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YStrano
GitHub Repository: YStrano/DataScience_GA
 Path: blob/master/lessons/lesson_17/Granger Causality.ipynb
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Kernel: Python 3

Chicken and Eggs and Granger Causality

Data set on US egg production and estimates of US chicken population.

%matplotlib inline
import pandas as pd
import numpy as np
from statsmodels.tsa.stattools import grangercausalitytests
df = pd.read_csv('data/ChickEgg.csv')
df.head()
/anaconda3/lib/python3.6/site-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead. from pandas.core import datetools 
df.set_index('DATE', inplace=True)
df.plot(subplots=True)
array([<matplotlib.axes._subplots.AxesSubplot object at 0x10f9db9b0>, <matplotlib.axes._subplots.AxesSubplot object at 0x112c066d8>], dtype=object)
Image in a Jupyter notebook

Change to percents for stationarity

df = df.diff()
df.plot(subplots=True)
array([<matplotlib.axes._subplots.AxesSubplot object at 0x112cde9b0>, <matplotlib.axes._subplots.AxesSubplot object at 0x112d898d0>], dtype=object)
Image in a Jupyter notebook
df.head()

Null Hypothesis is that the time series in the second column does not granger cause the first column

Do eggs granger-cause chickens?

(Null hypothesis: Eggs do not granger cause chickens)

g_cause = grangercausalitytests(df.dropna(), maxlag=12)
Granger Causality number of lags (no zero) 1 ssr based F test: F=10.3694 , p=0.0023 , df_denom=49, df_num=1 ssr based chi2 test: chi2=11.0043 , p=0.0009 , df=1 likelihood ratio test: chi2=9.9819 , p=0.0016 , df=1 parameter F test: F=10.3694 , p=0.0023 , df_denom=49, df_num=1 Granger Causality number of lags (no zero) 2 ssr based F test: F=3.9196 , p=0.0268 , df_denom=46, df_num=2 ssr based chi2 test: chi2=8.6913 , p=0.0130 , df=2 likelihood ratio test: chi2=8.0254 , p=0.0181 , df=2 parameter F test: F=3.9196 , p=0.0268 , df_denom=46, df_num=2 Granger Causality number of lags (no zero) 3 ssr based F test: F=2.9318 , p=0.0441 , df_denom=43, df_num=3 ssr based chi2 test: chi2=10.2270 , p=0.0167 , df=3 likelihood ratio test: chi2=9.3049 , p=0.0255 , df=3 parameter F test: F=2.9318 , p=0.0441 , df_denom=43, df_num=3 Granger Causality number of lags (no zero) 4 ssr based F test: F=4.1762 , p=0.0064 , df_denom=40, df_num=4 ssr based chi2 test: chi2=20.4635 , p=0.0004 , df=4 likelihood ratio test: chi2=17.1001 , p=0.0018 , df=4 parameter F test: F=4.1762 , p=0.0064 , df_denom=40, df_num=4 Granger Causality number of lags (no zero) 5 ssr based F test: F=3.0577 , p=0.0208 , df_denom=37, df_num=5 ssr based chi2 test: chi2=19.8339 , p=0.0013 , df=5 likelihood ratio test: chi2=16.6014 , p=0.0053 , df=5 parameter F test: F=3.0577 , p=0.0208 , df_denom=37, df_num=5 Granger Causality number of lags (no zero) 6 ssr based F test: F=2.6883 , p=0.0303 , df_denom=34, df_num=6 ssr based chi2 test: chi2=22.2967 , p=0.0011 , df=6 likelihood ratio test: chi2=18.2477 , p=0.0056 , df=6 parameter F test: F=2.6883 , p=0.0303 , df_denom=34, df_num=6 Granger Causality number of lags (no zero) 7 ssr based F test: F=2.0445 , p=0.0807 , df_denom=31, df_num=7 ssr based chi2 test: chi2=21.2368 , p=0.0034 , df=7 likelihood ratio test: chi2=17.4607 , p=0.0147 , df=7 parameter F test: F=2.0445 , p=0.0807 , df_denom=31, df_num=7 Granger Causality number of lags (no zero) 8 ssr based F test: F=2.2817 , p=0.0509 , df_denom=28, df_num=8 ssr based chi2 test: chi2=29.3360 , p=0.0003 , df=8 likelihood ratio test: chi2=22.5870 , p=0.0039 , df=8 parameter F test: F=2.2817 , p=0.0509 , df_denom=28, df_num=8 Granger Causality number of lags (no zero) 9 ssr based F test: F=1.8727 , p=0.1040 , df_denom=25, df_num=9 ssr based chi2 test: chi2=29.6642 , p=0.0005 , df=9 likelihood ratio test: chi2=22.6744 , p=0.0070 , df=9 parameter F test: F=1.8727 , p=0.1040 , df_denom=25, df_num=9 Granger Causality number of lags (no zero) 10 ssr based F test: F=2.2821 , p=0.0513 , df_denom=22, df_num=10 ssr based chi2 test: chi2=44.6039 , p=0.0000 , df=10 likelihood ratio test: chi2=30.5999 , p=0.0007 , df=10 parameter F test: F=2.2821 , p=0.0513 , df_denom=22, df_num=10 Granger Causality number of lags (no zero) 11 ssr based F test: F=1.8222 , p=0.1209 , df_denom=19, df_num=11 ssr based chi2 test: chi2=44.3087 , p=0.0000 , df=11 likelihood ratio test: chi2=30.2510 , p=0.0014 , df=11 parameter F test: F=1.8222 , p=0.1209 , df_denom=19, df_num=11 Granger Causality number of lags (no zero) 12 ssr based F test: F=1.2835 , p=0.3149 , df_denom=16, df_num=12 ssr based chi2 test: chi2=39.4674 , p=0.0001 , df=12 likelihood ratio test: chi2=27.6455 , p=0.0062 , df=12 parameter F test: F=1.2835 , p=0.3149 , df_denom=16, df_num=12

Reverse the Order

Do Chickens Granger cause Eggs?

