{"id":1789,"date":"2025-01-12T07:43:00","date_gmt":"2025-01-11T23:43:00","guid":{"rendered":"https:\/\/blog.laoyulaoyu.top\/?p=1789"},"modified":"2024-12-17T16:59:25","modified_gmt":"2024-12-17T08:59:25","slug":"har%e6%a8%a1%e5%9e%8b%e5%ae%9e%e6%88%98%ef%bc%9a%e8%82%a1%e5%b8%82%e5%a4%a7%e7%9b%98%e4%b8%ad%e7%9a%84%e8%b5%9a%e9%92%b1%e7%a7%98%e7%b1%8d","status":"publish","type":"post","link":"https:\/\/laoyulaoyu.com\/index.php\/2025\/01\/12\/har%e6%a8%a1%e5%9e%8b%e5%ae%9e%e6%88%98%ef%bc%9a%e8%82%a1%e5%b8%82%e5%a4%a7%e7%9b%98%e4%b8%ad%e7%9a%84%e8%b5%9a%e9%92%b1%e7%a7%98%e7%b1%8d\/","title":{"rendered":"HAR\u6a21\u578b\u5b9e\u6218\uff1a\u80a1\u5e02\u5927\u76d8\u4e2d\u7684\u8d5a\u94b1\u79d8\u7c4d"},"content":{"rendered":"\n

\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

\"\"<\/figure>\n\n\n\n
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\u5199\u5728\u524d\u9762\u7684\u8bdd\uff1a<\/strong>\u5927\u5bb6\u597d\uff0c\u4eca\u5929\u6211\u8981\u548c\u5927\u5bb6\u5206\u4eab\u7684\u662f\u6ce2\u52a8\u7387\u4ea4\u6613\u4e2d\u7684\u4e00\u4e2a\u91cd\u8981\u6a21\u578b\u2014\u2014\u5f02\u8d28\u81ea\u56de\u5f52\uff08HAR\uff09\u6a21\u578b\u3002\u8fd9\u4e2a\u6a21\u578b\u80fd\u6355\u6349\u4e0d\u540c\u65f6\u95f4\u8de8\u5ea6\u7684\u6ce2\u52a8\u7387\u6301\u7eed\u6027\uff0c\u7b80\u5355\u53c8\u6709\u6548<\/mark>\u3002\u901a\u8fc7\u5bf9SPY\uff08\u6807\u666e500 ETF\uff09\u7684\u5b9e\u6218\u6570\u636e\uff0c\u4f60\u4f1a\u53d1\u73b0\u5b83\u5728\u9884\u6d4b\u6ce2\u52a8\u7387\u548c\u5236\u5b9a\u4ea4\u6613\u7b56\u7565\u4e0a\u7684\u72ec\u7279\u4f18\u52bf\u3002\u8ba9\u6211\u4eec\u4e00\u8d77\u63a2\u7d22\u8fd9\u4e2a\u795e\u79d8\u7684\u4ea4\u6613\u795e\u5668\u5427\uff01<\/pre>\n<\/blockquote>\n\n\n\n
\u4e00\u3001HAR \u6a21\u578b\u4ecb\u7ecd<\/strong><\/h2>\n\n\n\n
\u4ea4\u6613\u4e2d\u4e00\u4e2a\u4ee4\u4eba\u5934\u75bc\u7684\u95ee\u9898\u4fbf\u662f\u6ce2\u52a8\u6027\uff0c\u5b83\u65f6\u5e38\u5bfc\u81f4\u76c8\u5229\u77ac\u95f4\u8f6c\u4e3a\u4e8f\u635f\uff0c\u6216\u4e8f\u635f\u8f6c\u4e3a\u76c8\u5229\u3002\u56e0\u6b64\uff0c\u5728\u4ece\u4e8b\u6ce2\u52a8\u6027\u4ea4\u6613\u65f6\uff0c\u52a1\u5fc5\u4fdd\u6301\u9ad8\u5ea6\u8b66\u60d5\u3002\u5e78\u8fd0\u7684\u662f\uff0c\u6709\u591a\u79cd\u9884\u6d4b\u6ce2\u52a8\u7387\u7684\u6a21\u578b\u53ef\u4f9b\u9009\u62e9\u4ee5\u8f85\u52a9\u4ea4