data processing¶

In [1]:
import pandas as pd
pd.set_option('display.max_columns', None)
import numpy as np
from datetime import datetime
In [2]:
from statsmodels.tsa.arima_process import ArmaProcess
In [3]:
import matplotlib.pyplot as plt
import seaborn as sns
In [4]:
from causalimpact import CausalImpact

setup¶

In [5]:
np.random.seed(42)
arprarams = np.array([0.95, 0.05])
maparams = np.array([0.6, 0.3])
arma_process = ArmaProcess.from_coeffs(arcoefs=arprarams, macoefs=maparams)
x = 10 + arma_process.generate_sample(nsample=500)
y = 2 * x + np.random.normal(size=500)
y[300:] += 10

create date¶

In [6]:
dates = pd.date_range(start='2021-01-01', freq='D', periods=500)
data = pd.DataFrame({'dates':dates, 'y':y, 'x':x})
data.set_index('dates', inplace=True)
In [7]:
data.head()
Out[7]:
y x
dates
2021-01-01 21.919606 10.496714
2021-01-02 23.172702 10.631643
2021-01-03 21.278713 11.338640
2021-01-04 26.909878 13.173454
2021-01-05 27.260727 13.955685

set pre and post periods¶

In [8]:
print(f'the time series start date is :{data.index.min()}')
print(f'the time series end date is :{data.index.max()}')
print(f'the treatment start date is :{data.index[300]}')

the time series start date is :2021-01-01 00:00:00
the time series end date is :2022-05-15 00:00:00
the treatment start date is :2021-10-28 00:00:00

visialize the time¶

In [9]:
plt.figure(figsize=(16,5))
sns.lineplot(x=data.index, y=data['x'])
sns.lineplot(x=data.index, y=data['y'])
plt.axvline(x=data.index[300], color='black')
Out[9]:
<matplotlib.lines.Line2D at 0x1ba93404990>
In [10]:
pre_period = [str(data.index.min())[:10], str(data.index[299])[:10]]
post_period = [str(data.index[300])[:10], str(data.index.max())[:10]]
print(f'the pre period is {pre_period}')
print(f'the post period is {post_period}')

the pre period is ['2021-01-01', '2021-10-27']
the post period is ['2021-10-28', '2022-05-15']

raw difference¶

In [11]:
pre_daily_average = data['y'][:300].mean()
post_daily_average = data['y'][300:].mean()

print(f'pre daily average is {pre_daily_average}')
print(f'post daily average is {post_daily_average}')

pre daily average is -1.6403416947312546
post daily average is 50.08461262581729

causal impact time series¶

In [12]:
impact = CausalImpact(data=data, pre_period=pre_period, post_period=post_period)

C:\Users\yandiher\AppData\Local\Programs\Python\Python311\Lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  self._init_dates(dates, freq)
C:\Users\yandiher\AppData\Local\Programs\Python\Python311\Lib\site-packages\statsmodels\base\optimizer.py:17: FutureWarning: Keyword arguments have been passed to the optimizer that have no effect. The list of allowed keyword arguments for method lbfgs is: m, pgtol, factr, maxfun, epsilon, approx_grad, bounds, loglike_and_score. The list of unsupported keyword arguments passed include: standardize, nseasons. After release 0.14, this will raise.
  warnings.warn(
C:\Users\yandiher\AppData\Local\Programs\Python\Python311\Lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency D will be used.
  self._init_dates(dates, freq)
In [13]:
impact.plot()
In [15]:
print(impact.summary())

Posterior Inference {Causal Impact}
                          Average            Cumulative
Actual                    50.08              10016.92
Prediction (s.d.)         40.03 (1.2)        8005.59 (239.36)
95% CI                    [37.64, 42.33]     [7527.61, 8465.89]

Absolute effect (s.d.)    10.06 (1.2)        2011.33 (239.36)
95% CI                    [7.76, 12.45]      [1551.03, 2489.31]

Relative effect (s.d.)    25.12% (2.99%)     25.12% (2.99%)
95% CI                    [19.37%, 31.09%]   [19.37%, 31.09%]

Posterior tail-area probability p: 0.0
Posterior prob. of a causal effect: 100.0%

For more details run the command: print(impact.summary('report'))
In [17]:
print(impact.summary(output='report'))

Analysis report {CausalImpact}


During the post-intervention period, the response variable had
an average value of approx. 50.08. By contrast, in the absence of an
intervention, we would have expected an average response of 40.03.
The 95% interval of this counterfactual prediction is [37.64, 42.33].
Subtracting this prediction from the observed response yields
an estimate of the causal effect the intervention had on the
response variable. This effect is 10.06 with a 95% interval of
[7.76, 12.45]. For a discussion of the significance of this effect,
see below.


Summing up the individual data points during the post-intervention
period (which can only sometimes be meaningfully interpreted), the
response variable had an overall value of 10016.92.
By contrast, had the intervention not taken place, we would have expected
a sum of 8005.59. The 95% interval of this prediction is [7527.61, 8465.89].


The above results are given in terms of absolute numbers. In relative
terms, the response variable showed an increase of +25.12%. The 95%
interval of this percentage is [19.37%, 31.09%].


This means that the positive effect observed during the intervention
period is statistically significant and unlikely to be due to random
fluctuations. It should be noted, however, that the question of whether
this increase also bears substantive significance can only be answered
by comparing the absolute effect (10.06) to the original goal
of the underlying intervention.


The probability of obtaining this effect by chance is very small
(Bayesian one-sided tail-area probability p = 0.0).
This means the causal effect can be considered statistically
significant.