12: Granger Causality

from statsmodels.tsa.stattools import grangercausalitytests
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

#build the time series, just a simple AR(1)
t1 = [0.1*np.random.normal()]
for _ in range(100):
    t1.append(0.5*t1[-1] + 0.1*np.random.normal())

#build the time series that is granger caused by t1
t2 = [item + 0.1*np.random.normal() for item in t1]

#adjust t1 and t2
t1 = t1[3:]
t2 = t2[:-3]

plt.figure(figsize=(10,4))
plt.plot(t1, color='b')
plt.plot(t2, color='r')

plt.legend(['t1', 't2'], fontsize=16)

<matplotlib.legend.Legend at 0x7fc1d5f71d90>

ts_df = pd.DataFrame(columns=['t2', 't1'], data=zip(t2,t1))

ts_df

	t2	t1
0	-0.074890	-0.052559
1	0.041190	-0.091463
2	-0.250354	-0.154409
3	-0.048394	-0.061625
4	-0.088648	0.075002
...	...	...
93	-0.065850	-0.082384
94	-0.014395	-0.060732
95	0.031564	-0.021469
96	-0.018472	-0.173017
97	-0.039406	-0.116893

98 rows × 2 columns

gc_res = grangercausalitytests(ts_df, 3)

Granger Causality
number of lags (no zero) 1
ssr based F test:         F=0.0378  , p=0.8462  , df_denom=94, df_num=1
ssr based chi2 test:   chi2=0.0391  , p=0.8433  , df=1
likelihood ratio test: chi2=0.0390  , p=0.8434  , df=1
parameter F test:         F=0.0378  , p=0.8462  , df_denom=94, df_num=1

Granger Causality
number of lags (no zero) 2
ssr based F test:         F=4.5927  , p=0.0126  , df_denom=91, df_num=2
ssr based chi2 test:   chi2=9.6901  , p=0.0079  , df=2
likelihood ratio test: chi2=9.2317  , p=0.0099  , df=2
parameter F test:         F=4.5927  , p=0.0126  , df_denom=91, df_num=2

Granger Causality
number of lags (no zero) 3
ssr based F test:         F=19.5546 , p=0.0000  , df_denom=88, df_num=3
ssr based chi2 test:   chi2=63.3302 , p=0.0000  , df=3
likelihood ratio test: chi2=48.5265 , p=0.0000  , df=3
parameter F test:         F=19.5546 , p=0.0000  , df_denom=88, df_num=3