python - 向 Pandas 添加趋势线

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在这张图上添加一个线性趋势(带截距)。此外，我想仅以 2006 年之前的数据为条件来计算此趋势。

我在这里找到了一些答案，但它们都包含 statsmodels。首先，这些答案可能不是最新的:pandas 已改进，现在本身包含一个 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运行季度变量，但大多数情况下有更舒适的方法吗？

                            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

如何以最简单的方式估计此趋势并将预测值作为一列添加到我的数据框中？

Answer 1

这是一个关于如何使用 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)