{"id":49781,"date":"2025-07-30T19:41:42","date_gmt":"2025-07-30T11:41:42","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/49781.html"},"modified":"2025-07-30T19:41:42","modified_gmt":"2025-07-30T11:41:42","slug":"%e9%87%91%e8%9e%8d%e6%b3%a2%e5%8a%a8%e7%8e%87%e7%9a%84%e6%8d%95%e6%89%8b%ef%bc%9agarch%e6%a8%a1%e5%9e%8b%ef%bc%8c%e6%8f%ad%e7%a7%98%e5%b8%82%e5%9c%ba%e6%b3%a2%e5%8a%a8%e7%9a%84","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/49781.html","title":{"rendered":"\u91d1\u878d\u6ce2\u52a8\u7387\u7684\u201c\u6355\u624b\u201d\uff1aGARCH\u6a21\u578b\uff0c\u63ed\u79d8\u5e02\u573a\u6ce2\u52a8\u7684\u201c\u805a\u96c6\u5bc6\u7801\u201d"},"content":{"rendered":"<p>\u5728\u91d1\u878d\u5e02\u573a\u4e2d\uff0c\u6211\u4eec\u5e38\u5e38\u89c2\u5bdf\u5230\u8fd9\u6837\u7684\u73b0\u8c61\uff1a\u80a1\u5e02\u66b4\u8dcc\u540e\uff0c\u5f80\u5f80\u4f1a\u8fde\u7740\u51e0\u5929\u5267\u70c8\u6ce2\u52a8\uff1b\u800c\u5728\u5e73\u7a33\u671f\uff0c\u6ce2\u52a8\u53c8\u4f1a\u6301\u7eed\u4f4e\u8ff7\u3002\u8fd9\u79cd\u201c\u9ad8\u6ce2\u52a8\u8ddf\u7740\u9ad8\u6ce2\u52a8\uff0c\u4f4e\u6ce2\u52a8\u8ddf\u7740\u4f4e\u6ce2\u52a8\u201d\u7684\u7279\u6027\uff0c\u88ab\u79f0\u4e3a\u6ce2\u52a8\u805a\u7c7b\uff08Volatility Clustering\uff09\u3002<\/p>\n<p>\u8fc7\u53bb\u7684\u65f6\u95f4\u5e8f\u5217\u6a21\u578b\uff08\u5982ARIMA\uff09\u4e3b\u8981\u5173\u6ce8\u201c\u5747\u503c\u201d\u7684\u9884\u6d4b\uff0c\u5374\u65e0\u6cd5\u6355\u6349\u8fd9\u79cd\u201c\u6ce2\u52a8\u7387\u7684\u52a8\u6001\u53d8\u5316\u201d\u3002\u4eca\u5929\uff0c\u6211\u4eec\u5c06\u4ecb\u7ecd\u4e13\u95e8\u4e3a\u91d1\u878d\u65f6\u95f4\u5e8f\u5217\u8bbe\u8ba1\u7684\u6a21\u578b\u2014\u2014\u5e7f\u4e49\u81ea\u56de\u5f52\u6761\u4ef6\u5f02\u65b9\u5dee\u6a21\u578b\uff08Generalized Autoregressive Conditional Heteroskedasticity\uff0c\u7b80\u79f0GARCH\u6a21\u578b\uff09\u3002\u5b83\u80fd\u7cbe\u51c6\u6355\u6349\u6ce2\u52a8\u7387\u7684\u805a\u7c7b\u7279\u6027\uff0c\u662f\u91d1\u878d\u98ce\u9669\u7ba1\u7406\u3001\u671f\u6743\u5b9a\u4ef7\u7684\u201c\u6838\u5fc3\u5de5\u5177\u201d\u3002<\/p>\n<h3>\u4e00\u3001\u4e3a\u4ec0\u4e48\u9700\u8981GARCH\uff1f\u6ce2\u52a8\u805a\u7c7b\u7684\u201c\u75db\u70b9\u201d<\/h3>\n<h4>1. \u91d1\u878d\u6570\u636e\u7684\u7279\u6b8a\u4e4b\u5904<\/h4>\n<p>\u91d1\u878d\u65f6\u95f4\u5e8f\u5217\uff08\u5982\u80a1\u7968\u6536\u76ca\u7387\u3001\u6c47\u7387\u6ce2\u52a8\uff09\u6709\u4e00\u4e2a\u663e\u8457\u7279\u5f81\uff1a\u6ce2\u52a8\u7387\u4e0d\u662f\u6052\u5b9a\u7684\uff0c\u800c\u662f\u968f\u65f6\u95f4\u53d8\u5316\u7684\u3002\u4f8b\u5982\uff1a<\/p>\n<ul>\n<li>2008\u5e74\u91d1\u878d\u5371\u673a\u671f\u95f4\uff0c\u7f8e\u80a1\u5355\u6708\u8dcc\u5e45\u5e38\u8d8510%\uff0c\u6ce2\u52a8\u7387\u98d9\u5347\uff1b<\/li>\n<li>2020\u5e74\u75ab\u60c5\u521d\u671f\uff0c\u5168\u7403\u80a1\u5e02\u6ce2\u52a8\u7387\u521b\u5386\u53f2\u65b0\u9ad8\uff1b<\/li>\n<li>\u800c\u5728\u7ecf\u6d4e\u5e73