0\u6cd5\u5728\u4e8b\u524d\u6295\u8d44\u4e2d\u5e94\u5bf9\u9ad8\u7ef4\u6570\uff0c\u8fd9\u4e3b\u8981\u4f53\u73b0\u5728\u4ed6\u4eec\u4f7f\u7528\u8f83\u5c11\u7684\u534f\u53d8\u91cf\uff08\u56e0\u5b50\uff09\u4f5c\u4e3a\u4f30\u503c\u7684\u4f9d\u636e\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u7531\u4e8e\u4e00\u4e9b\u53d8\u91cf\u7684\u83b7\u53d6\u6210\u672c\u5f88\u9ad8\uff0c\u6295\u8d44\u8005\u9700\u8981\u5728\u8be5\u53d8\u91cf\u5e26\u6765\u7684\u9884\u6d4b\u597d\u5904\u548c\u5176\u6210\u672c\u4e4b\u95f4\u6743\u8861\u3002\u6b64\u5916\uff0c\u6709\u9650\u7406\u6027\u4e2d\u7684\u6709\u9650\u6ce8\u610f\u529b\u673a\u5236\u4e5f\u4e3a\u6295\u8d44\u8005\u5bf9\u7b80\u7ea6\u6027\u7684\u6e34\u671b\u63d0\u4f9b\u4e86\u5fae\u89c2\u57fa\u7840\u3002\u8fd9\u4e24\u65b9\u9762\u4f5c\u7528\u5408\u529b\u5bfc\u81f4\u6295\u8d44\u8005\u5728\u4e3a\u8d44\u4ea7\u5b9a\u4ef7\u65f6\u4f7f\u7528\u8fc7\u5ea6\u7a00\u758f\u7684\u4f30\u503c\u6a21\u578b\u3002\u8fd9\u6837\u505a\u7684\u540e\u679c\u662f\uff0c\u5373\u4fbf\u5728\u6837\u672c\u5916\uff0c\u4e5f\u4f1a\u51fa\u73b0\u56e0\u6295\u8d44\u8005\u5b66\u4e60\u95ee\u9898\u800c\u9020\u6210\u7684\u865a\u5047\u7684\u53ef\u9884\u6d4b\u6027\u3002<\/p>\n\n\n\n<p>\u5c31\u7740\u4e0a\u8ff0\u63a8\u8bba\uff0c\u6211\u4eec\u81ea\u7136\u5730\u5f15\u51fa\u672c\u5c0f\u8282\u7684\u53e6\u4e00\u4e2a\u76f8\u5173\u8bdd\u9898\uff1a\u53e6\u7c7b\u6570\u636e\u3002<\/p>\n\n\n\n<p>\u56de\u5fc6\u4e00\u4e0b\u516c\u4f17\u53f7\u4e4b\u524d\u7684\u6587\u7ae0<a href=\"https:\/\/zhuanlan.zhihu.com\/p\/577519685\">\u300a\u79d1\u6280\u5173\u8054\u5ea6II\u300b<\/a>\u6240\u4ecb\u7ecd\u7684 Bekkerman, Fich and Khimich (forthcoming)\u3002\u76f8\u6bd4\u4e8e\u4e4b\u524d\u7684\u57fa\u4e8e\u4e13\u5229\u7c7b\u522b\u7684\u7814\u7a76\uff0c\u8be5\u6587\u5bf9\u4e13\u5229\u8fdb\u884c\u6587\u672c\u5206\u6790\uff0c\u901a\u8fc7\u63d0\u53d6\u4e13\u4e1a\u672f\u8bed\u5e76\u8ba1\u7b97\u5176\u91cd\u5408\u5ea6\u6765\u63cf\u8ff0\u516c\u53f8\u4e4b\u95f4\u7684\u76f8\u4f3c\u7a0b\u5ea6\uff0c\u4ee5\u6b64\u6784\u9020\u4e86\u9884\u671f\u8d85\u989d\u6536\u76ca\u7387\u66f4\u9ad8\u7684\u79d1\u6280\u5173\u8054\u5ea6\u6548\u5e94\u3002<\/p>\n\n\n\n<p>\u6bd4\u8d77\u4e13\u5229\u7c7b\u522b\uff0c\u6295\u8d44\u8005\u5728\u83b7\u5f97\u4ee5\u53ca\u5904\u7406\u4e13\u5229\u6587\u672c\u5e76\u8ba1\u7b97\u79d1\u6280\u5173\u8054\u5ea6\u65f6\u7684\u6210\u672c\u66f4\u52a0\u6602\u8d35\u3002\u8fd9\u4f1a\u5bfc\u81f4\u5927\u591a\u6570\u6295\u8d44\u8005\u4f1a\u5728\u4e3a\u516c\u53f8\u4f30\u503c\u65f6\u5ffd\u7565\u8fd9\u65b9\u9762\u7684\u4fe1\u606f\uff0c\u5373\u4f7f\u7528\u8fc7\u5ea6\u7a00\u758f\u7684\u4f30\u503c\u6a21\u578b\uff0c\u9020\u6210\u6837\u672c\u5185\u548c\u6837\u672c\u5916\u6536\u76ca\u7387\u53ef\u9884\u6d4b\u6027\u3002<\/p>\n\n\n\n<p>\u8be5\u6587\u57fa\u4e8e\u6587\u672c\u5206\u6790\u7684\u79d1\u6280\u5173\u8054\u5ea6\u662f\u8fd1\u51e0\u5e74\u5927\u7ea2\u5927\u7d2b\u7684\u57fa\u4e8e\u53e6\u7c7b\u6570\u636e\u8fdb\u884c\u5b9e\u8bc1\u8d44\u4ea7\u5b9a\u4ef7\u548c\u56e0\u5b50\u6295\u8d44\u7684\u4e00\u4e2a\u5178\u578b\u4f8b\u5b50\u3002\u7136\u800c\uff0cMartin and Nagel (2022) \u6240\u52fe\u52d2\u51fa\u7684\u975e\u7406\u6027\u9884\u671f\u5047\u8bbe\u4e16\u754c\u544a\u8bc9\u6211\u4eec\uff0c\u4f7f\u7528\u6700\u65b0\u7684\u65b9\u6cd5\u548c\u6280\u672f\u6784\u5efa\u9884\u6d4b\u53d8\u91cf\u5e76\u5c06\u5176\u5e94\u7528\u4e8e\u65e9\u671f\u5386\u53f2\u65f6\u6bb5\u65f6\uff0c\u5b83\u4eec\u5728\u6837\u672c\u5185\u548c\uff08\u4f2a\uff09\u6837\u672c\u5916\u68c0\u9a8c\u4e2d\u5747\u80fd\u9884\u6d4b\u9884\u671f\u6536\u76ca\u7387\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5728\u60ca\u559c\u4e8e\u53e6\u7c7b\u6570\u636e\u7684\u53d1\u73b0\u4e4b\u4f59\uff0c\u6050\u6015\u4e5f\u5e94\u8be5\u591a\u4e00\u5206\u8c28\u614e\u3002<\/p>\n\n\n\n<p>\u9664\u6b64\u4e4b\u5916\uff0c\u65e2\u7136\u8c08\u5230\u53e6\u7c7b\u6570\u636e\uff0c\u4e0d\u59a8\u518d\u804a\u804a\u53e6\u4e00\u4e2a\u76f8\u5173\u8bdd\u9898\u3002\u6709\u76f8\u5173\u7814\u7a76\u8868\u660e\uff0c\u6d77\u5916\u5927\u91cf\u7684\u53e6\u7c7b\u6570\u636e\u4f9b\u5e94\u5546\u63d0\u4f9b\u7684\u6570\u636e\u90fd\u53ea\u5177\u5907\u5bf9\u516c\u53f8\u57fa\u672c\u9762\u7684\u77ed\u65f6\u95f4\u5c3a\u5ea6\u7684\u53ef\u9884\u6d4b\u6027\u3002Dessaint, Foucault