\u6613\u51b3\u7b56\uff0c\u6bd4\u5982\u88ab\u5e7f\u6cdb\u4f7f\u7528\u7684GARCH\uff08\u5e7f\u4e49\u81ea\u56de\u5f52\u6761\u4ef6\u5f02\u65b9\u5dee\uff09\u6a21\u578b\u3002\u4f46\u672c\u6587\u5c06\u91cd\u70b9\u63a2\u8ba8\u53e6\u4e00\u79cd\u9887\u5177\u6f5c\u529b\u7684\u6a21\u578b\u2014\u2014\u5f02\u8d28\u81ea\u56de\u5f52\uff08HAR\uff09\u6a21\u578b\u3002<\/p>\n\n\n\n
1.1 \u4ec0\u4e48\u662f HAR \u6a21\u578b\uff1f<\/strong><\/h3>\n\n\n\n
HAR<\/strong>\uff08Heterogeneous Autoregressive Model\uff09\u6a21\u578b\u662f\u4e00\u79cd\u7528\u4e8e\u7ecf\u6d4e\u91d1\u878d\u65f6\u95f4\u5e8f\u5217\u5206\u6790\uff0c\u7279\u522b\u662f\u6ce2\u52a8\u7387\u65f6\u95f4\u5e8f\u5217\u5206\u6790\u7684\u7edf\u8ba1\u6a21\u578b\u3002<\/p>\n\n\n\n
HAR\u6a21\u578b\u7684\u6838\u5fc3\u601d\u60f3\u662f<\/strong>\u901a\u8fc7\u8003\u8651\u4e0d\u540c\u65f6\u95f4\u5c3a\u5ea6\u4e0a\u7684\u5386\u53f2\u6570\u636e\u6765\u6355\u6349\u65f6\u95f4\u5e8f\u5217\u7684\u52a8\u6001\u7279\u5f81\u3002<\/p>\n\n\n\n
\u8be5\u6a21\u578b\u80fd\u591f\u6709\u6548\u5730\u6355\u6349\u77ed\u671f\u548c\u957f\u671f\u7684\u4f9d\u8d56\u5173\u7cfb\uff0c\u4ece\u800c\u4e3a\u7814\u7a76\u8005\u63d0\u4f9b\u66f4\u4e3a\u51c6\u786e\u7684\u9884\u6d4b\u7ed3\u679c\u3002<\/p>\n\n\n\n
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1.2 HAR\u6a21\u578b\u7684\u57fa\u672c\u6982\u5ff5<\/strong><\/h3>\n\n\n\n
HAR\u6a21\u578b\u7684\u57fa\u672c\u6784\u5efa\u662f\u57fa\u4e8e\u81ea\u56de\u5f52\uff08AR\uff09\u6a21\u578b\u7684\u6269\u5c55\u3002\u4e0e\u6ce8\u91cd\u77ed\u671f\u81ea\u76f8\u5173\u6027\u7684 GARCH \u7b49\u7b80\u5355\u6a21\u578b\u4e0d\u540c\uff0c\u5f02\u8d28\u81ea\u56de\u5f52\uff08HAR\uff09\u6a21\u578b\u65e8\u5728\u6355\u6349\u6ce2\u52a8\u7387\u5728\u591a\u4e2a\u65f6\u95f4\u8de8\u5ea6\u4e0a\u7684\u6301\u7eed\u6027\u3002HAR \u6a21\u578b\u5305\u542b\u4e86\u4e0d\u540c\u65f6\u671f\u7684\u8fc7\u5f80\u6ce2\u52a8\u6027\uff0c\u901a\u5e38\u662f\u6bcf\u65e5\u3001\u6bcf\u5468\u548c\u6bcf\u6708\uff08\u5982 1 \u5929\u30015 \u5929\u548c 22 \u5929\u6ede\u540e\u671f\uff09\u3002\u8fd9\u79cd\u5f02\u8d28\u6027\u4f7f\u5f97HAR\u6a21\u578b\u80fd\u591f\u66f4\u597d\u5730\u53cd\u6620\u5e02\u573a\u7684\u590d\u6742\u6027\u548c\u6ce2\u52a8\u6027\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n

1.3 HAR \u548c GARCH \u6a21\u578b\u7684\u5bf9\u6bd4<\/strong><\/h3>\n\n\n\n
