{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 分位数VAR模型"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 原理讲解\n",
"\n",
"参考文献：\n",
"1. VAR for VaR: Measuring tail dependence using multivariate regression quantiles\n",
"2. 分位数向量自回归分布滞后模型及脉冲响应分析"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 使用 statsmodels 库实现\n",
"\n",
"### QVAR 模型估计"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
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"<style scoped>\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>const</th>\n",
" <th>hs300_1</th>\n",
" <th>hs300_2</th>\n",
" <th>sz_1</th>\n",
" <th>sz_2</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>hs300</th>\n",
" <td>17.229937</td>\n",
" <td>1.390869</td>\n",
" <td>-0.369268</td>\n",
" <td>-0.589803</td>\n",
" <td>0.549461</td>\n",
" </tr>\n",
" <tr>\n",
" <th>sz</th>\n",
" <td>11.392195</td>\n",
" <td>0.345127</td>\n",
" <td>-0.324991</td>\n",
" <td>0.502069</td>\n",
" <td>0.463664</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" const hs300_1 hs300_2 sz_1 sz_2\n",
"hs300 17.229937 1.390869 -0.369268 -0.589803 0.549461\n",
"sz 11.392195 0.345127 -0.324991 0.502069 0.463664"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import pandas as pd\n",
"import statsmodels.regression.quantile_regression as qr\n",
"import statsmodels.api as sm\n",
"\n",
"data = pd.read_excel('../数据/上证指数与沪深300.xlsx')\n",
"Y = data['hs300']\n",
"X = data['sz']\n",
"\n",
"def lag_list(Y, X, p=1, q=1, Yname='', Xname='', exogenous=[]):\n",
" '''\n",
" 待估计方程：y = c + y(-1) +....+y(-p) + x(-1) + ... + x(-q) + exogenous\n",
" 获取自回归分布滞后模型的估计向量\n",
"\n",
" Parameters\n",
" ----------\n",
" Y : 被估计变量\n",
" X : 估计变量\n",
" p : ADL 模型 Y 的滞后阶数，标量默认为1\n",
" q : ADL 模型 X 的滞后阶数，标量默认为1\n",
" Yname : 被响应变量名\n",
" Xname : 响应变量名\n",
" exogenous : 外生变量\n",
"\n",
" Returns\n",
" -------\n",
" ADLy : ADL 模型被解释变量\n",
" ADLx : ADL 模型解释变量\n",
"\n",
" '''\n",
" if not Yname:\n",
" Yname = 'y'\n",
" if not Xname:\n",
" Xname = 'x'\n",
" \n",
" ADLx = pd.DataFrame()\n",
" T = len(Y)\n",
" ADLy = pd.Series(list(Y[max(p, q):T]), name=Yname)\n",
" for i in range(1, p+1):\n",
" name = f'{Yname}_{i}'\n",
" ADLx[name] = list(Y[max(p, q)-i:T-i])\n",
" for i in range(1, q+1):\n",
" name = f'{Xname}_{i}'\n",
" ADLx[name] = list(X[max(p, q)-i:T-i])\n",
" \n",
" # 增加控制变量\n",
" if type(exogenous) == pd.Series:\n",
" ADLx[exogenous.name] = list(exogenous[:0-max(p, q)])\n",
" elif type(exogenous) == pd.DataFrame:\n",
" for name in exogenous.columns:\n",
" ADLx[name] = list(exogenous[name][:0-max(p, q)])\n",
" \n",
" # 增加常数项\n",
" ADLx = sm.add_constant(ADLx)\n",
" return ADLy, ADLx\n",
"\n",
"\n",
"def qvar(Y, X, P, Q, Yname='', Xname='', exogenous=[]):\n",
" '''\n",
" 待估计方程：y = c + y(-1) +....+y(-p) + x(-1) + ... + x(-q) + exogenous\n",
" x = c + y(-1) +....+y(-p) + x(-1) + ... + x(-q) + exogenous\n",
" 估计 QVAR 模型\n",
"\n",
" Parameters\n",
" ----------\n",
" Y : 被估计变量\n",
" X : 估计变量\n",
" P : QVAR 模型的滞后阶数\n",
" Q : 分位点\n",
" Yname : 被响应变量名\n",
" Xname : 响应变量名\n",
" exogenous : 外生变量\n",
" \n",
" Returns\n",
" -------\n",
" res1, res2 : 两模型估计结果\n",
" \n",
" '''\n",
" ADLy, ADLx = lag_list(Y, X ,P, P, Yname, Xname, exogenous)\n",
" mod = qr.QuantReg(ADLy, ADLx)\n",
" res1 = mod.fit(Q)\n",
" \n",
" ADLy, ADLx = lag_list(X, Y ,P, P, Xname, Yname, exogenous)\n",
" mod = qr.QuantReg(ADLy, ADLx)\n",
" res2 = mod.fit(Q)\n",
" \n",
" return res1, res2\n",
"\n",
"res1, res2 = qvar(Y, X, 2, 0.3, 'hs300', 'sz')\n",
"beta1 = res1.params\n",
"beta2 = res2.params\n",
"pd.DataFrame([beta1, beta2], ['hs300', 'sz'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 脉冲响应分析"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
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" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1.224023e+06</td>\n",
" <td>868179.613056</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>8.681796e+05</td>\n",
" <td>645978.438493</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
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"text/plain": [
" 0 1\n",
"0 1.224023e+06 868179.613056\n",
"1 8.681796e+05 645978.438493"
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"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
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],
"source": [
"import numpy as np\n",
"\n",
"def OIRF(res1, res2, p):\n",
" '''\n",
" 估计脉冲响应函数\n",
"\n",
" Parameters\n",
" ----------\n",
" res1, res2 : 两模型估计结果\n",
" p : 滞后阶数\n",
" \n",
" Returns\n",
" -------\n",
" OIRF\n",
" \n",
" '''\n",
" pass\n",
"p = 2\n",
"resid = pd.DataFrame([res1.resid, res2.resid]).T # 残差序列\n",
"# 正交化分解，估计P2矩阵\n",
"a = resid.T @ resid\n",
"a=a/(len()-2*p-1);\n",
"P2 = chol(a, 'lower');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## matlab实现\n",
"可以参考 matlab 代码：[QVAR 模型](https://github.com/lei940324/econometrics/tree/master/matlab代码/分位数回归/VAR模型)"
]
}
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