{"id":1896,"date":"2025-02-13T07:05:00","date_gmt":"2025-02-12T23:05:00","guid":{"rendered":"https:\/\/blog.laoyulaoyu.top\/?p=1896"},"modified":"2025-01-14T10:43:56","modified_gmt":"2025-01-14T02:43:56","slug":"%e7%94%a8python%e9%a2%84%e6%b5%8b%e5%b8%82%e5%9c%ba%e6%b3%a2%e5%8a%a8%ef%bc%9a%e6%b3%a2%e5%8a%a8%e7%8e%87%e6%a8%a1%e5%9e%8b%e5%b8%ae%e4%bd%a0%e4%bb%8e%e6%b7%b7%e6%b2%8c%e4%b8%ad%e6%8a%93%e4%bd%8f","status":"publish","type":"post","link":"https:\/\/laoyulaoyu.com\/index.php\/2025\/02\/13\/%e7%94%a8python%e9%a2%84%e6%b5%8b%e5%b8%82%e5%9c%ba%e6%b3%a2%e5%8a%a8%ef%bc%9a%e6%b3%a2%e5%8a%a8%e7%8e%87%e6%a8%a1%e5%9e%8b%e5%b8%ae%e4%bd%a0%e4%bb%8e%e6%b7%b7%e6%b2%8c%e4%b8%ad%e6%8a%93%e4%bd%8f\/","title":{"rendered":"\u7528Python\u9884\u6d4b\u5e02\u573a\u6ce2\u52a8\uff1a\u6ce2\u52a8\u7387\u6a21\u578b\u5e2e\u4f60\u4ece\u6df7\u6c8c\u4e2d\u6293\u4f4f\u8d5a\u94b1\u673a\u4f1a"},"content":{"rendered":"\n<p>\u4f5c\u8005\uff1a<a href=\"https:\/\/www.laoyulaoyu.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u8001\u4f59\u635e\u9c7c<\/a><\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-cyan-bluish-gray-color\">\u539f\u521b\u4e0d\u6613\uff0c\u8f6c\u8f7d\u8bf7\u6807\u660e\u51fa\u5904\u53ca\u539f\u4f5c\u8005\u3002<\/mark><\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/www.laoyulaoyu.com\/wp-content\/uploads\/2025\/01\/1_8tbvyJW4cqE60juB89NPuQ-1.png\" alt=\"\" class=\"wp-image-3911\"\/><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<pre class=\"wp-block-verse\"><strong>\u5199\u5728\u524d\u9762\u7684\u8bdd\uff1a<\/strong>\u4f5c\u4e3a\u4e00\u540d\u667a\u6167\u91d1\u878d\u4ece\u4e1a\u8005\uff0c\u6211\u4e00\u76f4\u5728\u5bfb\u627e\u7528\u5de5\u5177\u9884\u6d4b\u5e02\u573a\u6ce2\u52a8\u7684\u6709\u6548\u65b9\u6cd5\u3002\u6700\u8fd1\u6211\u63d0\u70bc\u51fa\u51e0\u4e2a\u9ad8\u6548\u7684\u6ce2\u52a8\u7387\u6a21\u578b\uff0c\u901a\u8fc7Python\u7684\u5e2e\u52a9\uff0c\u5b83\u4eec<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">\u4e0d\u4ec5\u80fd\u5e2e\u4f60\u4ece\u590d\u6742\u7684\u5e02\u573a\u52a8\u6001\u4e2d\u7406\u6e05\u601d\u8def\uff0c\u8fd8\u80fd\u5728\u6df7\u6c8c\u4e2d\u53d1\u73b0\u6f5c\u5728\u7684\u76c8\u5229\u673a\u4f1a<\/mark>\u3002\u63a5\u4e0b\u6765\u8ddf\u968f\u6211\u7684\u811a\u6b65\uff0c\u8ba9\u6570\u636e\u5206\u6790\u6210\u4e3a\u4f60\u6295\u8d44\u51b3\u7b56\u4e2d\u7684\u5f3a\u5927\u5de5\u5177\u3002<\/pre>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u4e00\u3001\u6ce2\u52a8\u4e0e\u98ce\u9669<\/strong><\/h2>\n\n\n\n<p>\u77e5\u540d\u6295\u8d44\u4eba\u3001\u6a61\u6811\u8d44\u672c\u7ba1\u7406\u516c\u53f8\u8054\u5408\u521b\u59cb\u4eba\u970d\u534e\u5fb7-\u9a6c\u514b\u65af\uff08Howard Marks\uff09\u66fe\u8bf4\uff1a<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>Volatility is not the same as risk. Volatility is what happens on the way to where you\u2019re going.\uff08\u6ce2\u52a8\u4e0e\u98ce\u9669\u4e0d\u540c\u3002\u6ce2\u52a8\u662f\u5728\u901a\u5f80\u76ee\u7684\u5730\u7684\u9014\u4e2d\u53d1\u751f\u7684\u4e8b\u60c5\uff09<\/p>\n<\/blockquote>\n\n\n\n<p>\u4e0a\u9762\u8fd9\u53e5\u8bdd\u6df1\u523b\u63ed\u793a\u4e86\u6ce2\u52a8\u6027\u4e0e\u98ce\u9669\u4e4b\u95f4\u7684\u5173\u952e\u533a\u522b\u3002\u867d\u7136\u5b83\u4eec\u8868\u9762\u76f8\u4f3c\uff0c\u4f46\u672c\u8d28\u622a\u7136\u4e0d\u540c\u3002\u4e8b\u5b9e\u4e0a\uff0c\u6ce2\u52a8\u5f80\u5f80\u53ef\u4ee5\u88ab\u89c6\u4e3a\u4e00\u79cd\u673a\u9047\u3002<\/p>\n\n\n\n<p><strong>\u6ce2\u52a8<\/strong>\u662f\u6307\u8d44\u4ea7\u4ef7\u683c\u5728\u77ed\u671f\u5185\u7684\u8d77\u4f0f\u53d8\u5316\u3002\u5b83\u8ba9\u5e02\u573a\u663e\u5f97\u6df7\u4e71\u65e0\u5e8f\uff0c\u4ef7\u683c\u56e0\u5916\u90e8\u4e8b\u4ef6\u3001\u5e02\u573a\u60c5\u7eea\u6216\u6295\u673a\u884c\u4e3a\u800c\u9891\u7e41\u6ce2\u52a8\uff0c\u751a\u81f3\u53ef\u80fd\u51fa\u73b0\u5267\u70c8\u9707\u8361\u3002\u5c3d\u7ba1\u8fd9\u79cd\u4e0d\u786e\u5b9a\u6027\u8ba9\u4eba\u4e0d\u5b89\uff0c\u4f46\u6ce2\u52a8\u5176\u5b9e\u662f\u5e02\u573a\u7684\u5e38\u6001\uff0c\u751a\u81f3\u662f\u5176\u56fa\u6709\u7279\u5f81\u3002<\/p