\u8ba9\u6211\u4eec\u6765\u6bd4\u8f83\u4e00\u4e0b GARCH \u6a21\u578b\u548c HAR \u6a21\u578b\uff0c\u770b\u770b\u5b83\u4eec\u7684\u4f18\u7f3a\u70b9\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u4e0b\u9762\u662fHAR\u6a21\u578b\u81ea\u8eab\u7684\u4f18\u7f3a\u70b9\u5206\u6790\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u4e8c\u3001HAR \u6a21\u578b\u7684\u5e94\u7528<\/strong><\/h2>\n\n\n\n

2.1 \u5e94\u7528\u6982\u8ff0<\/strong><\/h3>\n\n\n\n
HAR\u6a21\u578b\u5728\u91d1\u878d\u5e02\u573a\u7684\u6ce2\u52a8\u7387\u9884\u6d4b\u4e2d\u8868\u73b0\u51fa\u8272\u3002\u901a\u8fc7\u5c06\u4e0d\u540c\u65f6\u95f4\u5c3a\u5ea6\u7684\u5386\u53f2\u6570\u636e\u7ed3\u5408\u8d77\u6765\uff0cHAR\u6a21\u578b\u80fd\u591f\u6355\u6349\u5230\u5e02\u573a\u7684\u77ed\u671f\u6ce2\u52a8\u548c\u957f\u671f\u8d8b\u52bf\u3002\u8fd9\u4f7f\u5f97\u5b83\u5728\u98ce\u9669\u7ba1\u7406\u3001\u8d44\u4ea7\u5b9a\u4ef7\u548c\u6295\u8d44\u7ec4\u5408\u4f18\u5316\u7b49\u9886\u57df\u5f97\u5230\u4e86\u5e7f\u6cdb\u5e94\u7528\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u5f02\u8d28\u81ea\u56de\u5f52\uff08HAR\uff09\u6a21\u578b\u662f\u4e00\u79cd\u5f3a\u5927\u7684\u5de5\u5177\uff0c\u80fd\u591f\u901a\u8fc7\u8003\u8651\u4e0d\u540c\u65f6\u95f4\u5c3a\u5ea6\u7684\u5386\u53f2\u6570\u636e\u6765\u63d0\u9ad8\u65f6\u95f4\u5e8f\u5217\u9884\u6d4b\u7684\u51c6\u786e\u6027\u3002\u5176\u5728\u91d1\u878d\u9886\u57df\u7684\u5e94\u7528\uff0c\u5c24\u5176\u662f\u5728\u6ce2\u52a8\u7387\u5efa\u6a21\u65b9\u9762\uff0c\u5c55\u73b0\u4e86\u5176\u72ec\u7279\u7684\u4f18\u52bf\u3002<\/p>\n\n\n\n
2.2 \u5e94\u7528\u5b9e\u4f8b<\/strong><\/h3>\n\n\n\n
\u4e0b\u9762\u6211\u4eec\u4ee5SPY\uff08\u6807\u666e500 ETF\uff09\u7684\u6ce2\u52a8\u7387\u9884\u6d4b\u4e3a\u4f8b\uff0cHAR\u6a21\u578b\u901a\u8fc7\u5206\u6790\u5386\u53f2\u6ce2\u52a8\u7387\u6570\u636e\u6765\u9884\u6d4b\u672a\u6765\u6ce2\u52a8\u7387\u7684\u53d8\u5316\u8d8b\u52bf\u3002<\/p>\n\n\n\n
\u6211\u7528Python\u5b9e\u73b0\u4e86\u5982\u4f55\u5e94\u7528HAR\u6a21\u578b\u8fdb\u884c\u6570\u636e\u5206\u6790\u548c\u7b56\u7565\u5236\u5b9a\uff0c\u5305\u62ec\u8ba1\u7b97\u6eda\u52a8\u6ce2\u52a8\u7387\u548c\u751f\u6210\u4e70\u5356\u4fe1\u53f7\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u6a21\u578b\u6821\u51c6\u91c7\u7528\u666e\u901a\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff08OLS\uff09\uff0c\u5373\u8bef\u5dee\u9879\u6700\u5c0f\u5316\u6cd5\uff0c\u5b83\u63d0\u4f9b\u8d1d\u5854\u7cfb\u6570\u7684\u95ed\u5f0f\u89e3\u3002OLS \u7684\u65b9\u7a0b\u5982\u4e0b\uff1a<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u5176\u4e2d\uff1a<\/strong>y \u662f\u56e0\u53d8\u91cf\uff08\u88ab\u89e3\u91ca\u53d8\u91cf\uff09\u3001x \u662f\u81ea\u53d8\u91cf\uff08\u89e3\u91ca\u53d8\u91cf\uff09\u3001\u03b20\u200b \u662f\u622a\u8ddd\u9879\u3001\u03b21\u200b \u662f\u659c\u7387\uff08\u8d1d\u5854\u7cfb\u6570\uff09\u3001\u03f5 \u662f\u8bef\u5dee\u9879\u3002OLS \u7684\u76ee\u6807\u662f\u627e\u5230\u53c2\u6570 \u03b20\u200b \u548c \u03b21\u200b \uff0c\u4f7f\u5f97\u8bef\u5dee\u9879 \u03f5 \u7684\u5e73\u65b9\u548c\u6700\u5c0f\u5316\u3002<\/p>\n\n\n\n
\u672c\u4f8b\u8868\u660e\u4e86HAR\u6a21\u578b\u6709\u52a9\u4e8e\u6295\u8d44\u8005\u5236\u5b9a\u66f4\u4e3a\u5408\u7406\u7684\u6295\u8d44\u7b56\u7565\u548c\u98ce\u9669\u7ba1\u7406\u63aa\u65bd\u3002\u5b9e\u73b0\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n\n\n\n
import numpy as np\nimport pandas as pd\nimport yfinance as yf\nimport matplotlib.pyplot as plt\n\n# Fetch historical data\nticker = \"SPY\"  # Example ticker\ndata = yf.download(ticker, start=\"2023-06-01\", end=\"2024-01-01\")\n\n# Calculate daily returns\ndata['Return'] = data['Adj Close'].pct_change().dropna()\n\n# Calculate 5-day rolling realized volatility\ndata['Volatility'] = data['Return'].rolling(window=5).std()\n\n# Rolling mean and standard deviation of volatility\ndata['Rolling_Mean_Vol'] = data['Volatility'].rolling(window=5).mean()\ndata['Rolling_Std_Vol'] = data['Volatility'].rolling(window=5).std()\n\n# Corrected upper and lower bands\ndata['Upper_Band'] = data['Rolling_Mean_Vol'] + 1.5 * data['Rolling_Std_Vol']\ndata['Lower_Band'] = data['Rolling_Mean_Vol'] - 1.5 * data['Rolling_Std_Vol']\n\n# Buy and sell signals\ndata['Buy_Signal'] = data['Volatility'] < data['Lower_Band']\ndata['Sell_Signal'] = data['Volatility'] > data['Upper_Band']\n\nplt.figure(figsize=(14, 8))\nplt.plot(data['Volatility'], label='Volatility', color='blue', linewidth=1.5)\nplt.plot(data['Upper_Band'], label='Upper Band (2 Std Dev)', linestyle='--', color='red', linewidth=1.2)\nplt.plot(data['Lower_Band'], label='Lower