将趋势线添加到 pandas [英] Add trend line to pandas
问题描述
我有以下时间序列数据:
I have time-series data, as followed:
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此图中添加线性趋势(带有截距).另外，我只想以2006年之前的数据为条件来计算这种趋势.
I would like to add, in the most simple way, a linear trend (with intercept) onto this graph. Also, I would like to compute this trend only conditional on data before, say, 2006.
我在这里找到了一些答案，但是都包括了statsmodels.首先，这些答案可能不是最新的:pandas得到改进，现在本身包括OLS组件.其次，statsmodels似乎是在每个时间段内估计单个固定效果，而不是线性趋势.我想我可以重新计算一个运行季度的变量，但是最可行的方法是这样做吗?
I've found some answers here, but they all include statsmodels. First of all, these answers might be not up to date: pandas improved, and now itself includes an OLS component. Second, statsmodels appears to estimate an individual fixed-effect for each time period, instead of a linear trend. I suppose I could recalculate a running-quarter variable, but there most be a more comfortable way of doing this?
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算此趋势并将预测值作为列添加到我的数据框中?
How do I, in the simplest way possible, estimate this trend and add the predicted values as a column to my data frame?
推荐答案
下面是一个简单的示例，说明如何使用pandas.ols进行操作:
Here's a quick example on how to do this using pandas.ols:
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)
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