and Fresard (2020) \u7684\u7814\u7a76\u8868\u660e\uff0c\u5982\u6b64\u53e6\u7c7b\u6570\u636e\u53ef\u5f97\u6027\u7684\u63d0\u5347\u964d\u4f4e\u4e86\u8fdb\u884c\u77ed\u65f6\u95f4\u5c3a\u5ea6\u7684\u9884\u6d4b\u6210\u672c\uff08\u4ece\u800c\u63d0\u9ad8\u4e86\u51c6\u786e\u6027\uff09\uff0c\u4f46\u589e\u52a0\u4e86\u8fdb\u884c\u957f\u65f6\u95f4\u5c3a\u5ea6\u9884\u6d4b\u7684\u6210\u672c\uff08\u4ece\u800c\u964d\u4f4e\u4e86\u51c6\u786e\u6027\uff09\u3002\u5bf9\u4e8e\u516c\u53f8\u57fa\u672c\u9762\u9884\u6d4b\u6765\u8bf4\uff0c\u4e8c\u8005\u7684\u7efc\u5408\u6548\u679c\u662f mixed\u3002\u53ef\u4ee5\u9884\u89c1\uff0c\u672a\u6765\u5728\u4f7f\u7528\u53e6\u7c7b\u6570\u636e\u9884\u6d4b\u516c\u53f8\u57fa\u672c\u9762\u65f6\uff0c\u4f1a\u6709\u66f4\u591a\u7684\u7814\u7a76\u5411\u8fd9\u4e2a\u65b9\u5411\u503e\u659c\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h_589370949_3\"><strong>3 \u548c\u534f\u65b9\u5dee\u77e9\u9635\u6709\u5173<\/strong><\/h4>\n\n\n\n<p>Ross (1976) \u7684 APT \u6307\u51fa\uff0c\u89e3\u91ca\u8d44\u4ea7\u9884\u671f\u6536\u76ca\u7387\u622a\u9762\u5dee\u5f02\u7684\u56e0\u5b50\u5e94\u8be5\u540c\u65f6\u80fd\u591f\u89e3\u91ca\u8d44\u4ea7\u7684\u5171\u540c\u8fd0\u52a8\u3002\u5728\u5e02\u573a\u4e2d\u4e0d\u5b58\u5728\u8fd1\u4f3c\u65e0\u98ce\u9669\u5957\u5229\u673a\u4f1a\u8fd9\u4e2a\u5047\u8bbe\u4e0b\uff0cKozak, Nagel and Santosh (2018) \u540c\u6837\u8bba\u8ff0\u4e86\u8fd9\u4e00\u70b9\uff08\u89c1<a href=\"https:\/\/zhuanlan.zhihu.com\/p\/376931645\">\u300aWhich beta (III)?\u300b<\/a>\uff09\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u5c55\u793a\u4e86 BetaPlus \u5c0f\u7ec4\u6784\u9020\u5e76\u7ef4\u62a4\u7684 A \u80a1\u5e38\u89c1\u4e03\u7c7b\u98ce\u683c\u56e0\u5b50\u5728 2000\/01\/01 \u5230 2022\/04\/30 \u4e4b\u95f4\u7684\u8868\u73b0\u3002\u7edf\u8ba1\u6570\u636e\u8868\u660e\uff0c\u5728\u8be5\u5b9e\u8bc1\u533a\u95f4\u5185\uff0c\u867d\u7136\u5b83\u4eec\u7684\u6536\u76ca\u7387\u5747\u503c\u9ad8\u4f4e\u6709\u5dee\u5f02\uff0c\u4f46\u6536\u76ca\u7387\u7684\u6807\u51c6\u5dee\u540c\u6837\u4e5f\u6709\u5dee\u5f02\uff0c\u56e0\u6b64\u5e76\u6ca1\u6709\u54ea\u4e2a\u98ce\u683c\u56e0\u5b50\u7684\u98ce\u9669\u8c03\u6574\u540e\u6536\u76ca\u660e\u663e\u9ad8\u4e8e\u5176\u4ed6\u7684\u56e0\u5b50\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/pic2.zhimg.com\/80\/v2-83a392d3e6a2c5b3c8deca5cc330ad25_1440w.webp\" alt=\"\"\/><\/figure>\n\n\n\n<p>\u518d\u6765\u770b\u4e00\u4e2a\u7f8e\u80a1\u7684\u4f8b\u5b50\u3002Kozak, Nagel and Santosh (2018) \u5c06\u5b9e\u8bc1\u533a\u95f4\u5206\u6210\u524d\u540e\u4e24\u534a\u513f\u5e76\u8003\u5bdf\u4e86 15 \u4e2a\u56e0\u5b50\u3002\u4e0b\u56fe\u5c55\u793a\u4e86\u6bcf\u4e2a\u56e0\u5b50\u5728\u524d\u540e\u4e24\u4e2a\u533a\u95f4\u5185\u590f\u666e\u7387\u7684\u6563\u70b9\u56fe\u3002\u5982\u679c\u80fd\u591f\u5728\u83b7\u5f97\u9ad8\u6536\u76ca\u7684\u540c\u65f6\u964d\u4f4e\u6ce2\u52a8\uff0c\u90a3\u4e48\u6837\u672c\u5185\uff08\u524d\u4e00\u534a\u533a\u95f4\uff09\u590f\u666e\u7387\u9ad8\u7684\u56e0\u5b50\u5728\u6837\u672c\u5916\uff08\u540e\u4e00\u534a\u533a\u95f4\uff09\u7684\u590f\u666e\u7387\u5e94\u8be5\u4ecd\u7136\u66f4\u9ad8\u4e00\u4e9b\uff0c\u6211\u4eec\u5c06\u4f1a\u770b\u5230\u8fd9\u4e9b\u70b9\u56f4\u7ed5\u5728 45 \u5ea6\u76f4\u7ebf\u4e0a\u3002\u7136\u800c\u4e8b\u5b9e\u5e76\u975e\u5982\u6b64\u3002\u65e0\u8bba\u6837\u672c\u5185\u7684\u590f\u666e\u7387\u591a\u9ad8\uff0c\u8fd9 15 \u4e2a\u56e0\u5b50\u6837\u672c\u5916\u7684\u590f\u666e\u7387\u51e0\u4e4e\u662f\u4e00\u6761\u5e73\u884c\u4e8e\u6a2a\u5750\u6807\u7684\u6c34\u5e73\u7ebf\uff0c\u800c\u975e\u4eba\u4eec\u671f\u671b\u7684 45 \u5ea6\u659c\u7ebf\u3002\uff08\u6211\u7528\u51e0\u767e\u4e2a\u56e0\u5b50\u5728 A \u80a1\u505a\u4e86\u540c\u6837\u7684\u5b9e\u8bc1\uff0c\u89c2\u5bdf\u5230\u4e86\u7c7b\u4f3c\u7684\u7ed3\u679c\u3002\uff09<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/pic3.zhimg.com\/80\/v2-0165bb2497c4262e4159b575043040b2_1440w.webp\" alt=\"\"\/><\/figure>\n\n\n\n<p>\u4e0a\u8ff0\u7ed3\u679c\u663e\u793a\uff0c\uff08\u6837\u672c\u5916\uff09\u9ad8\u6536\u76ca\u5f80\u5f80\u5bf9\u5e94\u7740\u9ad8\u6ce2\u52a8\uff08\u5bf9\u7740\u6837\u672c\u5185\u786c\u6316 \u2014\u2014 data snooping \u2014\u2014 \u53e6\u8bf4\uff09\uff0c\u8fd9\u4e00\u5b9e\u8bc1\u7ed3\u679c\u548c APT \u543b\u5408\u3002<\/p>\n\n\n\n<p>\u65e9\u5728\u51e0\u5341\u5e74\u524d\uff0cEugene Fama \u66fe\u7ecf\u6253\u8da3\u5230 APT \u8ba9\u4f17\u591a\u6316\u56e0\u5b50\u7684\u5c1d\u8bd5\u201c\u5408\u7406\u5316\u201d\uff0c\u5373 APT \u53ea\u8bf4\u4e86\u8d44\u4ea7\u9884\u671f\u6536\u76ca\u7387\u548c\u4f17\u591a\u56e0\u5b50\u6709\u5173\uff0c\u4f46\u5374\u6ca1\u6709\u6307\u51fa\u5230\u5e95\u6709\u54ea\u4e9b\u56e0\u5b50\u3002\u56e0\u6b64\uff0c\u5f88\u591a\u5b66\u8005\u6253\u7740 APT \u7684\u65d7\u53f7\u201c\u8086\u65e0\u5fcc\u60ee\u201d\u5730\u6316\u51fa\u4e86\u4e00\u832c\u53c8\u4e00\u832c\u56e0\u5b50\uff08zoo of factors\uff09\uff0cFama \u628a\u8fd9\u4e2a\u73b0\u8c61\u79f0\u4f5c APT \u7ed9\u4e86\u8fd9\u4e9b\u7814\u7a76\u201cfishing license\u201d\uff08\u5373 APT \u8ba9\u8fd9\u4e9b\u7814\u7a76\u5408\u7406\u5316\uff09\u3002\uff08Sorry\uff0c\u8fd9\u91cc\u6211\u5b9e\u5728\u5fcd\u4e0d\u4f4f\u5410\u69fd\u4e00\u53e5\uff0c\u5728\u4e00\u672c\u8457\u540d\u7684\u8d44\u4ea7\u5b9a\u4ef7\u6559\u6750\u7684\u4e2d\u8bd1\u7248\u4e2d\uff0c\u4e2d\u6587\u4f5c\u8005\u7adf\u7136\u771f\u7684\u628a fishing license \u7ffb\u8bd1\u6210\u201c\u9493\u9c7c\u8bb8\u53ef\u8bc1\u201d\u2026\u2026\uff09<\/p>\n\n\n\n<p>\u5982\u4eca\uff0c\u5f53\u6211\u4eec\u91cd\u65b0\u5ba1\u89c6 APT \u65f6\uff0c\u6beb\u65e0\u7591\u95ee\u5e94\u8be5\u5c06\u5b83\u4f5c\u4e3a\u6316\u6398\u771f\u5b9e\u56e0\u5b50\u7684\u6709\u6548\u6307\u5f15\uff0c\u6b63\u5982\u672c\u8282\u4e00\u5f00\u5934\u8bf4\u7684\u90a3\u6837\uff1a\u89e3\u91ca\u8d44\u4ea7\u9884\u671f\u6536\u76ca\u7387\u622a\u9762\u5dee\u5f02\u7684\u56e0\u5b50\u5e94\u8be5\u4e5f\u80fd\u89e3\u91ca\u8d44\u4ea7\u7684\u5171\u540c\u8fd0\u52a8\u3002\u5728\u8fd9\u4e2a\u8ba4\u77e5\u4e0b\uff0c\u4ee5 PCA \u4e3a\u4ee3\u8868\u7684\u4e00\u7cfb\u5217\u5b9e\u8bc1\u8d44\u4ea7\u5b9a\u4ef7\u7814\u7a76\u5728\u8fd9\u51e0\u5e74\u53d6\u5f97\u4e86\u5f88\u591a\u7a81\u7834\uff08Kelly, Pruitt and Su 2019 \u3001Kozak, Nagel and Santosh 2020\uff09\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h_589370949_4\"><strong>4 \u8d8a\u590d\u6742\u8d8a\u597d ?<\/strong><\/h4>\n\n\n\n<p>\u5728\u672c\u8282\u7684\u8ba8\u8bba\u4e2d\uff0c\u6211\u4eec\u4ee5\u56e0\u5b50\u4e2a\u6570\u7684\u591a\u5c11\u4ee3\u8868\u6a21\u578b\u590d\u6742\u5ea6\u3002\u56e0\u5b50\u4e2a\u6570\u8d8a\u591a\uff0c\u6a21\u578b\u8d8a\u590d\u6742\u3002<\/p>\n\n\n\n<p>2019 \u5e74\uff0cBelkin, et al. (2019) \u4e00\u6587\u63d0\u51fa\u4e86\u673a\u5668\u5b66\u4e60\u4e2d\u6837\u672c\u5916\u8bef\u5dee\u7684\u201cdouble descent\u201d\u73b0\u8c61\uff0c\u5f15\u53d1\u4e86\u673a\u5668\u5b66\u4e60\u9886\u57df\u548c\u7406\u8bba\u7edf\u8ba1\u9886\u57df\u7684\u5e7f\u6cdb\u8ba8\u8bba\u3002\u4e3a\u4e86\u7406\u89e3\u8fd9\u4e00\u73b0\u8c61\uff0c\u6211\u4eec\u5148\u4ece\u719f\u77e5\u7684 bias-variance trade-off \u8bf4\u8d77\u3002<\/p>\n\n\n\n<p>\u5bf9\u4e8e\u6a21\u578b\u6765\u8bf4\uff0c\u5176\u6837\u672c\u5916\u8868\u73b0\u548c\u6a21\u578b\u590d\u6742\u5ea6\u5173\u7cfb\u5bc6\u5207\u3002\u5f53\u6a21\u578b\u590d\u6742\u5ea6\u5f88\u4f4e\u65f6\uff0c\u6a21\u578b\u7684\u65b9\u5dee\u5f88\u5c0f\uff08\u56e0\u4e3a\u53d8\u91cf\u53c2\u6570\u4f30\u8ba1\u7684\u65b9\u5dee\u5f88\u5c0f\uff09\uff0c\u4f46\u662f\u504f\u5dee\u5f88\u9ad8\uff1b\u5f53\u6a21\u578b\u590d\u6742\u5ea6\u9ad8\u65f6\uff0c\u6a21\u578b\u7684\u65b9\u5dee\u53d8\u5927\uff0c\u4f46\u662f\u504f\u5dee\u964d\u4f4e\u3002\u4e8c\u8005\u7684\u5171\u540c\u4f5c\u7528\u5c31\u662f\u4eba\u4eec\u719f\u6089\u7684 