使用 statsmodels.sandbox.regression.gmm.GMM 的问题 [英] Issue with using statsmodels.sandbox.regression.gmm.GMM
问题描述
我想使用 gmm 估算利率过程.
I wanna estimate interest rate process using gmm.
所以，我引用了这段代码.https://github.com/josef-pkt/misc/blob/master/notebooks/ex_gmm_gamma.ipynb
So, I referenced a this code. https://github.com/josef-pkt/misc/blob/master/notebooks/ex_gmm_gamma.ipynb
以下是我的代码.
import numpy as np
import pandas as pd
from statsmodels.sandbox.regression.gmm import GMM
cd = np.array([1.5, 1.5, 1.7, 2.2, 2.0, 1.8, 1.8, 2.2, 1.9, 1.6, 1.8, 2.2, 2.0, 1.5, 1.1, 1.5, 1.4, 1.7, 1.42, 1.9])
dcd = np.array([0, 0.2 ,0.5, -0.2, -0.2, 0, 0.4, -0.3, -0.3, 0.2, 0.4, -0.2, -0.5, -0.4, 0.4, -0.1, 0.3, -0.28, 0.48, 0.2])
inst = np.column_stack((np.ones(len(cd)), cd))
class gmm(GMM):
def momcond(self, params):
p0, p1, p2, p3 = params
endog = self.endog
exog = self.exog
inst = self.instrument
error1 = endog - p0 - p1 * exog
error2 = (endog - p0 - p1 * exog) ** 2 - p2 * (exog ** (2 * p3)) / 12
error3 = (endog - p0 - p1 * exog) * inst[:,0]
error4 = ((endog - p0 - p1 * exog) ** 2 - p2 * (exog ** (2 * p3)) / 12) * inst[:,1]
g = np.column_stack((error1, error2, error3, error4))
return g
beta0 = np.array([0.1, 0.1, 0.01, 1])
gmm(endog = dcd, exog = cd, instrument = inst, k_moms=4, k_params=4).fit(beta0)
但是，它会出现这样的错误.
But, it rises an error like this.
ValueError: shapes (80,) and (4,4) not aligned: 80 (dim 0) != 4 (dim 0)
你能不能解决这个问题.
Could you please solve this problem.
推荐答案
形状问题是因为 exog 是一个列数组(向量)，索引仪器是 1-D 广播到 80列.我给exog加了一个squeeze，这样exog也是一维的
The shape problem is because exog is a column array (vector) and the indexed instrument is 1-D which broadcasts to the 80 columns. I added a squeeze to exog, so that exog is also 1-D
第二个问题是时刻条件3的仪器索引有错字，应该使用error3 = (endog - p0 - p1 * exog) * inst[:,1]
修复形状问题后，拟合会引发 LinalgError，因为 error1 和 error3 相同.
The second problem is that there is a typo in the index of the instrument for moment condition 3, which should use
error3 = (endog - p0 - p1 * exog) * inst[:,1]
After fixing the shape problem, the fit raises a LinalgError because error1 and error3 were the same.
做了这两个改变后对我有用，但我不知道估计的参数在应用程序中是否有意义.
It works for me after making these two changes, but I don't know whether the estimated parameters make sense in the application.
cd = np.array([1.5, 1.5, 1.7, 2.2, 2.0, 1.8, 1.8, 2.2, 1.9, 1.6, 1.8, 2.2, 2.0, 1.5, 1.1, 1.5, 1.4, 1.7, 1.42, 1.9])
dcd = np.array([0, 0.2 ,0.5, -0.2, -0.2, 0, 0.4, -0.3, -0.3, 0.2, 0.4, -0.2, -0.5, -0.4, 0.4, -0.1, 0.3, -0.28, 0.48, 0.2])
inst = np.column_stack((np.ones(len(cd)), cd))
class gmm(GMM):
def momcond(self, params):
p0, p1, p2, p3 = params
endog = self.endog
exog = self.exog.squeeze()
inst = self.instrument
error1 = endog - p0 - p1 * exog
error2 = (endog - p0 - p1 * exog) ** 2 - p2 * (exog ** (2 * p3)) / 12
error3 = (endog - p0 - p1 * exog) * inst[:,1]
error4 = ((endog - p0 - p1 * exog) ** 2 - p2 * (exog ** (2 * p3)) / 12) * inst[:,1]
g = np.column_stack((error1, error2, error3, error4))
return g
beta0 = np.array([0.1, 0.1, 0.01, 1])
res = gmm(endog = dcd, exog = cd, instrument = inst, k_moms=4, k_params=4).fit(beta0)
GMM 中存在一个用于摘要的错误，该错误基于不正确且过短的参数名称列表.我们可以覆盖参数名称，然后总结工作
There is a bug in GMM for summary which is based on an incorrect and too short list of parameter names. We can override the parameter names, then summary works
res.model.exog_names[:] = 'p0 p1 p2 p3'.split()
print(res.summary())
gmm Results
==============================================================================
Dep. Variable: y Hansen J: 1.487e-10
Model: gmm Prob (Hansen J): nan
Method: GMM
Date: Wed, 14 Mar 2018
Time: 09:38:38
No. Observations: 20
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
p0 0.9890 0.243 4.078 0.000 0.514 1.464
p1 -0.5524 0.129 -4.281 0.000 -0.805 -0.299
p2 1.2224 0.940 1.300 0.193 -0.620 3.065
p3 -0.3376 0.641 -0.527 0.598 -1.593 0.918
==============================================================================
额外
在修正版本中，仪器中的常数不再使用.所以它可以被移除，或者矩条件可以在仪器中向量化，如下所示.请注意，我将 endog 转换为二维列数组，因此它与 exog 和乐器的形状相匹配.
In the corrected version the constant in the instrument is not used anymore. So it could be removed, or the moment conditions could be vectorized in instruments as in the following. Note, I convert endog to 2-d column array, so it matches the shape of exog and instruments.
class gmm(GMM):
def momcond(self, params):
p0, p1, p2, p3 = params
endog = self.endog[:, None]
exog = self.exog
inst = self.instrument
error3 = (endog - p0 - p1 * exog) * inst
error4 = ((endog - p0 - p1 * exog) ** 2 - p2 * (exog ** (2 * p3)) / 12) * inst
g = np.column_stack((error3, error4))
return g
beta0 = np.array([0.1, 0.1, 0.01, 1])
res = gmm(endog = dcd, exog = cd, instrument = inst, k_moms=4, k_params=4).fit(beta0)
res.model.exog_names[:] = 'p0 p1 p2 p3'.split()
print(res.summary())
调试
我们可以检查用户提供的矩条件是否具有正确的形状，但只需创建模型实例并调用 momcond
We can check that the user provided moment conditions have the correct shape but just creating the model instance and calling momcond
mod = gmm(endog = dcd, exog = cd, instrument = inst, k_moms=4, k_params=4)
mod.momcond(beta0).shape
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