时间序列回归：EAP.time_series_regress

实证资产定价中的时间序列回归多用于估计资产的因子暴露（beta值）。此外，时间序列分析可以通过GRS检验来考察资产收益率是否存在未被风险因子（risk factor）解释的异象（anomaly）。

本文根据Bail et al.的著作Empirical Asset Pricing编写相关程序，时间序列回归的模块是EAP.time_series_regress，下面将对该模块进行详细介绍。本文的Package已发布于Github:

Github: GitHub - whyecofiliter/EAP: empirical asset pricing
 

time_series_regress

class TS_regress()

This class is designed for time series regression,

$$
r_{i,t} = \beta_if_t + \epsilon_{i,t}
$$

to obtain the beta for each asset.

def __init__(self, list_y, factor):

This function initializes the object.

input :

list_y : The return matrix with i rows and t columns.

factor : The factor risk premium return series.

def ts_regress(self, newey_west=True):

This function is for conducting the time series regression.

input :

newey_west ： conduct the newey_west adjustment or not.

output :

self.alpha : The regression alpha.

self.e_mat : The error matrix

Example

from statsmodels.base.model import Model
from statsmodels.tools.tools import add_constant
from EAP.time_series_regress import TS_regress
​
X = np.random.normal(loc=0.0, scale=1.0, size=(2000,10))
y_list = []
for i in range(10) :
    b = np.random.uniform(low=0.1, high=1.1, size=(10,1))
    e = np.random.normal(loc=0.0, scale=1.0, size=(2000,1))
    y = X.dot(b) + e 
    y_list.append(y)
​
re = TS_regress(y_list, X)

def fit(self, **kwargs):

This function runs the function, ts_regress.

Example

# continue the previous code
re.fit()

def summary(self):

This function summarize the result, including the GRS test.

Example

# continue the previous code
re.summary()
=============================================================================
----------------------------------- GRS Test -------------------------------- 
​
GRS Statistics: 
 [[0.67160203]]
GRS p_value: 
 [[0.75175471]]
------------------------------------------------------------------------------

def grs(self):

This function conducts the GRS test.

output :

grs_stats : The GRS statistics.

p_value : The p_value.

Example

# continue the previous code
print(re.grs())
==============================================
(array([[0.67160203]]), array([[0.75175471]]))