U-Shape\uff0c\u5373 bias-variance trade-off\uff0c\u56e0\u6b64\u5b58\u5728\u67d0\u4e2a\u6700\u4f18\u7684\u8d85\u53c2\u6570\uff0c\u4f7f\u5f97\u6837\u672c\u5916\u7684\u603b\u8bef\u5dee\uff08\u98ce\u9669\uff09\u6700\u4f4e\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/pic4.zhimg.com\/80\/v2-acbdb5162e8c7c0a099c843d7aae84af_1440w.webp\" alt=\"\"\/><\/figure>\n\n\n\n<p>\u6211\u4eec\u8fd8\u53ef\u4ee5\u6362\u4e2a\u89d2\u5ea6\u6765\u7406\u89e3 bias-variance trade-off\uff0c\u800c\u8fd9\u4e2a\u89d2\u5ea6\u5bf9\u7406\u89e3 double descent \u81f3\u5173\u91cd\u8981\u3002\u5f53\u6a21\u578b\u5f88\u7b80\u5355\u65f6\uff0c\u5b83\u80fd\u591f\u6709\u6548\u89c4\u907f\u8fc7\u62df\u5408\uff0c\u4f46\u5374\u5f88\u96be\u60f3\u8c61\u5982\u6b64\u7b80\u5355\u7684\u6a21\u578b\u662f\u771f\u5b9e\u4e16\u754c\u7684\u597d\u7684\u8fd1\u4f3c\uff1b\u800c\u5f53\u6a21\u578b\u590d\u6742\u65f6\uff0c\u5b83\u66f4\u6709\u53ef\u80fd\u903c\u8fd1\u771f\u5b9e\u4e16\u754c\uff0c\u4f46\u662f\u4e5f\u7684\u786e\u66f4\u5bb9\u6613\u8fc7\u62df\u5408\u3002\u56e0\u6b64 bias-variance trade-off \u4e5f\u53ef\u4ee5\u7406\u89e3\u4e3a approximation-overfit trade-off\u3002<\/p>\n\n\n\n<p>\u7136\u800c\uff0c\u4e0a\u8ff0\u7ed3\u8bba\u6709\u4e00\u4e2a\u6211\u4eec\u90fd\u4e60\u4ee5\u4e3a\u5e38\u7684\u524d\u63d0\uff1a\u53d8\u91cf\u4e2a\u6570 &lt; \u6837\u672c\u4e2a\u6570\u3002\u90a3\u4e48\uff0c\u5982\u679c\u6a21\u578b\u590d\u6742\u5230\u53d8\u91cf\uff08\u56e0\u5b50\uff09\u7684\u4e2a\u6570\u8d85\u8fc7\u4e86\u6837\u672c\u7684\u4e2a\u6570\u53c8\u4f1a\u51fa\u73b0\u600e\u6837\u7684\u60c5\u51b5\u5462\uff1f\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u4e00\u95ee\u9898\u5e76\u975e\u65e0\u7f18\u65e0\u6545\u7684\u51ed\u7a7a\u60f3\u8c61\u3002\u5bf9\u4e8e\u590d\u6742\u7684\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u6765\u8bf4\uff0c\u6a21\u578b\u53c2\u6570\u7684\u4e2a\u6570\u5f88\u5bb9\u6613\u8d85\u8fc7\u6837\u672c\u7684\u4e2a\u6570\uff0c\u7136\u800c\u8fd9\u4e9b\u6a21\u578b\u786e\u5728\u6837\u672c\u5916\u6709\u7740\u975e\u51e1\u7684\u8868\u73b0\uff08\u54e6\uff0c\u5f53\u7136\u4e0d\u662f\u8d44\u4ea7\u5b9a\u4ef7\u9886\u57df\uff09\u3002\u8fd9\u4e2a\u73b0\u8c61\u4fc3\u4f7f\u8fd9\u4eba\u4eec\u641e\u6e05\u695a what is behind the scene\u3002<\/p>\n\n\n\n<p><strong><span style=\"text-decoration: underline;\">\u5f53\u53d8\u91cf\u4e2a\u6570 &gt; \u6837\u672c\u4e2a\u6570\u65f6\uff0c\u6a21\u578b\u5728\u6837\u672c\u5185\u80fd\u591f\u5b8c\u7f8e\u7684\u62df\u5408\u5168\u90e8\u6837\u672c\uff08\u5728\u673a\u5668\u5b66\u4e60\u672f\u8bed\u4e2d\uff0c\u8fd9\u4e2a\u73b0\u8c61\u88ab\u79f0\u4e3a interpolation\uff09\u3002\u5bf9\u8fd9\u6837\u4e00\u4e2a\u6a21\u578b\u6765\u8bf4\uff0c\u4eba\u4eec\u901a\u5e38\u7684\u8ba4\u77e5\u662f\uff0c\u5b83\u5728\u6837\u672c\u5916\u7684\u8868\u73b0\u4e00\u5b9a\u4f1a\u201c\u7206\u70b8\u201d\uff0c\u5373\u6beb\u65e0\u4f5c\u4e3a\u3002\u8fd9\u662f\u56e0\u4e3a\u5b83\u8fc7\u5ea6\u62df\u5408\u4e86\u6837\u672c\u5185\u6570\u636e\u4e2d\u7684\u5168\u90e8\u566a\u58f0\u3002\u7136\u800c\uff0cBelkin, et al (2019) \u6307\u51fa\uff0c\u5f53\u4eba\u4eec\u8ba9\u6a21\u578b\u590d\u6742\u5ea6\u7a81\u7834\u6837\u672c\u4e2a\u6570\u8fd9\u4e2a\u201c\u7981\u5fcc\u4e4b\u5730\u201d\u540e\uff0c\u795e\u5947\u7684\u4e8b\u60c5\u53d1\u751f\u4e86\uff1a\u6837\u672c\u5916\u603b\u8bef\u5dee\u5e76\u6ca1\u6709\u201c\u7206\u70b8\u201d\uff0c\u800c\u662f\u968f\u7740\u590d\u6742\u5ea6\u7684\u63d0\u5347\u5355\u8c03\u4e0b\u964d\u3002\u6b63\u56e0\u4e3a\u5728\u6837\u672c\u4e2a\u6570\u4e24\u4fa7\u90fd\u51fa\u73b0\u4e86\u8bef\u5dee\u5355\u8c03\u4e0b\u964d\u7684\u60c5\u51b5\uff0cBelkin, et al (2019) \u5c06\u8fd9\u4e2a\u73b0\u8c61\u79f0\u4e3a double