你现在是一个编程专家,请你写一个代码,可以基于dcc-mvgarch模型,根据N个资产的价格时间序列计算N个资产之间的动态相关性矩阵
时间: 2024-02-16 22:05:23 浏览: 98
dcc_mvgarch.rar_dcc_dcc mvgarch_dcc-garch_exactlypog_时间序列
好的,以下是一个Python脚本,可以基于dcc-mvgarch模型,计算N个资产之间的动态相关性矩阵:
```python
import numpy as np
import pandas as pd
from arch import arch_model
from scipy.optimize import minimize
# 定义DCC-MV-GARCH模型
def dcc_mvgarch(params, data):
p = len(data) # 资产个数
omega = np.zeros([p, p])
alpha = np.zeros([p, p])
beta = np.zeros([p, p])
dcc = np.zeros([p, p])
# 提取参数
for i in range(p):
omega[i,i] = params[i]
alpha[i,i] = params[p+i]
beta[i,i] = params[2*p+i]
for j in range(i+1, p):
omega[i,j] = params[3*p+(i*(i-1)//2)+(j-i-1)]
alpha[i,j] = params[3*p+(p*(p-1)//2)+(i*(i-1)//2)+(j-i-1)]
beta[i,j] = params[3*p+(2*p*(p-1)//2)+(i*(i-1)//2)+(j-i-1)]
# 计算条件方差
am = arch_model(data, vol='GARCH', p=1, q=1, dist='Normal')
res = am.fit(disp='off')
eps = res.resid
sigma2 = res.conditional_volatility**2
# 计算DCC系数
for i in range(p):
dcc[i,i] = 1.0
for j in range(i+1, p):
dcc[i,j] = dcc[j,i] = (omega[i,j] + alpha[i,j]*eps[:,i]*eps[:,j] \
+ beta[i,j]*sigma2[:,i]*sigma2[:,j]) / \
np.sqrt((omega[i,i] + alpha[i,i]*sigma2[:,i] \
+ beta[i,i]*sigma2[:,i]**2) * \
(omega[j,j] + alpha[j,j]*sigma2[:,j] \
+ beta[j,j]*sigma2[:,j]**2))
return dcc
# 定义目标函数
def obj_func(params, data):
dcc = dcc_mvgarch(params, data)
return -np.sum(np.log(np.diag(dcc))) + np.sum(np.log(1-dcc**2))
# 计算动态相关性矩阵
def calc_dynamic_corr(data):
p = len(data) # 资产个数
x0 = np.ones([3*p+(p*(p-1)//2)]) / (3*p+(p*(p-1)//2))
bounds = [(0.0, 1.0)]*p + [(0.0, 1.0)]*p + [(0.0, 1.0)]*p \
+ [(0.0, 1.0)]*(p*(p-1)//2) # 参数范围
res = minimize(obj_func, x0, args=(data,), bounds=bounds)
params = res.x
dcc = dcc_mvgarch(params, data)
return pd.DataFrame(dcc, index=data.columns, columns=data.columns)
# 测试代码
if __name__ == '__main__':
np.random.seed(12345)
data = pd.DataFrame(np.random.randn(1000, 3), columns=['A', 'B', 'C'])
corr = calc_dynamic_corr(data)
print(corr)
```
这个代码使用了arch包来拟合GARCH模型,并使用scipy.optimize包中的minimize函数来求解DCC-MV-GARCH模型的参数。最后返回一个DataFrame,包含N个资产之间的动态相关性矩阵。
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