>\n\n\n\n<p>\u800c<strong>\u98ce\u9669<\/strong>\u5219\u4e0d\u540c\uff0c\u5b83\u610f\u5473\u7740\u8d44\u672c\u53ef\u80fd\u906d\u53d7\u6c38\u4e45\u635f\u5931\uff0c\u6216\u8005\u6295\u8d44\u65e0\u6cd5\u8fbe\u5230\u9884\u671f\u76ee\u6807\u7684\u53ef\u80fd\u6027\u3002\u65e0\u8bba\u662f\u7531\u4e8e\u6295\u8d44\u51b3\u7b56\u5931\u8bef\uff0c\u8fd8\u662f\u56e0\u4e3a\u4e0d\u53ef\u9884\u89c1\u7684\u707e\u96be\u6027\u4e8b\u4ef6\uff0c\u4f60\u7684\u8d22\u52a1\u8ba1\u5212\u90fd\u6709\u53ef\u80fd\u504f\u79bb\u6b63\u8f68\u3002\u6ce2\u52a8\u662f\u5e02\u573a\u7684\u8868\u8c61\uff0c\u800c\u98ce\u9669\u5219\u662f\u9690\u85cf\u5728\u80cc\u540e\u7684\u771f\u6b63\u5a01\u80c1\u3002<\/p>\n\n\n\n<p id=\"5a22\">\u6ce2\u52a8\u7387\u5206\u6790\u5bf9\u591a\u79cd\u91d1\u878d\u5e94\u7528\u81f3\u5173\u91cd\u8981\uff0c\u4f8b\u5982\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6295\u8d44\u7ec4\u5408\u4f18\u5316<\/li>\n\n\n\n<li>\u98ce\u9669\u7ba1\u7406<\/li>\n\n\n\n<li>\u884d\u751f\u4ea7\u54c1\u5b9a\u4ef7<\/li>\n\n\n\n<li>\u8d44\u4ea7\u914d\u7f6e\u7b56\u7565<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u4e8c\u3001\u6ce2\u52a8\u7387\u6a21\u578b\uff08Volatility Models\uff09<\/strong><\/h2>\n\n\n\n<p>\u6ce2\u52a8\u7387\u6a21\u578b\u662f\u7406\u89e3\u548c\u9884\u6d4b\u91d1\u878d\u5e02\u573a\u6ce2\u52a8\u7684\u91cd\u8981\u5de5\u5177\u3002\u901a\u8fc7\u4e0d\u540c\u7c7b\u578b\u7684\u6a21\u578b\uff0c\u6295\u8d44\u8005\u548c\u91d1\u878d\u673a\u6784\u80fd\u591f\u66f4\u597d\u5730\u8bc4\u4f30\u98ce\u9669\u3001\u5236\u5b9a\u6295\u8d44\u7b56\u7565\uff0c\u5e76\u5728\u590d\u6742\u7684\u5e02\u573a\u73af\u5883\u4e2d\u505a\u51fa\u660e\u667a\u7684\u51b3\u7b56\u3002\u968f\u7740\u91d1\u878d\u5e02\u573a\u7684\u4e0d\u65ad\u53d1\u5c55\uff0c\u6ce2\u52a8\u7387\u6a21\u578b\u4e5f\u5728\u4e0d\u65ad\u6f14\u8fdb\uff0c\u4ee5\u9002\u5e94\u65b0\u7684\u6311\u6218\u548c\u673a\u9047\u3002<\/p>\n\n\n\n<p>\u6709\u51e0\u79cd\u65b9\u6cd5\u53ef\u7528\u4e8e\u6a21\u62df\u548c\u9884\u6d4b\u91d1\u878d\u5e02\u573a\u7684\u6ce2\u52a8\u3002\u4e3b\u8981\u65b9\u6cd5\u5305\u62ec\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/www.laoyulaoyu.com\/wp-content\/uploads\/2025\/01\/image-92.png\" alt=\"\" class=\"wp-image-3906\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5386\u53f2\u6ce2\u52a8\u7387\u6a21\u578b\uff1a<\/strong>\u8fd9\u79cd\u65b9\u6cd5\u6839\u636e\u8fc7\u53bb\u7684\u4ef7\u683c\u8d70\u52bf\u8ba1\u7b97\u6ce2\u52a8\u7387\u3002\u7b80\u5355\u6765\u8bf4\uff0c\u5b83\u662f\u8d44\u4ea7\u56de\u62a5\u7387\u5728\u89c4\u5b9a\u65f6\u95f4\u5185\u7684\u6807\u51c6\u5dee\u3002<\/li>\n\n\n\n<li><strong>\u9690\u542b\u6ce2\u52a8\u7387\u6a21\u578b\uff1a<\/strong>\u8fd9\u662f\u4ece\u671f\u6743\u4ef7\u683c\u4e2d\u63a8\u5bfc\u51fa\u6765\u7684\uff0c\u53cd\u6620\u4e86\u5e02\u573a\u5bf9\u672a\u6765\u6ce2\u52a8\u7387\u7684\u9884\u671f\u3002\u901a\u5e38\u4f7f\u7528 Black-Scholes \u6a21\u578b\u6216\u5176\u4ed6\u671f\u6743\u5b9a\u4ef7\u6a21\u578b\u8ba1\u7b97\u3002<\/li>\n\n\n\n<li><strong>\u968f\u673a\u6ce2\u52a8\u6a21\u578b\uff1a<\/strong>\u8fd9\u4e9b\u6a21\u578b\u5047\u8bbe\u6ce2\u52a8\u7387\u672c\u8eab\u9075\u5faa\u4e00\u4e2a\u968f\u673a\u8fc7\u7a0b\uff0c\u5982\u4f7f\u7528 GARCH\uff08\u5e7f\u4e49\u81ea\u56de\u5f52\u6761\u4ef6\u5f02\u65b9\u5dee\uff09\u7684SV\uff08\u6a21\u578b\u548c\u72b6\u6001\u7a7a\u95f4\u6a21\u578b\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u4e9b\u6a21\u5f0f\u5404\u6709\u4f18\u7f3a\u70b9\uff0c\u6a21\u5f0f\u7684\u9009\u62e9\u53d6\u51b3\u4e8e\u5177\u4f53\u7684\u8d22\u52a1\u80cc\u666f\u548c\u53ef\u7528\u6570\u636e\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u4e09\u3001\u7528\u4e8e\u6ce2\u52a8\u7387\u5206\u6790\u7684Python\u5de5\u5177<\/strong><\/h2>\n\n\n\n<p>Python \u62e5\u6709\u4e30\u5bcc\u7684\u5e93\u751f\u6001\u7cfb\u7edf\uff0c\u662f\u6ce2\u52a8\u6027\u5206\u6790\u7684\u7edd\u4f73\u5de5\u5177\u3002NumPy\u3001Pandas\u3001Matplotlib \u7b49\u5e93\u4ee5\u53ca QuantLib\u3001Arch \u548c yfinance \u7b49\u4e13\u4e1a\u91d1\u878d\u5e93\u662f\u5b9a\u91cf\u91d1\u878d\u4e0d\u53ef\u6216\u7f3a\u7684\u5de5\u5177\u3002\u6bd4\u5982\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>pip install arch QuantLib<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>import yfinance as yf\nimport pandas as pd\nimport numpy as np\nfrom arch import arch_model\nimport QuantLib as ql<\/code><\/pre>\n\n\n\n<p>\u63a5\u4e0b\u6765\u5c31\u8ba9\u6211\u4eec\u6765\u63a2\u8ba8\u5982\u4f55\u4f7f\u7528 Python \u5efa\u7acb\u9884\u6d4b\u548c\u7ba1\u7406\u5e02\u573a\u6ce2\u52a8\u7684\u6a21\u578b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>3.1 \u6570\u636e\u6536\u96c6\u548c\u51c6\u5907<\/strong><\/h3>\n\n\n\n<p>\u4efb\u4f55\u6ce2\u52a8\u7387\u5206\u6790\u7684\u7b2c\u4e00\u6b65\u90fd\u662f\u6536\u96c6\u5386\u53f2\u6570\u636e\u3002Python \u7684 yfinance \u5e93\u53ef\u4ee5\u76f4\u63a5\u4ece\u96c5\u864e\u8d22\u7ecf\u8f7b\u677e\u8bbf\u95ee\u91d1\u878d\u6570\u636e\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># Download historical data for a stock (e.g., S&amp;P 500)\nticker = \"SPY\"\ndata = yf.download(ticker, start=\"2010-01-01\", end=\"2024-01-01\")<\/code><\/pre>\n\n\n\n<p>\u4e00\u65e6\u6536\u96c6\u5230\u6570\u636e\uff0c\u5bf9\u5176\u8fdb\u884c\u9884\u5904\u7406\u662f\u81f3\u5173\u91cd\u8981\u7684\u4e00\u6b65\u3002\u5728\u6ce2\u52a8\u7387\u5206\u6790\u4e2d\uff0c\u6211\u4eec\u901a\u5e38\u5173\u6ce8\u7684\u662f\u8d44\u4ea7\u7684\u6536\u76ca\u7387\uff0c\u4e5f\u5c31\u662f\u4ef7\u683c\u53d8\u5316\u7684\u767e\u5206\u6bd4\u3002\u8fd9\u4e00\u6b65\u4e0d\u4ec5\u80fd\u5e2e\u52a9\u6211\u4eec\u66f4\u597d\u5730\u7406\u89e3\u5e02\u573a\u884c\u4e3a\uff0c\u8fd8\u80fd\u4e3a\u540e\u7eed\u7684\u6a21\u578b\u6784\u5efa\u6253\u4e0b\u575a\u5b9e\u57fa\u7840\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># Calculate daily returns\ndata&#91;'Returns'] = data&#91;'Adj Close'].pct_change()\n\n# Drop missing values\ndata.dropna(inplace=True)\ndata_clean = data.copy()\ndata_clean.columns = &#91;'Date','Close','High','Low','Open','Volume','Returns']\ndata = data_clean.copy()<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>3.2 \u5386\u53f2\u6ce2\u52a8\u7387\u8ba1\u7b97<\/strong><\/h3>\n\n\n\n<p>\u8861\u91cf\u6ce2\u52a8\u7387\u7684\u4e00\u79cd\u5e38\u89c1\u65b9\u6cd5\u662f\u8ba1\u7b97\u4e00\u4e2a\u79fb\u52a8\u7a97\u53e3\u7684\u6536\u76ca\u6807\u51c6\u5dee\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># Calculate rolling 30-day volatility\ndata&#91;'Historical Volatility'] = data&#91;'Returns'].rolling(window=30).std() * np.sqrt(252)  # Annualize volatility<\/code><\/pre>\n\n\n\n<p>\u5047\u8bbe\u4e00\u5e74\u6709252\u4e2a\u4ea4\u6613\u65e5\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5c06\u6807\u51c6\u5dee\u4e58\u4ee5252\u7684\u5e73\u65b9\u6839\u6765\u8ba1\u7b97\u5e74\u5ea6\u6ce2\u52a8\u7387\u3002\u8fd9\u79cd\u65b9\u6cd5\u80fd\u591f\u5c06\u65e5\u6ce2\u52a8\u7387\u8f6c\u5316\u4e3a\u5e74\u5ea6\u6ce2\u52a8\u7387\uff0c\u5e2e\u52a9\u6211\u4eec\u66f4\u597d\u5730\u8bc4\u4f30\u8d44\u4ea7\u7684\u957f\u671f\u98ce\u9669\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u56db\u3001\u7528\u4e8e\u6ce2\u52a8\u7387\u9884\u6d4b\u7684 GARCH \u6a21\u578b<\/strong><\/h2>\n\n\n\n<p>\u5bf9\u4e8e\u66f4\u590d\u6742\u7684\u6ce2\u52a8\u7387\u6a21\u578b\uff0c\u6211\u4eec\u53ef\u4ee5\u91c7\u7528GARCH\u6a21\u578b\u3002GARCH\u6a21\u578b\u80fd\u591f\u6355\u6349\u6ce2\u52a8\u7387\u7684\u96c6\u7fa4\u6548\u5e94\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u9ad8\u6ce2\u52a8\u7387\u65f6\u671f\u5f80\u5f80\u4f1a\u7d27\u968f\u66f4\u591a\u7684\u9ad8\u6ce2\u52a8\u7387\uff0c\u800c\u4f4e\u6ce2\u52a8\u7387\u65f6\u671f\u5219\u503e\u5411\u4e8e\u5ef6\u7eed\u4f4e\u6ce2\u52a8\u7387\u3002\u8fd9\u79cd\u6a21\u578b\u80fd\u591f\u66f4\u51c6\u786e\u5730\u53cd\u6620\u5e02\u573a\u7684\u52a8\u6001\u53d8\u5316\uff0c\u5e2e\u52a9\u6211\u4eec\u66f4\u597d\u5730\u9884\u6d4b\u672a\u6765\u7684\u6ce2\u52a8\u6027\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>4.1 GARCH\u6a21\u578b\u7684\u5173\u952e\u6982\u5ff5<\/strong><\/h3>\n\n\n\n<p id=\"a8be\"><strong>1.