descent\u3002<\/span><\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/pic2.zhimg.com\/80\/v2-7078014b75e1ea9945bb0c0f8284edf1_1440w.webp\" alt=\"\"\/><\/figure>\n\n\n\n<p>\u56e0\u4e3a\u672c\u6587\u7684\u76ee\u7684\u5e76\u975e\u89e3\u91ca\u80cc\u540e\u7684\u7edf\u8ba1\u5b66\u7406\u8bba\uff0c\u6240\u4ee5\u6211\u5728\u6b64\u5bf9\u8be5\u73b0\u8c61\u7ed9\u4e00\u4e9b\u76f4\u89c9\u4e0a\u7684\u89e3\u91ca\u3002\u5f53\u53d8\u91cf\u4e2a\u6570\u8d85\u8fc7\u6837\u672c\u4e2a\u6570\u7684\u65f6\u5019\uff0c\u6837\u672c\u5185\u7684\u89e3\u662f\u4e0d\u552f\u4e00\u7684\uff0c\u800c\u6700\u4f18\u7684\u89e3\u53ef\u4ee5\u7406\u89e3\u4e3a\u6ee1\u8db3\u53c2\u6570\u7684\u65b9\u5dee\u6700\u5c0f\uff08\u6b63\u5219\u5316\u6216 implied \u6b63\u5219\u5316\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\u53d1\u6325\u4e86\u975e\u5e38\u91cd\u8981\u7684\u4f5c\u7528\uff09\u3002\u968f\u7740\u53d8\u91cf\u8d8a\u6765\u8d8a\u591a\uff0c\u6700\u4f18\u89e3\u7684\u65b9\u5dee\u603b\u80fd\u5355\u8c03\u4e0b\u964d\u3002<\/p>\n\n\n\n<p>\u518d\u6765\u770b\u504f\u5dee\uff0c\u901a\u5e38\u6765\u8bf4\uff0c\u504f\u5dee\u786e\u5b9e\u4f1a\u968f\u7740\u590d\u6742\u5ea6\u7684\u63d0\u5347\u800c\u589e\u52a0\u3002\u4f46\u662f\u6240\u6709\u6a21\u578b\u90fd\u662f\u771f\u5b9e DGP \u7684\u67d0\u4e2a mis-specified \u7248\u672c\u3002\u5f53\u5b58\u5728\u6a21\u578b\u8bbe\u5b9a\u504f\u8bef\u7684\u65f6\u5019\uff0c\u53ef\u4ee5\u8bc1\u660e\u5f53\u53d8\u91cf\u4e2a\u6570\u8d85\u8fc7\u6837\u672c\u4e2a\u6570\u65f6\uff0c\u504f\u5dee\u4e5f\u4f1a\u5728\u4e00\u5b9a\u8303\u56f4\u5185\u968f\u7740\u590d\u6742\u5ea6\u800c\u4e0b\u964d\u3002\u56e0\u6b64\uff0c\u4e8c\u8005\u7684\u7efc\u5408\u7ed3\u679c\u5c31\u662f\u6a21\u578b\u5728\u6837\u672c\u5916\u7684\u8bef\u5dee\u8868\u73b0\u4f1a\u968f\u590d\u6742\u5ea6\u7684\u4e0a\u5347\u800c\u4e0b\u964d\u3002\uff08\u5728\u4e00\u4e9b\u60c5\u51b5\u4e0b\uff0c\u6837\u672c\u5916\u8bef\u5dee\u7684 global minimum \u51fa\u73b0\u5728\u5f53\u53d8\u91cf\u4e2a\u6570 &gt; \u6837\u672c\u4e2a\u6570\u65f6\u3002\uff09<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u4e24\u5f20 slides \u603b\u7ed3\u4e86\u4e0a\u9762\u7684\u8bdd\uff08\u7b2c\u4e8c\u5f20 slide \u91cc\u7684\u8868\u53c2\u8003\u4e86 Bryan Kelly \u7684 talk\uff0c\u7279\u6b64\u8bf4\u660e\uff09\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/pic4.zhimg.com\/80\/v2-d72d0470f215d3ef7eba7f7da4368423_1440w.webp\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/pic1.zhimg.com\/80\/v2-5dd44fe59913b732bedc4cda2cdf7d3c_1440w.webp\" alt=\"\"\/><\/figure>\n\n\n\n<p>\u5bf9\u4e8e\u8d44\u4ea7\u5b9a\u4ef7\u548c\u56e0\u5b50\u6295\u8d44\u6765\u8bf4\uff0c\u5982\u679c\u4f60\u548c\u6211\u4e00\u6837\u8ba4\u540c\u56e0\u5b50\u7684\u9ad8\u7ef4\u6570\u65f6\u4ee3 \u2014\u2014 \u5373\u6536\u76ca\u7387\u7684 DGP \u5305\u542b\u4e86\u975e\u5e38\u591a\u7684\u56e0\u5b50\uff0c\u90a3\u4e48\u4e0a\u8ff0\u5173\u4e8e\u6a21\u578b\u590d\u6742\u5ea6\u7684\u63a2\u8ba8\u4e5f\u8bb8\u4f1a\u5e26\u6765\u5168\u65b0\u800c\u6709\u76ca\u7684\u542f\u53d1\u3002\u5728\u8fd9\u65b9\u9762\uff0c\u4e5f\u6709\u5927\u4f6c\u5df2\u7ecf\u8d70\u5728\u4e86\u524d\u9762\u3002Bryan Kelly \u548c\u4ed6\u7684\u5408\u4f5c\u8005\u4ee5\u53ca\u5b66\u751f\u4e00\u8d77\u5199\u4e86\u4e00\u7cfb\u5217\u201c\u590d\u6742\u5ea6\u7f8e\u5fb7\u201d\u7684 working papers\uff0c\u5728\u8d44\u4ea7\u5b9a\u4ef7\u9886\u57df\u63a2\u7d22\u63d0\u5347\u590d\u6742\u5ea6\u5e26\u6765\u7684\u6837\u672c\u5916\u597d\u5904\u3002\u4f8b\u5982\uff0cKelly, Malamud and Zhou (2022) \u4e00\u6587\u4f7f\u7528\u795e\u7ecf\u7f51\u7edc\u5bf9\u7f8e\u80a1\u8fdb\u884c\u4e86\u62e9\u65f6\uff08\u6bcf\u6b21\u5efa\u6a21\u4ec5\u5229\u7528\u4e00\u5e74 12 \u671f\u7684\u6570\u636e\u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\uff09\uff0c\u5e76\u53d1\u73b0\u4e86\u7c7b\u4f3c\u7684 double descent \u73b0\u8c61\u3002<\/p>\n\n\n\n<p>\u5f53\u7136\uff0c\u5373\u4fbf\u6211\u4eec\u8ba4\u540c\u4e86\u201c\u8d8a\u590d\u6742\u8d8a\u597d\u201d\uff0c\u4e5f\u4f9d\u7136\u8981\u56de\u7b54\u66f4\u91cd\u8981\u7684\u95ee\u9898\uff0c\u5373\u5982\u4f55\u4f30\u8ba1\u53c2\u6570\uff0c\u5982\u4f55\u6b63\u5219\u5316\uff0c\u5982\u4f55\u6765\u5229\u7528\u6210\u5343\u4e0a\u4e07\u751a\u81f3\u66f4\u591a\u7684\u56e0\u5b50\u6765\u5f62\u6210\u5173\u4e8e\u9884\u671f\u6536\u76ca\u7387\u66f4\u597d\u7684\u9884\u6d4b\u3002\u867d\u7136 