(Null hypothesis: Chickens do not granger cause eggs)

df_reversed = df[df.columns[::-1]].copy()
df_reversed.head()

grangercausalitytests(df_reversed.dropna(), maxlag = 12)
Granger Causality number of lags (no zero) 1 ssr based F test: F=0.5434 , p=0.4646 , df_denom=49, df_num=1 ssr based chi2 test: chi2=0.5766 , p=0.4476 , df=1 likelihood ratio test: chi2=0.5734 , p=0.4489 , df=1 parameter F test: F=0.5434 , p=0.4646 , df_denom=49, df_num=1 Granger Causality number of lags (no zero) 2 ssr based F test: F=0.3865 , p=0.6816 , df_denom=46, df_num=2 ssr based chi2 test: chi2=0.8571 , p=0.6515 , df=2 likelihood ratio test: chi2=0.8500 , p=0.6538 , df=2 parameter F test: F=0.3865 , p=0.6816 , df_denom=46, df_num=2 Granger Causality number of lags (no zero) 3 ssr based F test: F=0.2245 , p=0.8788 , df_denom=43, df_num=3 ssr based chi2 test: chi2=0.7833 , p=0.8535 , df=3 likelihood ratio test: chi2=0.7772 , p=0.8549 , df=3 parameter F test: F=0.2245 , p=0.8788 , df_denom=43, df_num=3 Granger Causality number of lags (no zero) 4 ssr based F test: F=0.2817 , p=0.8881 , df_denom=40, df_num=4 ssr based chi2 test: chi2=1.3801 , p=0.8476 , df=4 likelihood ratio test: chi2=1.3611 , p=0.8509 , df=4 parameter F test: F=0.2817 , p=0.8881 , df_denom=40, df_num=4 Granger Causality number of lags (no zero) 5 ssr based F test: F=0.3181 , p=0.8989 , df_denom=37, df_num=5 ssr based chi2 test: chi2=2.0631 , p=0.8403 , df=5 likelihood ratio test: chi2=2.0200 , p=0.8464 , df=5 parameter F test: F=0.3181 , p=0.8989 , df_denom=37, df_num=5 Granger Causality number of lags (no zero) 6 ssr based F test: F=0.3060 , p=0.9295 , df_denom=34, df_num=6 ssr based chi2 test: chi2=2.5379 , p=0.8642 , df=6 likelihood ratio test: chi2=2.4717 , p=0.8716 , df=6 parameter F test: F=0.3060 , p=0.9295 , df_denom=34, df_num=6 Granger Causality number of lags (no zero) 7 ssr based F test: F=0.4101 , p=0.8887 , df_denom=31, df_num=7 ssr based chi2 test: chi2=4.2598 , p=0.7494 , df=7 likelihood ratio test: chi2=4.0739 , p=0.7712 , df=7 parameter F test: F=0.4101 , p=0.8887 , df_denom=31, df_num=7 Granger Causality number of lags (no zero) 8 ssr based F test: F=0.3128 , p=0.9546 , df_denom=28, df_num=8 ssr based chi2 test: chi2=4.0223 , p=0.8551 , df=8 likelihood ratio test: chi2=3.8525 , p=0.8702 , df=8 parameter F test: F=0.3128 , p=0.9546 , df_denom=28, df_num=8 Granger Causality number of lags (no zero) 9 ssr based F test: F=0.3113 , p=0.9638 , df_denom=25, df_num=9 ssr based chi2 test: chi2=4.9306 , p=0.8403 , df=9 likelihood ratio test: chi2=4.6734 , p=0.8618 , df=9 parameter F test: F=0.3113 , p=0.9638 , df_denom=25, df_num=9 Granger Causality number of lags (no zero) 10 ssr based F test: F=0.8446 , p=0.5935 , df_denom=22, df_num=10 ssr based chi2 test: chi2=16.5086 , p=0.0860 , df=10 likelihood ratio test: chi2=13.9716 , p=0.1743 , df=10 parameter F test: F=0.8446 , p=0.5935 , df_denom=22, df_num=10 Granger Causality number of lags (no zero) 11 ssr based F test: F=1.0149 , p=0.4700 , df_denom=19, df_num=11 ssr based chi2 test: chi2=24.6780 , p=0.0102 , df=11 likelihood ratio test: chi2=19.4126 , p=0.0541 , df=11 parameter F test: F=1.0149 , p=0.4700 , df_denom=19, df_num=11 Granger Causality number of lags (no zero) 12 ssr based F test: F=0.7956 , p=0.6507 , df_denom=16, df_num=12 ssr based chi2 test: chi2=24.4643 , p=0.0176 , df=12 likelihood ratio test: chi2=19.1852 , p=0.0842 , df=12 parameter F test: F=0.7956 , p=0.6507 , df_denom=16, df_num=12
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Conclusion:

Eggs granger cause chickens but chickens do not granger cause eggs!