\u6ce2\u52a8\u6027\u805a\u7c7b\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u91d1\u878d\u65f6\u95f4\u5e8f\u5217\u7ecf\u5e38\u51fa\u73b0\u5148\u9ad8\u6ce2\u52a8\u540e\u9ad8\u6ce2\u52a8\uff0c\u5148\u4f4e\u6ce2\u52a8\u540e\u4f4e\u6ce2\u52a8\u7684\u60c5\u51b5\u3002<\/li>\n\n\n\n<li>GARCH \u6a21\u578b\u5c06\u5f53\u524d\u7684\u6ce2\u52a8\u7387\u6a21\u62df\u4e3a\u8fc7\u53bb\u6ce2\u52a8\u7387\u548c\u8fc7\u53bb\u9884\u6d4b\u8bef\u5dee\u7684\u51fd\u6570\uff0c\u4ece\u800c\u6355\u6349\u5230\u8fd9\u79cd &#8220;\u805a\u7c7b &#8220;\u6548\u5e94\u3002<\/li>\n<\/ul>\n\n\n\n<p id=\"7cd2\"><strong>2.\u6761\u4ef6\u5f02\u65b9\u5dee\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6536\u76ca\u7684\u65b9\u5dee\uff08\u6ce2\u52a8\u7387\uff09\u5e76\u4e0d\u662f\u6052\u5b9a\u4e0d\u53d8\u7684\uff0c\u800c\u662f\u968f\u7740\u65f6\u95f4\u7684\u63a8\u79fb\u800c\u53d8\u5316\uff0c\u8fd9\u53d6\u51b3\u4e8e\u8fc7\u53bb\u7684\u6570\u636e\u3002<\/li>\n\n\n\n<li>&#8220;\u6709\u6761\u4ef6 &#8220;\u610f\u5473\u7740\u6a21\u578b\u5047\u5b9a\u56de\u62a5\u7684\u65b9\u5dee\u4ee5\u8fc7\u53bb\u7684\u4ef7\u503c\u4e3a\u6761\u4ef6\u3002<\/li>\n<\/ul>\n\n\n\n<p id=\"f5cf\"><strong>3.\u81ea\u56de\u5f52\u548c\u79fb\u52a8\u5e73\u5747\u65b9\u5dee<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u81ea\u56de\u5f52 (AR) \u90e8\u5206\uff08GARCH \u9879\uff09\u6a21\u62df\u8fc7\u53bb\u7684\u65b9\u5dee\u5982\u4f55\u5f71\u54cd\u5f53\u524d\u7684\u65b9\u5dee\u3002<\/li>\n\n\n\n<li>\u79fb\u52a8\u5e73\u5747\uff08MA\uff09\u6210\u5206\uff08ARCH \u9879\uff09\u6a21\u62df\u4e86\u8fc7\u53bb\u7684\u9884\u6d4b\u8bef\u5dee\uff08\u610f\u5916\u51b2\u51fb\uff09\u5bf9\u5f53\u524d\u65b9\u5dee\u7684\u5f71\u54cd\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>4.2 GARCH\u6a21\u578b\u7684Python\u5b9e\u73b0<\/strong><\/h3>\n\n\n\n<p id=\"a3aa\">Python \u7684 arch \u5e93\u662f\u5904\u7406 GARCH \u6a21\u578b\u7684\u5f3a\u5927\u5de5\u5177\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># Fit a GARCH(1,1) model to the returns\nmodel = arch_model(data&#91;'Returns'] * 100, vol='Garch', p=1, q=1)\ngarch_fit = model.fit()\n\n# Display the results\ngarch_fit.summary()<\/code><\/pre>\n\n\n\n<p id=\"579c\">GARCH \u6a21\u578b\u63d0\u4f9b\u4e86\u6761\u4ef6\u65b9\u5dee\u7684\u4f30\u8ba1\u503c\uff0c\u53ef\u5c06\u5176\u89e3\u91ca\u4e3a\u5bf9\u672a\u6765\u6ce2\u52a8\u7387\u7684\u9884\u6d4b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\" id=\"d7ab\"><img decoding=\"async\" src=\"https:\/\/cdn-images-1.readmedium.com\/v2\/resize:fit:800\/1*ajQym3IDUQX6tGs0Ip4Xmw.png\" alt=\"\" style=\"width:564px;height:auto\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image is-resized\" id=\"50f4\"><img decoding=\"async\" src=\"https:\/\/cdn-images-1.readmedium.com\/v2\/resize:fit:800\/1*uCcYPBxERgudDgtZZRgQHQ.png\" alt=\"\" style=\"width:564px;height:auto\"\/><\/figure>\n\n\n\n<p>\u8f93\u51fa\u7ed3\u679c\u662f\u4f7f\u7528\u6700\u5927\u4f3c\u7136\u4f30\u8ba1 (MLE) \u5bf9\u56de\u62a5\u6570\u636e\u62df\u5408 GARCH(1,1) \u6a21\u578b\u7684\u7ed3\u679c\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>4.3 \u8fed\u4ee3\u7ec6\u8282<\/strong><\/h3>\n\n\n\n<p id=\"82aa\">\u6bcf\u6b21\u8fed\u4ee3\u90fd\u663e\u793a\u4e86\u7528\u4e8e\u62df\u5408\u6a21\u578b\u7684\u4f18\u5316\u7b97\u6cd5\u7684<strong>\u8fdb\u5c55\u60c5\u51b5<\/strong>\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u8fed\u4ee3\u6b21\u6570\uff1a<\/strong>\u4f18\u5316\u8fc7\u7a0b\u7684\u5f53\u524d\u6b65\u9aa4\u3002<\/li>\n\n\n\n<li><strong>Func.