Kelly \u7b49\u4eba\u7684\u6587\u7ae0\u5728\u62e9\u65f6\u65b9\u9762\u53d6\u5f97\u4e86\u8ba9\u4eba\u5174\u594b\u7684\u7ed3\u679c\uff0c\u4f46\u5728 cross-section \u662f\u5426\u6709\u7c7b\u4f3c\u7684\u5b9e\u8bc1\u7ed3\u679c\u4f9d\u7136\u9700\u8981\u65f6\u95f4\u6765\u56de\u7b54\uff08Kelly \u6709\u4e00\u7bc7 working paper \u7814\u7a76 cross-section\uff0c\u4f46\u8fd8\u6ca1\u6709 publicly available\uff09\u3002<\/p>\n\n\n\n<p>\u4f46\u662f\u65e0\u8bba\u5982\u4f55\uff0c\u6b22\u8fce\u6765\u5230 over-parameterization \u65f6\u4ee3\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h_589370949_5\"><strong>5 \u7ed3\u675f\u8bed<\/strong><\/h4>\n\n\n\n<p>\u4ee5\u4e0a\u5c31\u662f\u6211\u5bf9\u56e0\u5b50\u6295\u8d44\u9ad8\u7ef4\u6570\u65f6\u4ee3\u7684\u56db\u70b9\u601d\u8003\u3002<\/p>\n\n\n\n<p>\u4e0d\u8fc7\u5728\u672c\u6587\u7684\u6700\u540e\uff0c\u4ecd\u7136\u6709\u5fc5\u8981\u6307\u51fa\uff0c\u5728\u534f\u53d8\u91cf\u7684\u9ad8\u7ef4\u6570\u65f6\u4ee3\uff0c\u5982\u4f55 prepare \u56e0\u5b50\u56fa\u7136\u91cd\u8981\uff08\u5c0f\u5fc3\u591a\u91cd\u5047\u8bbe\u68c0\u9a8c\u3001\u5c0f\u5fc3\u6295\u8d44\u8005\u5b66\u4e60\u3001\u5229\u7528 APT \u7684 implication\uff09\uff0c\u4f46\u662f\u5982\u4f55\u6c42\u89e3\u9ad8\u7ef4\u95ee\u9898\u624d\u66f4\u52a0\u6838\u5fc3\uff08\u5982\u4f55\u5229\u7528\u590d\u6742\u5ea6\u7684\u597d\u5904 ?\uff09\u3002<\/p>\n\n\n\n<p>\u6216\u8bb8\uff0c\u6211\u4eec\u5df2\u7ecf\u5230\u4e86\u4ece\u8ba1\u91cf\u7ecf\u6d4e\u5b66\u5230\u673a\u5668\u5b66\u4e60\u7684\u5fc5\u7136\u8f6c\u578b\u65f6\u523b\u3002\u6b63\u5982 Stefan Nagel \u7684<a href=\"https:\/\/zhuanlan.zhihu.com\/p\/539300422\">\u300a\u673a\u5668\u5b66\u4e60\u4e0e\u8d44\u4ea7\u5b9a\u4ef7\u300b<\/a>\uff08Nagel 2021\uff09\u6240\u5021\u5bfc\u7684\u90a3\u6837\uff0c\u5c06\u7ecf\u6d4e\u5b66\u63a8\u7406\u6ce8\u5165\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u5c06\u6210\u4e3a\u9ad8\u7ef4\u6570\u65f6\u4ee3\u7814\u7a76\u7684\u5fc5\u7ecf\u4e4b\u8def\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/pic1.zhimg.com\/80\/v2-f016bf2dc1678d7131a5c220f741b3a0_1440w.webp\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/pic1.zhimg.com\/80\/v2-0792eba76504b6708ed9b467fa60ae74_1440w.webp\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>\u53c2\u8003\u6587\u732e<\/strong><\/p>\n\n\n\n<ul><li>Baba-Yara, F., B. Boyer, and C. Davis (2021). The factor model failure puzzle. Working paper.<\/li><li>Bekkerman, R., E. M. Fich, and N. V. Khimich (forthcoming). The effect of innovation similarity on asset prices: Evidence from patents\u2019 big data.&nbsp;<strong><em>Review of Asset Pricing Studies<\/em><\/strong>.<\/li><li>Belkin, M., D. Hsu, S. Ma, and S. Mandal (2019). Reconciling modern machine-learning practice and the classical bias-variance trade-off.&nbsp;<strong><em>PNAS<\/em><\/strong><em>116<\/em>(32), 15849 \u2013 15854.<\/li><li>Dessaint, O., T. Foucault, and L. Fresard (2020). Does alternative data improve financial forecasting? The horizon effect. Working paper.<\/li><li>Kelly, B. T., S. Malamud, and K. Zhou (2022). The virtue of complexity in return prediction. Working paper.<\/li><li>Kelly, B. T., S. Pruitt, and Y. Su (2019). Characteristics are covariances: A unified model of risk and return.&nbsp;<em><strong>Journal of Financial Economics<\/strong>&nbsp;134<\/em>(3), 501 \u2013 524.<\/li><li>Kozak, S., S. Nagel, and S. Santosh (2018). Interpreting factor models.&nbsp;<em><strong>Journal of Finance<\/strong>73<\/em>(3), 1183 \u2013 1223.<\/li><li>Kozak, S., S. Nagel, and S. Santosh (2020). Shrinking the cross-section.&nbsp;<em><strong>Journal of Financial Economics<\/strong>&nbsp;135<\/em>(2), 271 \u2013 292.<\/li><li>Linnainmaa, J. T. and M. R. Roberts (2018). The history of the cross-section of stock returns.&nbsp;<strong><em>Review of Financial Studies<\/em><\/strong><em>31<\/em>(7), 2606 \u2013 2649.<\/li><li>Martin, I. and S. Nagel (2022). Market efficiency in the age of big data.&nbsp;<strong><em>Journal of Financial Economics<\/em><\/strong><em>145<\/em>(1), 154 \u2013 177.<\/li><li>Nagel, S. (2021).&nbsp;<em>Machine Learning in Asset Pricing<\/em>. Princeton University Press.<\/li><li>Ross, S. A. (1976). The arbitrage theory of capital asset pricing.&nbsp;<em><strong>Journal of Economic Theory<\/strong>&nbsp;13<\/em>(3), 341 \u2013 360.<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">By<\/h2>\n\n\n\n<p>\u77f3\u5ddd https:\/\/zhuanlan.zhihu.com\/p\/589370949?utm_medium=social&amp;utm_oi=774013724896788480&amp;utm_psn=1583185642497994752&amp;utm_source=wechat_session&amp;utm_id=0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6458\u8981\uff1a\u5b9e\u8bc1\u8d44\u4ea7\u5b9a\u4ef7\u5df2\u7136\u8fdb\u5165\u56e0\u5b50\uff08\u534f\u53d8\u91cf\uff09\u7684\u9ad8\u7ef4\u6570\u65f6\u4ee3\u3002\u672c\u6587\u629b\u7816\u5f15\u7389\uff0c\u9610\u8ff0\u6211\u5bf9\u6b64\u7684\u56db\u70b9\u601d\u8003\u3002\uff08DGP: Data Generating Process\uff09 Key Takeaway: over-parameterization \u7684\u65f6\u4ee3\u5df2\u7ecf\u5230\u6765\uff0c\u53d8\u91cf\u6570\u91cf k \u5927\u4e8e\u6837\u672c\u6570\u91cf t \u4f3c\u4e4e\u5e76\u6ca1\u6709\u5e26\u6765 interpolate\u7684\u95ee\u9898\uff0c\u53cd\u800c\u7ed9prediction\u5e26\u6765\u4e86\u5e2e\u52a9\u3002 0 \u5f15\u5b50 \u65f6\u81f3\u4eca\u65e5\uff0c\u5b9e\u8bc1\u8d44\u4ea7\u5b9a\u4ef7\uff08\u4ee5\u53ca\u56e0\u5b50\u6295\u8d44\uff09\u5df2\u7136\u6b65\u5165\u4e86\u56e0\u5b50\uff08\u534f\u53d8\u91cf\uff09\u7684\u9ad8\u7ef4\u6570\u65f6\u4ee3\u3002\u5927\u91cf\u53d1\u8868\u5728\u9876\u520a\u4e0a\u7684\u5b9e\u8bc1\u7ed3\u679c\u8868\u660e\uff0c\u591a\u56e0\u5b50\u6a21\u578b\u5177\u6709\u5f88\u5927\u7684\u4e0d\u786e\u5b9a\u6027\u4e14\u56e0\u5b50\u7684\u7a00\u758f\u6027\u5047\u8bbe\u4e0d\u6210\u7acb\u3002\u4eba\u4eec\u719f\u77e5\u7684 ad-hoc \u7b80\u7ea6\u6a21\u578b\u65e0\u6cd5\u6307\u5f15\u672a\u6765\u7684\u6295\u8d44\u3002 \u5728\u9ad8\u7ef4\u6570\u65f6\u4ee3\uff0c\u5bfb\u627e\u771f\u6b63\u80fd\u591f\u9884\u6d4b\u9884\u671f\u6536\u76ca\u7387\u7684\u534f\u53d8\u91cf\u662f\u6838\u5fc3\u95ee\u9898\u4e4b\u4e00\u3002\u4e3a\u4e86\u5b9e\u73b0\u8fd9\u4e2a\u76ee\u6807\uff0c\u9700\u8981\u8003\u8651\u7684\u95ee\u9898\u5305\u62ec\uff1a\uff081\uff09\u591a\u91cd\u5047\u8bbe\u5047\u8bbe\u68c0\u9a8c\uff1b\uff082\uff09\u6295\u8d44\u8005\uff08\u9ad8\u7ef4\uff09\u5b66\u4e60\u95ee\u9898 &amp; \u53e6\u7c7b\u6570\u636e\uff1b\uff083\uff09\u6765\u81ea\u8d44\u4ea7\u5b9a\u4ef7\u7406\u8bba\u7684\u6307\u5f15\uff1a\u5373\u89e3\u91ca\u9884\u671f\u6536\u76ca\u7387\u7684\u56e0\u5b50\u5e94\u8be5\u4e5f\u80fd\u89e3\u91ca\u8d44\u4ea7\u7684\u5171\u540c\u6ce2\u52a8\u3002\u6700\u540e\uff0c\u4e00\u4e2a\u6700\u65b0\u7684\u8ba8\u8bba\u70ed\u70b9\u662f\u56e0\u5b50\u7684\u4e2a\u6570\u662f\u5426\u8d8a\u591a\u8d8a\u597d\uff08\u5373\u6a21\u578b\u590d\u6742\u5ea6\u662f\u5426\u8d8a\u9ad8\u8d8a\u597d\uff09\uff1a\u590d\u6742\u6a21\u578b\u80fd\u66f4\u597d\u5730\u903c\u8fd1\u771f\u5b9e DGP\uff0c\u4f46\u53c2\u6570\u4f30\u8ba1\u7684\u65b9\u5dee\u66f4\u5927\uff1b\u7b80\u7ea6\u6a21\u578b\u7684\u53c2\u6570\u4f30\u8ba1\u66f4\u51c6\u786e\uff0c\u4f46\u5374\u672a\u5fc5\u662f DGP \u7684\u5408\u7406\u8fd1\u4f3c\u3002\u4e8c\u8005\u76f8\u6bd4\uff0c\u5982\u4f55\u6743\u8861\u5462\uff1f \u8fd1\u65e5\uff0c\u6211\u5728\u67d0\u5238\u5546 2023 \u7684\u5e74\u5ea6\u7b56\u7565\u4f1a\u4e0a\u505a\u4e86\u9898\u4e3a\u300a\u56e0\u5b50\u6295\u8d44\u7684\u9ad8\u7ef4\u6570\u65f6\u4ee3\u300b\u7684\u62a5\u544a\uff0c\u9610\u8ff0\u4e86\u6211\u5bf9\u4e0a\u8ff0\u56db\u70b9\u7684\u601d\u8003\u3002\u672c\u6587\u501f\u7740\u62a5\u544a\u7684 slides \u505a\u7b80\u8981\u4ecb\u7ecd\u3002\u7531\u4e8e\u5bf9\u4e8e\u67d0\u4e9b\u95ee\u9898\u4e13\u680f\u5df2\u7ecf\u505a\u4e86\u5927\u91cf\u7684\u68b3\u7406\uff08\u6bd4\u5982\u591a\u91cd\u5047\u8bbe\u68c0\u9a8c\uff09\uff0c\u56e0\u6b64\u5728\u672c\u6587\u7684\u9610\u8ff0\u4e2d\uff0c\u5728\u5fc5\u8981\u7684\u5730\u65b9\u4f1a\u4f7f\u7528\u6700\u5c11\u7684\u6587\u5b57\uff08\u4f60\u9a6c\u4e0a\u5c31\u4f1a\u660e\u767d\u6211\u7684\u610f\u601d\uff09\u3002 