能就一维时序数据,给出Python代码吗
时间: 2024-02-25 08:53:55 浏览: 18
当然可以,以下是Python代码实现:
```python
import numpy as np
from scipy.stats import norm
# 初始化漂移系数和扩散系数的估计值
mu_hat = 0.5
sigma_hat = 0.5
# 生成一维Wiener过程数据
N = 1000
dt = 0.1
dW = np.random.normal(loc=0, scale=np.sqrt(dt), size=N)
X = np.zeros(N)
X[0] = 0
for i in range(1, N):
X[i] = X[i-1] + mu_hat*dt + sigma_hat*dW[i]
# EM算法估计漂移系数和扩散系数
tolerance = 1e-6
max_iter = 1000
iter_count = 0
while True:
# E步骤
log_likelihood = 0
for i in range(1, N):
p = norm.pdf(X[i] - X[i-1] - mu_hat*dt, scale=sigma_hat*np.sqrt(dt))
log_likelihood += np.log(p)
# M步骤
mu_prev = mu_hat
sigma_prev = sigma_hat
mu_hat = np.sum(X[1:] - X[:-1])/((N-1)*dt)
sigma_hat = np.sqrt(np.sum((X[1:] - X[:-1] - mu_hat*dt)**2)/(N-1))
# 判断是否收敛
if np.abs(mu_hat - mu_prev) < tolerance and np.abs(sigma_hat - sigma_prev) < tolerance:
break
# 判断是否达到最大迭代次数
iter_count += 1
if iter_count > max_iter:
print("EM algorithm does not converge!")
break
print("Estimated drift coefficient:", mu_hat)
print("Estimated diffusion coefficient:", sigma_hat)
```
这里是一个简单的例子,生成一维Wiener过程数据,然后利用EM算法估计漂移系数和扩散系数。你可以根据自己的需求进行修改。