Band (2 Std Dev)', linestyle='--', color='green', linewidth=1.2)\n\n# Plot buy signals with enhanced formatting\nplt.scatter(data.index[data['Buy_Signal']], data['Volatility'][data['Buy_Signal']],\n            label='Buy Signal', color='lime', marker='o', s=100, edgecolor='black', zorder=5)\n\n# Plot sell signals with enhanced formatting\nplt.scatter(data.index[data['Sell_Signal']], data['Volatility'][data['Sell_Signal']],\n            label='Sell Signal', color='red', marker='x', s=100, linewidth=2, zorder=5)\n\n# Chart title and legend\nplt.title(f\"Enhanced Volatility Band Trading Strategy for {ticker}\", fontsize=16)\nplt.legend(fontsize=12)\nplt.xlabel('Date', fontsize=12)\nplt.ylabel('Volatility', fontsize=12)\n\n# Grid and layout\nplt.grid(alpha=0.3)\nplt.tight_layout()\n\n# Show the chart\nplt.show()<\/code><\/pre>\n\n\n\n
\u4e09\u3001\u89c2\u70b9\u603b\u7ed3<\/strong><\/h2>\n\n\n\n
\u5f02\u8d28\u81ea\u56de\u5f52\uff08HAR\uff09\u6a21\u578b\u901a\u8fc7\u63ed\u793a\u77ed\u671f\u3001\u4e2d\u671f\u548c\u957f\u671f\u6ce2\u52a8\u7387\u7684\u72ec\u7279\u7279\u5f81\uff0c\u4e3a\u7814\u7a76\u548c\u9884\u6d4b\u5b9e\u9645\u6ce2\u52a8\u7387\u63d0\u4f9b\u4e86\u4e00\u4e2a\u76f4\u89c2\u4e14\u9ad8\u6548\u7684\u89e3\u51b3\u65b9\u6848\u3002\u5f97\u76ca\u4e8e\u5176\u57fa\u4e8e\u7ebf\u6027\u56de\u5f52\u7684\u76f4\u89c2\u7ed3\u6784\uff0c\u8be5\u6a21\u578b\u5de7\u5999\u5730\u5c06\u6bcf\u65e5\u3001\u6bcf\u5468\u548c\u6bcf\u6708\u7684\u5386\u53f2\u6ce2\u52a8\u7387\u6570\u636e\u7ed3\u5408\u8d77\u6765\uff0c\u65e2\u4fdd\u6301\u4e86\u6a21\u578b\u7684\u7b80\u6d01\u6027\uff0c\u53c8\u786e\u4fdd\u4e86\u5f3a\u5927\u7684\u89e3\u91ca\u80fd\u529b\u3002\u5c3d\u7ba1HAR\u6a21\u578b\u5728\u6355\u6349\u6781\u9ad8\u9891\u7387\u7684\u5e02\u573a\u52a8\u6001\u65b9\u9762\u53ef\u80fd\u4e0d\u5982GARCH\u6a21\u578b\uff0c\u4f46\u5176\u5728\u9884\u6d4b\u591a\u671f\u6ce2\u52a8\u7387\u65b9\u9762\u7684\u53ef\u9760\u6027\u5df2\u5728\u6295\u8d44\u7ec4\u5408\u4f18\u5316\u3001\u98ce\u9669\u8bc4\u4f30\u548c\u884d\u751f\u4ea7\u54c1\u5b9a\u4ef7\u7b49\u591a\u4e2a\u91d1\u878d\u9886\u57df\u5f97\u5230\u4e86\u9a8c\u8bc1\u3002\u56e0\u6b64\uff0cHAR\u6a21\u578b\u65e0\u7591\u662f\u6ce2\u52a8\u7387\u5efa\u6a21\u9886\u57df\u7684\u4e00\u4e2a\u91cd\u8981\u4e14\u5b9e\u7528\u7684\u5de5\u5177\u3002<\/p>\n\n\n\n