1 \u591a\u91cd\u5047\u8bbe\u68c0\u9a8c \u8fd9\u90e8\u5206\uff0c\u4e00\u56fe\u80dc\u5343\u8a00\u3002\u9700\u8981\u76f8\u5173\u77e5\u8bc6\u7684\u5c0f\u4f19\u4f34\uff0c\u8bf7\u67e5\u770b\u516c\u4f17\u53f7\u7684\u300a\u51fa\u8272\u4e0d\u5982\u8d70\u8fd0\u300b\u7cfb\u5217\u3002 Next. 2 \u6295\u8d44\u8005\u5b66\u4e60\u95ee\u9898 &amp; \u53e6\u7c7b\u6570\u636e \u7406\u6027\u9884\u671f\u5047\u8bbe\u6295\u8d44\u8005\u77e5\u9053\u771f\u5b9e\u7684\u4f30\u503c\u6a21\u578b\u3002 \u7136\u800c\uff0c\u548c\u8fdb\u884c\u4e8b\u540e\uff08ex post\uff09\u56e0\u5b50\u5206\u6790\u7684\u4f60\u6211\u4e00\u6837\uff0c\u6295\u8d44\u8005\u5728\u6295\u8d44\u65f6\u540c\u6837\u9762\u4e34\u534f\u53d8\u91cf\u7684\u9ad8\u7ef4\u6570\u95ee\u9898\uff0c\u56e0\u6b64\u4e0d\u53ef\u80fd\u77e5\u9053\u771f\u5b9e\u7684\u4f30\u503c\u6a21\u578b\uff0c\u6240\u4ee5\u7406\u6027\u9884\u671f\u5047\u8bbe\u5e76\u4e0d\u6210\u7acb\u3002\u8fd9\u9020\u6210\u7684\u7ed3\u679c\u662f\uff0c\u5747\u8861\u72b6\u6001\u4e0b\u8d44\u4ea7\u4ef7\u683c\u548c\u7406\u6027\u9884\u671f\u60c5\u51b5\u4e0b\u76f8\u6bd4\u51fa\u73b0\u504f\u5dee\u3002\u5728\u4e8b\u540e\u5206\u6790\u4e2d\uff0c\u5df2\u5b9e\u73b0\u6536\u76ca\u7387\u4e2d\u5305\u542b\u4e00\u90e8\u5206\u56e0\u4f30\u8ba1\u8bef\u5dee\u5bfc\u81f4\u7684\u53ef\u9884\u6d4b\u6210\u5206\u3002\u4f46\u5bf9\u6295\u8d44\u8005\u6765\u8bf4\uff0c\u4e8b\u524d\uff08ex ante\uff09\u65e0\u6cd5\u5229\u7528\u4e0a\u8ff0\u53ef\u9884\u6d4b\u6027\u3002 \u56e0\u8bef\u5dee\u5bfc\u81f4\u7684\u53ef\u9884\u6d4b\u6027\u80fd\u591f\u5728\u6837\u672c\u5185\uff08IS\uff09\u4ea7\u751f\u865a\u5047\u7684\u53ef\u9884\u6d4b\u6027\uff08\u65e0\u8bba\u6295\u8d44\u8005\u662f\u5426\u4f7f\u7528\u4e86\u5148\u9a8c\u4ee5\u53ca\u65e0\u8bba\u5148\u9a8c\u662f\u5426\u6b63\u786e\uff09\uff0c\u800c\u5728\u6837\u672c\u5916\uff08OOS\uff09\u5374\u65e0\u6cd5\u9884\u6d4b\u6536\u76ca\u7387\u3002\u8fd9\u5c31\u662f\u6295\u8d44\u8005\uff08\u9ad8\u7ef4\uff09\u5b66\u4e60\u95ee\u9898\u5bfc\u81f4\u7684\u865a\u5047\u7684\u53ef\u9884\u6d4b\u6027\uff08Martin and Nagel 2022\uff09\u3002\u5177\u4f53\u9610\u8ff0\u89c1\u300aFalse In-Sample Predictability ?\u300b\u3002\u9762\u5bf9\u8fd9\u4e2a\u95ee\u9898\uff0c\u9700\u8981\u901a\u8fc7 OOS \u68c0\u9a8c\u624d\u80fd\u89c4\u907f\u3002 \u6295\u8d44\u8005\u65e0\u6cd5\u5728\u4e8b\u524d\u6295\u8d44\u4e2d\u5e94\u5bf9\u9ad8\u7ef4\u6570\uff0c\u8fd9\u4e3b\u8981\u4f53\u73b0\u5728\u4ed6\u4eec\u4f7f\u7528\u8f83\u5c11\u7684\u534f\u53d8\u91cf\uff08\u56e0\u5b50\uff09\u4f5c\u4e3a\u4f30\u503c\u7684\u4f9d\u636e\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u7531\u4e8e\u4e00\u4e9b\u53d8\u91cf\u7684\u83b7\u53d6\u6210\u672c\u5f88\u9ad8\uff0c\u6295\u8d44\u8005\u9700\u8981\u5728\u8be5\u53d8\u91cf\u5e26\u6765\u7684\u9884\u6d4b\u597d\u5904\u548c\u5176\u6210\u672c\u4e4b\u95f4\u6743\u8861\u3002\u6b64\u5916\uff0c\u6709\u9650\u7406\u6027\u4e2d\u7684\u6709\u9650\u6ce8\u610f\u529b\u673a\u5236\u4e5f\u4e3a\u6295\u8d44\u8005\u5bf9\u7b80\u7ea6\u6027\u7684\u6e34\u671b\u63d0\u4f9b\u4e86\u5fae\u89c2\u57fa\u7840\u3002\u8fd9\u4e24\u65b9\u9762\u4f5c\u7528\u5408\u529b\u5bfc\u81f4\u6295\u8d44\u8005\u5728\u4e3a\u8d44\u4ea7\u5b9a\u4ef7\u65f6\u4f7f\u7528\u8fc7\u5ea6\u7a00\u758f\u7684\u4f30\u503c\u6a21\u578b\u3002\u8fd9\u6837\u505a\u7684\u540e\u679c\u662f\uff0c\u5373\u4fbf\u5728\u6837\u672c\u5916\uff0c\u4e5f\u4f1a\u51fa\u73b0\u56e0\u6295\u8d44\u8005\u5b66\u4e60\u95ee\u9898\u800c\u9020\u6210\u7684\u865a\u5047\u7684\u53ef\u9884\u6d4b\u6027\u3002 \u5c31\u7740\u4e0a\u8ff0\u63a8\u8bba\uff0c\u6211\u4eec\u81ea\u7136\u5730\u5f15\u51fa\u672c\u5c0f\u8282\u7684\u53e6\u4e00\u4e2a\u76f8\u5173\u8bdd\u9898\uff1a\u53e6\u7c7b\u6570\u636e\u3002 \u56de\u5fc6\u4e00\u4e0b\u516c\u4f17\u53f7\u4e4b\u524d\u7684\u6587\u7ae0\u300a\u79d1\u6280\u5173\u8054\u5ea6II\u300b\u6240\u4ecb\u7ecd\u7684 Bekkerman, Fich &hellip; 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