\u7a33\u671f\uff0c\u80a1\u5e02\u53ef\u80fd\u8fde\u7eed\u6570\u6708\u6ce2\u52a8\u5e45\u5ea6\u5c0f\u4e8e2%\u3002<\/li>\n<\/ul>\n<p>\u8fd9\u79cd\u201c\u6ce2\u52a8\u7387\u65f6\u53d8\u201d\u7684\u7279\u6027\uff0c\u7528\u4f20\u7edf\u7684\u201c\u540c\u65b9\u5dee\u201d\u6a21\u578b\uff08\u5047\u8bbe\u6ce2\u52a8\u7387\u6052\u5b9a\uff09\u65e0\u6cd5\u523b\u753b\u3002\u4f8b\u5982\uff0c\u7528ARIMA\u9884\u6d4b\u80a1\u7968\u6536\u76ca\u7387\u65f6\uff0c\u4f1a\u9ed8\u8ba4\u6bcf\u5929\u7684\u6ce2\u52a8\u98ce\u9669\u76f8\u540c\uff0c\u8fd9\u663e\u7136\u4e0e\u5b9e\u9645\u4e0d\u7b26\u3002<\/p>\n<h4>2. GARCH\u6a21\u578b\u7684\u6838\u5fc3\u4f7f\u547d<\/h4>\n<p>GARCH\u6a21\u578b\u7684\u6838\u5fc3\u601d\u60f3\uff1a\u6ce2\u52a8\u7387\uff08\u6761\u4ef6\u65b9\u5dee\uff09\u662f\u201c\u81ea\u76f8\u5173\u201d\u7684\u2014\u2014\u5f53\u524d\u7684\u6ce2\u52a8\u7387\u4e0d\u4ec5\u4e0e\u8fc7\u53bb\u7684\u6536\u76ca\u7387\u6ce2\u52a8\u6709\u5173\uff0c\u8fd8\u4e0e\u8fc7\u53bb\u7684\u6ce2\u52a8\u7387\u6709\u5173\u3002\u5b83\u901a\u8fc7\u5efa\u6a21\u201c\u6761\u4ef6\u65b9\u5dee\u201d\u7684\u52a8\u6001\u53d8\u5316\uff0c\u7cbe\u51c6\u6355\u6349\u6ce2\u52a8\u805a\u7c7b\u73b0\u8c61\u3002<\/p>\n<p>\u7b80\u5355\u8bf4\uff0cGARCH\u505a\u7684\u662f\uff1a\u9884\u6d4b\u201c\u6ce2\u52a8\u672c\u8eab\u201d\u7684\u53d8\u5316\u89c4\u5f8b\uff0c\u800c\u4e0d\u662f\u9884\u6d4b\u6536\u76ca\u7387\u7684\u5747\u503c\u3002<\/p>\n<h3>\u4e8c\u3001GARCH\u6a21\u578b\u7684\u6570\u5b66\u539f\u7406<\/h3>\n<h4>1. \u4eceARCH\u5230GARCH<\/h4>\n<p>GARCH\u6a21\u578b\u7684\u524d\u8eab\u662fARCH\uff08\u81ea\u56de\u5f52\u6761\u4ef6\u5f02\u65b9\u5dee\uff09\u6a21\u578b\uff0c\u7531\u6069\u683c\u5c14\uff08Engle\uff09\u4e8e1982\u5e74\u63d0\u51fa\uff08\u4ed6\u56e0\u6b64\u83b7\u8bfa\u8d1d\u5c14\u7ecf\u6d4e\u5b66\u5956\uff09\u3002ARCH\u6a21\u578b\u5047\u8bbe\u201c\u5f53\u524d\u6ce2\u52a8\u7387\u4f9d\u8d56\u8fc7\u53bbq\u671f\u7684\u6536\u76ca\u7387\u5e73\u65b9\u201d\uff0c\u4f46\u9ad8\u9636ARCH\u6a21\u578b\u53c2\u6570\u8fc7\u591a\uff0c\u5b9e\u7528\u6027\u53d7\u9650\u3002<\/p>\n<p>1986\u5e74\uff0c\u535a\u52d2\u65af\u83b1\u6587\uff08Bollerslev\uff09\u5728ARCH\u57fa\u7840\u4e0a\u63d0\u51faGARCH\u6a21\u578b\uff0c\u5f15\u5165\u201c\u8fc7\u53bb\u7684\u6ce2\u52a8\u7387\u201d\u4f5c\u4e3a\u89e3\u91ca\u53d8\u91cf\uff0c\u5927\u5e45\u7b80\u5316\u4e86\u6a21\u578b\u7ed3\u6784\u3002<\/p>\n<h4>2. \u6838\u5fc3\u516c\u5f0f\uff08GARCH(p, q)\u6a21\u578b\uff09<\/h4>\n<p>GARCH\u6a21\u578b\u7531\u4e24\u90e8\u5206\u7ec4\u6210\uff1a\u5747\u503c\u65b9\u7a0b\u548c\u6761\u4ef6\u65b9\u5dee\u65b9\u7a0b\u3002<\/p>\n<h5>\uff081\uff09\u5747\u503c\u65b9\u7a0b<\/h5>\n<p>\u901a\u5e38\u5047\u8bbe\u6536\u76ca\u7387\u7684\u5747\u503c\u4e3a0\uff08\u6216\u7b80\u5355\u5e38\u6570\uff09\uff0c\u6838\u5fc3\u5173\u6ce8\u6b8b\u5dee\u7684\u6ce2\u52a8\uff1a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">rt=\u03bc+\u03b5tr_t = \\\\mu + \\\\varepsilon_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03bc<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03b5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d\uff1a<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">rtr_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff1at\u65f6\u523b\u7684\u91d1\u878d\u8d44\u4ea7\u6536\u76ca\u7387\uff08\u5982\u80a1\u7968\u65e5\u6536\u76ca\u7387\uff09\uff1b<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03bc\\\\mu<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03bc<\/span><\/span><\/span><\/span><\/span>\uff1a\u5e38\u6570\u5747\u503c\uff08\u901a\u5e38\u63a5\u8fd10\uff09\uff1b<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b5t\\\\varepsilon_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03b5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff1a\u6b8b\u5dee\u9879\uff0c\u670d\u4ece\u5747\u503c\u4e3a0\u3001\u6761\u4ef6\u65b9\u5dee\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c3t2\\\\sigma_t^2<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0611em;vertical-align: -0.247em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.453em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u5206\u5e03\uff08<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b5t\u223cN(0,\u03c3t2)\\\\varepsilon_t \\\\sim N(0, \\\\sigma_t^2)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03b5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u223c<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.453em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\uff09\u3002<\/li>\n<\/ul>\n<h5>\uff082\uff09\u6761\u4ef6\u65b9\u5dee\u65b9\u7a0b\uff08GARCH\u7684\u6838\u5fc3\uff09<\/h5>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c3t2=\u03c9+\u03b11\u03b5t\u221212+\u03b12\u03b5t\u221222+&#8230;+\u03b1q\u03b5t\u2212q2+\u03b21\u03c3t\u221212+\u03b22\u03c3t\u221222+&#8230;+\u03b2p\u03c3t\u2212p2\\\\sigma_t^2 = \\\\omega + \\\\alpha_1 \\\\varepsilon_{t-1}^2 + \\\\alpha_2 \\\\varepsilon_{t-2}^2 + &#8230; + \\\\alpha_q \\\\varepsilon_{t-q}^2 + \\\\beta_1 \\\\sigma_{t-1}^2 + \\\\beta_2 \\\\sigma_{t-2}^2 + &#8230; + \\\\beta_p \\\\sigma_{t-p}^2<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0611em;vertical-align: -0.247em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.453em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c9<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1205em;vertical-align: -0.3064em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0037em\">\u03b1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0037em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03b5<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.4519em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3064em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 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