# statsmodels's granger causality tests return value

I'm a developer (with no background in statistics) and I need to use granger causality test, i cant seem to understand the results from the python statsmodels package.

Example result:

Granger Causality

('number of lags (no zero)', 3)

ssr based F test:         F=0.0108  , p=0.9984  , df_denom=193, df_num=3

ssr based chi2 test:   chi2=0.0336  , p=0.9984  , df=3

likelihood ratio test: chi2=0.0336  , p=0.9984  , df=3

parameter F test:         F=0.4715  , p=0.4931  , df_denom=193, df_num=1

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what is the difference between the 4 tests and how to get a conclusion from the p value.

1

Granger Causality test is to a hypothesis test with,

H0 : other time series does not effect the one we are focusing

H1 : H0 is false.

Eg. If X and Y are two time series and we want to know if X effects Y then,

H0 : X does not granger cause Y

H1 : X does granger cause Y , if p-value > 0.05 then H0 is accepted. i.e. X does not granger cause Y.

The test comprises of evaluating the p-value under various distribution.

SSR based F test : under this the statistic has an F-distribution under null Hypothesis.

SSR based Chi2 test : purpose of this test is to determine if a difference between observed data and expected data is due to chance, or if it is due to a relationship between the variables you are studying. Based on Chi2 distribution.

Likelihood ratio test : basically a ratio of the probability that a test result is correct to the probability that the test result is incorrect.

parameter F test : allows you to conclude whether two variables are related in the population. An F-value is the ratio of two variances, or technically, two mean squares. The F-test is called a parametric test because of the presence of parameters in the F- test. These parameters in the F-test are the mean and variance.