Question

我有时间序列数据，如下：

                  emplvl
date                    
2003-01-01  10955.000000
2003-04-01  11090.333333
2003-07-01  11157.000000
2003-10-01  11335.666667
2004-01-01  11045.000000
2004-04-01  11175.666667
2004-07-01  11135.666667
2004-10-01  11480.333333
2005-01-01  11441.000000
2005-04-01  11531.000000
2005-07-01  11320.000000
2005-10-01  11516.666667
2006-01-01  11291.000000
2006-04-01  11223.000000
2006-07-01  11230.000000
2006-10-01  11293.000000
2007-01-01  11126.666667
2007-04-01  11383.666667
2007-07-01  11535.666667
2007-10-01  11567.333333
2008-01-01  11226.666667
2008-04-01  11342.000000
2008-07-01  11201.666667
2008-10-01  11321.000000
2009-01-01  11082.333333
2009-04-01  11099.000000
2009-07-01  10905.666667

我想以最简单的方式将线性趋势（带截距）添加到此图表中。另外，我想计算这种趋势只是以2006年之前的数据为条件。

我在这里找到了一些答案，但它们都包括statsmodels。首先，这些答案可能不是最新的：pandas已得到改进，现在它本身包含一个OLS组件。其次，statsmodels似乎估计每个时间段的单个固定效应，而不是线性趋势。我想我可以重新计算一个四分之一的变量，但是大多数人都有更舒服的方法吗？

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                 emplvl   R-squared:                       1.000
Model:                            OLS   Adj. R-squared:                    nan
Method:                 Least Squares   F-statistic:                     0.000
Date:                tor, 14 apr 2016   Prob (F-statistic):                nan
Time:                        17:17:43   Log-Likelihood:                 929.85
No. Observations:                  40   AIC:                            -1780.
Df Residuals:                       0   BIC:                            -1712.
Df Model:                          39                                         
Covariance Type:            nonrobust                                         
============================================================================================================
                                               coef    std err          t      P>|t|      [95.0% Conf. Int.]
------------------------------------------------------------------------------------------------------------
Intercept                                 1.095e+04        inf          0        nan           nan       nan
date[T.Timestamp('2003-04-01 00:00:00')]   135.3333        inf          0        nan           nan       nan
date[T.Timestamp('2003-07-01 00:00:00')]   202.0000        inf          0        nan           nan       nan
date[T.Timestamp('2003-10-01 00:00:00')]   380.6667        inf          0        nan           nan       nan
date[T.Timestamp('2004-01-01 00:00:00')]    90.0000        inf          0        nan           nan       nan
date[T.Timestamp('2004-04-01 00:00:00')]   220.6667        inf          0        nan           nan       nan

我如何以最简单的方式估计这一趋势，并将预测值作为一列添加到我的数据框中？

Answer 1

以下是使用pandas.ols：

执行此操作的简单示例

import matplotlib.pyplot as plt
import pandas as pd

x = pd.Series(np.arange(50))
y = pd.Series(10 + (2 * x + np.random.randint(-5, + 5, 50)))
regression = pd.ols(y=y, x=x)
regression.summary

-------------------------Summary of Regression Analysis-------------------------

Formula: Y ~ <x> + <intercept>

Number of Observations:         50
Number of Degrees of Freedom:   2

R-squared:         0.9913
Adj R-squared:     0.9911

Rmse:              2.7625

F-stat (1, 48):  5465.1446, p-value:     0.0000

Degrees of Freedom: model 1, resid 48

-----------------------Summary of Estimated Coefficients------------------------
      Variable       Coef    Std Err     t-stat    p-value    CI 2.5%   CI 97.5%
--------------------------------------------------------------------------------
             x     2.0013     0.0271      73.93     0.0000     1.9483     2.0544
     intercept     9.5271     0.7698      12.38     0.0000     8.0183    11.0358
---------------------------------End of Summary---------------------------------

trend = regression.predict(beta=regression.beta, x=x[20:]) # slicing to only use last 30 points
data = pd.DataFrame(index=x, data={'y': y, 'trend': trend})
data.plot() # add kwargs for title and other layout/design aspects
plt.show() # or plt.gcf().savefig(path)

Answer 2

通常，您应该提前创建matplotlib图形和轴对象，并在其上显式绘制数据框：

from matplotlib import pyplot
import pandas
import statsmodels.api as sm

df = pandas.read_csv(...)

fig, ax = pyplot.subplots()
df.plot(x='xcol', y='ycol', ax=ax)

然后你仍然有那个轴对象直接用于绘制你的线：

model = sm.formula.ols(formula='ycol ~ xcol', data=df)
res = model.fit()
df.assign(fit=res.fittedvalues).plot(x='xcol', y='fit', ax=ax)

将趋势线添加到pandas

2 个答案: