Interpreting the results based on Granger Causality test

Question

I am trying to use Granger Causality test: https://www.statsmodels.org/stable/generated/statsmodels.tsa.stattools.grangercausalitytests.html

to assess whether "positivity score" affects value.

Here is the code I am using:

# Applying differencing
condensed_df['value'] = condensed_df['value'] - condensed_df['value'].shift(1)
condensed_df = condensed_df.drop(0)

# Running granger causality test
dct_pos_granger_causality = grangercausalitytests(condensed_df[["value", daily_avg_positive_score"]], maxlag = 4, verbose=False)

I have a total of 1,008 rows in the dataframe.

The results are as follows:

{1: ({'ssr_ftest': (0.005356633438031601, 0.941670291866298, 1003.0, 1), 'ssr_chi2test': (0.0053726552728412666, 0.9415686658133314, 1), 'lrtest': (0.005372640925997985, 0.9415687436896775, 1), 'params_ftest': (0.0053566334379265765, 0.9416702918669032, 1003.0, 1.0)})
 2: ({'ssr_ftest': (0.25177289420871873, 0.7774705403356538, 1000.0, 2), 'ssr_chi2test': (0.5060635173595247, 0.7764432226205071, 2), 'lrtest': (0.5059361470375734, 0.7764926721067107, 2), 'params_ftest': (0.25177289420872345, 0.7774705403356538, 1000.0, 2.0)})
 3: ({'ssr_ftest': (0.24649533124441178, 0.8638565929333925, 997.0, 3), 'ssr_chi2test': (0.7446779716230374, 0.862648253967841, 3), 'lrtest': (0.7444019401355035, 0.8627137383746588, 3), 'params_ftest': (0.2464953312443746, 0.8638565929334187, 997.0, 3.0)})
 4: ({'ssr_ftest': (0.6384235515822775, 0.6351740781255001, 994.0, 4), 'ssr_chi2test': (2.576816186064484, 0.6309354793595714, 4), 'lrtest': (2.57351178378849, 0.6315224927789413, 4), 'params_ftest': (0.6384235515823179, 0.6351740781254609, 994.0, 4.0)})}

I am struggling to interpret the results. Am I correct in thinking that, taking the 1st ssr_chi2test as an example, (0.0053726552728412666, 0.9415686658133314, 1), that 0.005 represents the test statistic, 0.94 the P-value and 1 the degrees of freedom?

If this is correct, then the null hypothesis can absolutely not be rejected, and potentially there is not enough data given that there is only one degree of freedom?

Any clarity would be appreciated!

Answer 1

(0.0053726552728412666, 0.9415686658133314, 1), that 0.005 represents the test statistic Yes, 0.94 represents the P-value - Yes. and 1 the degrees of freedom? No.

And 1,2,3 and 4 are ordinary serial numbers and not, degree of freedom.

At 10% level of confidence, you need at least 2.71(value of Chi-square). You have computed the chi-square = 2.576 and therefore, the null-hypothesis is acceptable. Your assertion - the null hypothesis can absolutely not be rejected- is valid in this particular case.