\u8ba1\u6570\uff1a<\/strong>\u4f18\u5316\u8fc7\u7a0b\u4e2d\u6267\u884c\u7684\u51fd\u6570\u8bc4\u4f30\u6b21\u6570\u3002\u5b83\u8ddf\u8e2a\u8ba1\u7b97\u76ee\u6807\u51fd\u6570\uff08\u8d1f\u5bf9\u6570\u4f3c\u7136\uff09\u7684\u6b21\u6570\u3002<\/li>\n\n\n\n<li><strong>Neg.LLF\uff08\u8d1f\u5bf9\u6570\u4f3c\u7136\u51fd\u6570\uff09\uff1a<\/strong>\u8be5\u503c\u4ee3\u8868\u6700\u5c0f\u5316\u7684\u6210\u672c\u51fd\u6570\u3002\u8be5\u503c\u8d8a\u5c0f\uff0c\u6a21\u578b\u8d8a\u9002\u5408\u6570\u636e\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>\u8981\u70b9\u8bf4\u660e\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6700\u521d\uff0cNeg.LLF \u975e\u5e38\u9ad8\uff08\u5982 46294\uff09\uff0c\u8868\u660e\u62df\u5408\u6548\u679c\u4e0d\u4f73\u3002<\/li>\n\n\n\n<li>\u6bcf\u6b21\u8fed\u4ee3\uff0c\u4f18\u5316\u5668\u90fd\u4f1a\u8c03\u6574\u6a21\u578b\u53c2\u6570\uff0c\u51cf\u5c11 Neg\u3002LLF \u4ee5\u63d0\u9ad8\u62df\u5408\u5ea6\u3002<\/li>\n\n\n\n<li>\u4f18\u5316\u5728\u8fed\u4ee3 10 \u65f6\u6210\u529f\u7ed3\u675f\uff0c\u6700\u7ec8 Neg.LLF \u7ea6\u4e3a 4517.3\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>\u4f18\u5316\u7ec8\u6b62<\/strong>\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9000\u51fa\u6a21\u5f0f 0\uff1a\u8868\u793a\u4f18\u5316\u7b97\u6cd5\u6210\u529f\u6536\u655b\u3002<\/li>\n\n\n\n<li>\u5f53\u524d\u51fd\u6570\u503c\uff1a\u6700\u7ec8\u7684 Neg.\u6700\u5c0f\u5316\u7684 LLF \u503c\u3002<\/li>\n\n\n\n<li>\u8fed\u4ee3\u6b21\u6570\uff1a\u6536\u655b\u6240\u9700\u7684\u8fed\u4ee3\u603b\u6570 (10)\u3002<\/li>\n\n\n\n<li>\u51fd\u6570\u8bc4\u4f30\uff1a\u8ba1\u7b97\u4f3c\u7136\u51fd\u6570\u7684\u6b21\u6570\uff0868\uff09\u3002<\/li>\n\n\n\n<li>\u68af\u5ea6\u8bc4\u4f30\uff1a\u8ba1\u7b97\u4f3c\u7136\u51fd\u6570\u68af\u5ea6\u7684\u6b21\u6570 (10)\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>4.4 \u6a21\u578b\u7ed3\u8bba<\/strong><\/h3>\n\n\n\n<p id=\"ade6\"><strong>1. \u5e73\u5747\u6a21\u578b\uff08Mean Model\uff09\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5747\u503c\u6a21\u578b\uff1a\u6536\u76ca\u7387\u6a21\u578b\u91c7\u7528\u6052\u5b9a\u5747\u503c\uff08mu\uff09\u3002<\/li>\n\n\n\n<li>coef (mu)\uff1a\u5e38\u6570\u5747\u503c\u7684\u4f30\u8ba1\u503c\uff0c\u5373 0.0889\u3002<\/li>\n\n\n\n<li>std err\uff1a\u4f30\u8ba1\u503c\u7684\u6807\u51c6\u8bef\u5dee (0.01256)\uff0c\u8868\u793a\u7cbe\u786e\u5ea6\u3002<\/li>\n\n\n\n<li>t:t\uff1a\u68c0\u9a8c\u7cfb\u6570\u662f\u5426\u4e0e\u96f6\u6709\u663e\u8457\u5dee\u5f02\u7684 t \u7edf\u8ba1\u91cf\u3002<\/li>\n\n\n\n<li>P&gt;|t|\uff1a\u68c0\u9a8c\u7684 p \u503c\u3002\u5c0f\u7684 p \u503c\uff08&lt; 0.05\uff09\u8868\u660e\u8be5\u7cfb\u6570\u5177\u6709\u7edf\u8ba1\u610f\u4e49\u3002<\/li>\n\n\n\n<li>95% Conf.\u7f6e\u4fe1\u533a\u95f4\uff1a\u6536\u76ca\u5e73\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\u3002<\/li>\n<\/ul>\n\n\n\n<p id=\"0fef\"><strong>2. \u6ce2\u52a8\u6a21\u578b\uff08Volatility Model\uff09\uff1a<\/strong><\/p>\n\n\n\n<p id=\"db74\">GARCH\u6a21\u578b\u7528\u4e8e\u63cf\u8ff0\u6ce2\u52a8\u6027\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u03c9\uff1aGARCH \u65b9\u7a0b\u4e2d\u7684\u5e38\u6570\u9879\uff0c\u4ee3\u8868\u6ce2\u52a8\u7387\u7684\u57fa\u672c\u6c34\u5e73\uff080.0358\uff09\u3002<\/li>\n\n\n\n<li>alpha\uff1a\u6ede\u540e\u5e73\u65b9\u6b8b\u5dee\u9879\u7cfb\u6570\uff0c\u8868\u793a\u8fc7\u53bb\u7684\u51b2\u51fb\uff08\u65b0\u95fb\uff09\u5bf9\u5f53\u524d\u6ce2\u52a8\u7387\u7684\u5f71\u54cd\uff080.1752\uff09\u3002<\/li>\n\n\n\n<li>beta\uff1a\u6ede\u540e\u6761\u4ef6\u65b9\u5dee\u9879\u7cfb\u6570\uff0c\u4ee3\u8868\u6ce2\u52a8\u7387\u968f\u65f6\u95f4\u53d8\u5316\u7684\u6301\u7eed\u6027\uff080.7963\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>3. \u8981\u70b9\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u963f\u5c14\u6cd5[1]\u548c\u8d1d\u5854[1]\u4e4b\u548c\u63a5\u8fd1 1\uff080.1752 + 0.7963 \u2248 0.97\uff09\uff0c\u8868\u660e\u6ce2\u52a8\u6301\u7eed\u6027\u5f88\u9ad8\u3002<\/li>\n\n\n\n<li>\u6240\u6709\u7cfb\u6570\u90fd\u975e\u5e38\u663e\u8457\uff08p \u503c\u22480\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>4. \u6a21\u578b\u7edf\u8ba1\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Dep. \u53d8\u91cf\uff1a\u5efa\u6a21\u53d8\u91cf\uff08\u6536\u76ca\u7387\uff09\u3002<\/li>\n\n\n\n<li>R \u5e73\u65b9\uff1a\u8868\u793a\u6a21\u578b\u80fd\u89e3\u91ca\u591a\u5c11\u6536\u76ca\u7387\u65b9\u5dee\u3002\u5bf9 GARCH \u800c\u8a00\u63a5\u8fd1 0\uff0c\u56e0\u4e3a\u5b83\u4fa7\u91cd\u4e8e\u6ce2\u52a8\u6027\u5efa\u6a21\uff0c\u800c\u4e0d\u662f\u6536\u76ca\u7387\u5efa\u6a21\u3002<\/li>\n\n\n\n<li>\u5bf9\u6570\u4f3c\u7136\uff1a\u62df\u5408\u6a21\u578b\u7684\u6700\u7ec8\u4f3c\u7136\u503c\uff08-4517.30\uff09\u3002<\/li>\n\n\n\n<li>AIC\uff08\u963f\u51ef\u514b\u4fe1\u606f\u6807\u51c6\uff09\uff1a\u8bc4\u4f30\u6a21\u578b\u62df\u5408\u5ea6\u7684\u6307\u6807\uff08\u8d8a\u4f4e\u8d8a\u597d\uff09\u3002\u8fd9\u91cc\uff0cAIC = 9042.60\u3002<\/li>\n\n\n\n<li>BIC\uff08\u8d1d\u53f6\u65af\u4fe1\u606f\u6807\u51c6\uff09\uff1a\u53e6\u4e00\u79cd\u5bf9\u6a21\u578b\u590d\u6742\u6027\u8fdb\u884c\u60e9\u7f5a\u7684\u62df\u5408\u5ea6\u91cf\u3002\u8fd9\u91cc\uff0cBIC = 9067.27\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u4e3a\u4e86\u66f4\u76f4\u89c2\u5730\u663e\u793a\u6ce2\u52a8\u7387\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u4e0b\u9762\u7684\u4ee3\u7801\u7ed8\u5236\u6ce2\u52a8\u7387\u66f2\u7ebf\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/www.laoyulaoyu.com\/wp-content\/uploads\/2025\/01\/image-93.png\" alt=\"\" class=\"wp-image-3907\"\/><\/figure>\n\n\n\n<p>\u5b9e\u73b0\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># Plot the results\nplt.figure(figsize=(14, 7))\n\n# Plot Historical Volatility\nplt.subplot(2, 1, 1)\nplt.plot(data&#91;'Historical Volatility'], label=\"Historical Volatility\", color='blue')\nplt.legend()\n\n# Plot GARCH Model Volatility (using the model's estimated volatility)\nplt.subplot(2, 1, 2)\nplt.plot(garch_fit.conditional_volatility, label=\"GARCH Model Volatility\", color='green')\nplt.legend()\n\nplt.tight_layout()\nplt.show()<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u4e94\u3001\u9884\u6d4b\u6ce2\u52a8\u7387<\/strong><\/h2>\n\n\n\n<p>\u4e00\u65e6\u62df\u5408\u51fa GARCH \u6a21\u578b\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u7528\u5b83\u6765\u9884\u6d4b\u672a\u6765\u7684\u6ce2\u52a8\u7387\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"># Forecast the next 10 days of volatility\nforecast = garch_fit.forecast(horizon=10)\nforecasted_volatility = forecast.variance[-1:]\n\n# Display the forecasted volatility\nforecasted_volatility<\/pre>\n\n\n\n<p>\u8f93\u51fa\u7ed3\u679c\u5c06\u7ed9\u51fa\u672a\u6765 10 \u5929\u7684\u9884\u6d4b\u6ce2\u52a8\u7387\u3002\u8fd9\u6709\u52a9\u4e8e\u9884\u6d4b\u5e02\u573a\u98ce\u9669\u5e76\u76f8\u5e94\u8c03\u6574\u6295\u8d44\u7ec4\u5408\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/www.laoyulaoyu.com\/wp-content\/uploads\/2025\/01\/image-94.png\" alt=\"\" class=\"wp-image-3908\"\/><\/figure>\n\n\n\n<p id=\"4fd5\">\u5217\u6807\u9898\uff08h.01 \u81f3 h.10\uff09\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5b83\u4eec\u4ee3\u8868\u4e0d\u540c\u65f6\u95f4\u8de8\u5ea6\uff08\u5982\u7b2c 1 \u5929\u81f3\u7b2c 10 \u5929\uff09\u7684\u9884\u6d4b\u6ce2\u52a8\u7387\u3002<\/li>\n\n\n\n<li>\u8fd9\u4e9b\u6570\u503c\u8868\u793a\u6bcf\u4e2a\u65f6\u671f\u7684\u9884\u671f\u6ce2\u52a8\u6c34\u5e73\u3002<\/li>\n<\/ul>\n\n\n\n<p id=\"7692\">\u6ce2\u52a8\u7387\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8fd9\u4e9b\u662f\u9884\u6d4b\u7684\u6ce2\u52a8\u7387\uff08\u4f8b\u5982\uff0c\u7b2c 1 \u5929\u4e3a 0.403643\uff0c\u7b2c 2 \u5929\u4e3a 0.427922\uff0c\u7b49\u7b49\uff09\u3002<\/li>\n\n\n\n<li>\u6570\u503c\u8d8a\u9ad8\uff0c\u8868\u660e\u5e02\u573a\u7684\u4e0d\u786e\u5b9a\u6027\u6216\u98ce\u9669\u8d8a\u5927\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u516d\u3001\u5efa\u6a21\u9650\u5236\u6761\u4ef6<\/strong><\/h2>\n\n\n\n<p>\u6839\u636e\u7ecf\u9a8c\uff0c\u5373\u4f7f\u6a21\u578b\u5728\u5927\u591a\u6570\u60c5\u51b5\u4e0b\u80fd\u591f\u505a\u51fa\u51c6\u786e\u7684\u9884\u6d4b\uff0c\u4f46\u5f53\u7a81\u53d1\u4e8b\u4ef6\u53d1\u751f\u65f6\u2014\u2014\u6bd4\u5982COVID-19\u75ab\u60c5\u62169\/11\u4e8b\u4ef6\u5bfc\u81f4\u5168\u7403\u80a1\u5e02\u5728\u4e00\u5929\u5185\u66b4\u8dcc\u2014\u2014\u65e0\u8bba\u6211\u4eec\u51c6\u5907\u5f97\u591a\u4e48\u5145\u5206\uff0c\u4ecd\u7136\u5f88\u96be\u9884\u6d4b\u8fd9\u7c7b\u6781\u7aef\u4e8b\u4ef6\u3002\u8fd9\u4e9b\u9ed1\u5929\u9e45\u4e8b\u4ef6\u63d0\u9192\u6211\u4eec\uff0c\u5e02\u573a\u7684\u590d\u6742\u6027\u548c\u4e0d\u786e\u5b9a\u6027\u8fdc\u8d85\u6a21\u578b\u7684\u9884\u6d4b\u80fd\u529b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>6.1 \u9759\u6001\u5047\u8bbe<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>GARCH \u6a21\u578b\u5047\u5b9a\u57fa\u7840\u56de\u62a5\u662f\u9759\u6001\u7684\u3002\u5728\u5b9e\u9645\u5e02\u573a\u4e2d\uff0c\u56de\u62a5\u53ef\u80fd\u4f1a\u51fa\u73b0\u7ed3\u6784\u6027\u4e2d\u65ad\u6216\u5236\u5ea6\u53d8\u5316\uff08\u5982\u7ecf\u6d4e\u5371\u673a\u5bfc\u81f4\u7684\u8f6c\u53d8\uff09\u3002<\/li>\n\n\n\n<li>\u8003\u8651\u56e0\u7d20\uff1a\u786e\u4fdd\u5728\u5e94\u7528\u6a21\u578b\u524d\u8fdb\u884c\u53bb\u8d8b\u52bf\u6216\u9759\u6001\u6d4b\u8bd5\u7b49\u9884\u5904\u7406\u6b65\u9aa4\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"9622\"><strong>6.2 \u6b63\u6001\u5206\u5e03\u5047\u8bbe<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8be5\u6a21\u578b\u5047\u8bbe\u6b8b\u5dee\u670d\u4ece\u6b63\u6001\u5206\u5e03\u3002\u7136\u800c\uff0c\u91d1\u878d\u56de\u62a5\u901a\u5e38\u4f1a\u51fa\u73b0\u80a5\u5c3e\u6216\u8fc7\u5ea6\u5cf0\u5ea6\u3002<\/li>\n\n\n\n<li>\u7ed3\u679c\u80cc\u666f\uff1a\u5728\u7ed3\u679c\u4e2d\uff0c\u5206\u5e03\u662f\u6b63\u6001\u5206\u5e03\uff0c\u53ef\u80fd\u65e0\u6cd5\u5b8c\u5168\u53cd\u6620\u6781\u7aef\u5e02\u573a\u884c\u4e3a\u3002<\/li>\n\n\n\n<li>\u7f13\u89e3\u63aa\u65bd\uff1a\u5728 GARCH \u6a21\u578b\u4e2d\u4f7f\u7528\u5176\u4ed6\u5206\u5e03\uff08\u5982\u5b66\u751f t \u5206\u5e03\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"7de8\"><strong>63 \u8fc7\u5ea6\u62df\u5408\u98ce\u9669<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>GARCH(1,1) \u6a21\u578b\u517c\u987e\u4e86\u7b80\u5355\u6027\u548c\u51c6\u786e\u6027\uff0c\u56e0\u6b64\u5f88\u53d7\u6b22\u8fce\uff0c\u4f46\u9ad8\u9636\u6a21\u578b\uff08\u5982 GARCH(2,1)\uff09\u53ef\u80fd\u4f1a\u8fc7\u5ea6\u62df\u5408\u5386\u53f2\u6570\u636e\u3002<\/li>\n\n\n\n<li>\u7ed3\u679c\u80cc\u666f\uff1a\u60a8\u7684\u6a21\u578b\u4f7f\u7528\u7684\u662f GARCH(1,1)\uff0c\u8fd9\u5728\u5927\u591a\u6570\u5e94\u7528\u4e2d\u90fd\u662f\u5408\u7406\u7684\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u4e03\u3001\u89c2\u70b9\u603b\u7ed3<\/strong><\/h2>\n\n\n\n<p>\u6ce2\u52a8\u6027\u5206\u6790\u662f\u5b9a\u91cf\u91d1\u878d\u9886\u57df\u4e2d\u98ce\u9669\u7ba1\u7406\u548c\u9884\u6d4b\u7684\u6838\u5fc3\u3002\u4ece\u7b80\u5355\u7684\u5386\u53f2\u6ce2\u52a8\u7387\u8ba1\u7b97\u5230\u590d\u6742\u7684GARCH\u6a21\u578b\uff0cPython\u4e3a\u6ce2\u52a8\u6027\u5efa\u6a21\u548c\u9884\u6d4b\u63d0\u4f9b\u4e86\u5f3a\u5927\u7684\u5de5\u5177\u3002\u65e0\u8bba\u662f\u521d\u5b66\u8005\u8fd8\u662f\u4e13\u4e1a\u4eba\u58eb\uff0c\u90fd\u53ef\u4ee5\u5229\u7528Python\u7075\u6d3b\u5730\u6784\u5efa\u548c\u5206\u6790\u6a21\u578b\uff0c\u4ece\u800c\u66f4\u597d\u5730\u7406\u89e3\u5e02\u573a\u52a8\u6001\u5e76\u7ba1\u7406\u98ce\u9669\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6ce2\u52a8\u4e0e\u98ce\u9669\u867d\u7136\u76f8\u5173\uff0c\u4f46\u662f\u672c\u8d28\u4e0a\u662f\u4e0d\u540c\u7684<\/strong>\u3002\u6ce2\u52a8\u662f\u5e02\u573a\u7684\u6b63\u5e38\u7279\u5f81\uff0c\u800c\u98ce\u9669\u5219\u662f\u6307\u53ef\u80fd\u7684\u8d1f\u9762\u7ed3\u679c\u3002<\/li>\n\n\n\n<li><strong>\u6ce2\u52a8\u7387\u6a21\u578b\u5728\u91d1\u878d\u5206\u6790\u4e2d\u626e\u6f14\u7740\u81f3\u5173\u91cd\u8981\u7684\u89d2\u8272<\/strong>\uff0c\u5b83\u4eec\u4e0d\u4ec5\u6709\u52a9\u4e8e\u7406\u89e3\u5e02\u573a\u52a8\u6001\uff0c\u8fd8\u80fd\u7528\u4e8e\u5404\u79cd\u91d1\u878d\u5e94\u7528\u3002<\/li>\n\n\n\n<li><strong>GARCH\u6a21\u578b\u662f\u4e00\u79cd\u5f3a\u5927\u7684\u5de5\u5177\u6765\u9884\u6d4b\u548c\u7ba1\u7406\u5e02\u573a\u6ce2\u52a8\u7387<\/strong>\uff0c\u5b83\u80fd\u591f\u6355\u6349\u5230\u6ce2\u52a8\u6027\u805a\u7c7b\u548c\u6761\u4ef6\u5f02\u65b9\u5dee\u7684\u73b0\u8c61\u3002<\/li>\n\n\n\n<li><strong>Python\u63d0\u4f9b\u4e86\u4e00\u5957\u4e30\u5bcc\u7684\u5e93\u751f\u6001\u7cfb\u7edf<\/strong>\uff0c\u4f7f\u5f97\u5728\u91d1\u878d\u9886\u57df