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我有一个时间序列的 pandas 数据帧df1，我检查我的时间序列是否是静止的，如果不是，我确实想检查是否存在协整，以防万一创建它们的 VECM。这是为了避免区分以使它们静止：

from statsmodels.tsa.stattools import adfuller #to check unit root in time series 
threshold=0.05 #significance level
coint = []
for column in df1.columns:
    result=adfuller(df1[column])
    if result[1]>threshold:
        print('P-value for ' + column + ' is: ' + str(result[1]))
        coint.append(column)
l = coint
combin = [comb for comb in combinations(l, 2)] # this is a list of all the pairwise columns which are non-stationary

在我检查成对列之间的协整之后：

import statsmodels.api as sm
df = df1.copy()
for comb in combin:
    i = comb[0]
    j = comb[1]
    x, y = df[j], df[i]
    var1 = adfuller(df[i])
    var2 = adfuller(df[j])
    x = sm.add_constant(x)
    result = sm.OLS(y,x).fit()
    b = result.params[1]
    x = df[j]
    diff = adfuller(y - b*x)
    print("The p-value for the ADF test on " + i +  " is ", var1[1])
    print("The p-value for the ADF test on " + j +  " is ", var2[1])
    print("The p-value for the ADF test on the difference is ", diff[1])
    if diff[1]<0.05:
        print('We have cointegration')
    else: print('We do not have cointegration')

我的问题是：

  1. 一旦验证了 2 个变量是协整的，我如何从它们构建协整变量？换句话说，我如何创建 VECM？

  2. 上面的协整测试是成对的，但我可能有多个协整，是否有一个库允许我在构建 VECM 后测试多个变量？

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