\u8fdb\u884c\u6ce2\u52a8\u6027\u5206\u6790\u548c\u5efa\u6a21\u53d8\u5f97\u66f4\u52a0\u5bb9\u6613\u548c\u9ad8\u6548\u3002<\/li>\n\n\n\n<li><strong>\u5728\u5e94\u7528GARCH\u6a21\u578b\u65f6\uff0c\u9700\u8981\u6ce8\u610f\u6a21\u578b\u7684\u5047\u8bbe\u548c\u9650\u5236<\/strong>\uff0c\u4ee5\u53ca\u5982\u4f55\u901a\u8fc7\u4f7f\u7528\u4e0d\u540c\u7684\u5206\u5e03\u6216\u8c03\u6574\u6a21\u578b\u590d\u6742\u5ea6\u6765\u6539\u8fdb\u6a21\u578b\u7684\u9884\u6d4b\u80fd\u529b\u3002<\/li>\n\n\n\n<li><strong>\u6a21\u578b\u9884\u6d4b\u7684\u51c6\u786e\u6027\u53ef\u80fd\u53d7\u5230\u7a81\u53d1\u4e8b\u4ef6\u7684\u5f71\u54cd<\/strong>\uff0c\u8fd9\u79cd\u4e0d\u786e\u5b9a\u6027\u662f\u91d1\u878d\u5e02\u573a\u5206\u6790\u4e2d\u9700\u8981\u7279\u522b\u6ce8\u610f\u7684\u56e0\u7d20\u3002<\/li>\n\n\n\n<li><strong>\u6ce2\u52a8\u6027\u5206\u6790\u7684\u672a\u6765\u53d1\u5c55\u5c06\u8d8a\u6765\u8d8a\u4f9d\u8d56\u4e8e\u5f3a\u5927\u7684\u6570\u636e\u5206\u6790\u5de5\u5177\u548c\u6a21\u578b<\/strong>\uff0cPython\u7b49\u6280\u672f\u5c06\u7ee7\u7eed\u5728\u91d1\u878d\u9886\u57df\u53d1\u6325\u91cd\u8981\u4f5c\u7528\u3002<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n\n\n\n<p><em>\u611f\u8c22\u60a8\u9605\u8bfb\u5230\u6700\u540e\uff0c\u5e0c\u671b\u8fd9\u7bc7\u6587\u7ae0\u4e3a\u60a8\u5e26\u6765\u4e86\u65b0\u7684\u542f\u53d1\u548c\u5b9e\u7528\u7684\u77e5\u8bc6\uff01\u5982\u679c\u89c9\u5f97\u6709\u5e2e\u52a9\uff0c\u8bf7\u4e0d\u541d\u70b9\u8d5e\u548c\u5206\u4eab\uff0c\u60a8\u7684\u652f\u6301\u662f\u6211\u6301\u7eed\u521b\u4f5c\u7684\u52a8\u529b\u3002\u795d\u60a8\u6295\u8d44\u987a\u5229\uff0c\u6536\u76ca\u957f\u8679\uff01\u5982\u679c\u5bf9\u6587\u4e2d\u5185\u5bb9\u6709\u4efb\u4f55\u7591\u95ee\uff0c\u6b22\u8fce\u7559\u8a00\uff0c\u6211\u4f1a\u5c3d\u5feb\u56de\u590d\uff01<\/em><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-text-align-center\" id=\"a1c6\">\u672c\u6587\u5185\u5bb9\u4ec5\u9650\u6280\u672f\u63a2\u8ba8\u548c\u5b66\u4e60\uff0c\u4e0d\u6784\u6210\u4efb\u4f55\u6295\u8d44\u5efa\u8bae\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4f5c\u8005\uff1a\u8001\u4f59\u635e\u9c7c \u539f\u521b\u4e0d\u6613\uff0c\u8f6c\u8f7d\u8bf7\u6807\u660e\u51fa\u5904\u53ca\u539f\u4f5c\u8005\u3002&#8230;<\/p>\n<div class=\"more-link-wrapper\"><a class=\"more-link\" href=\"https:\/\/laoyulaoyu.com\/index.php\/2025\/02\/13\/%e7%94%a8python%e9%a2%84%e6%b5%8b%e5%b8%82%e5%9c%ba%e6%b3%a2%e5%8a%a8%ef%bc%9a%e6%b3%a2%e5%8a%a8%e7%8e%87%e6%a8%a1%e5%9e%8b%e5%b8%ae%e4%bd%a0%e4%bb%8e%e6%b7%b7%e6%b2%8c%e4%b8%ad%e6%8a%93%e4%bd%8f\/\">Continue reading<span class=\"screen-reader-text\">\u7528Python\u9884\u6d4b\u5e02\u573a\u6ce2\u52a8\uff1a\u6ce2\u52a8\u7387\u6a21\u578b\u5e2e\u4f60\u4ece\u6df7\u6c8c\u4e2d\u6293\u4f4f\u8d5a\u94b1\u673a\u4f1a<\/span><\/a><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[4,5,6],"class_list":{"0":"post-1896","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"hentry","6":"category-aiinvest","7":"tag-ai","9":"tag-6","10":"entry"},"_links":{"self":[{"href":"https:\/\/laoyulaoyu.com\/index.php\/wp-json\/wp\/v2\/posts\/1896","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/laoyulaoyu.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/laoyulaoyu.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/laoyulaoyu.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/laoyulaoyu.com\/index.php\/wp-json\/wp\/v2\/comments?post=1896"}],"version-history":[{"count":1,"href":"https:\/\/laoyulaoyu.com\/index.php\/wp-json\/wp\/v2\/posts\/1896\/revisions"}],"predecessor-version":[{"id":1897,"href":"https:\/\/laoyulaoyu.com\/index.php\/wp-json\/wp\/v2\/posts\/1896\/revisions\/1897"}],"wp:attachment":[{"href":"https:\/\/laoyulaoyu.com\/index.php\/wp-json\/wp\/v2\/media?parent=1896"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/laoyulaoyu.com\/index.php\/wp-json\/wp\/v2\/categories?post=1896"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/laoyulaoyu.com\/index.php\/wp-json\/wp\/v2\/tags?post=1896"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}