Interpreting Granger Causality Tests and Their P Values
Summary
The document presents output from a Granger causality test and asks how to interpret its four reported statistics and p values. The included answer describes the null hypothesis as one series not Granger-causing another, and explains that the output reports SSR-based F and chi-square tests, a likelihood-ratio test, and a parameter F test. These statistics assess restrictions using different test formulations or distributions; the example shows that output can contain different p values across tests.
The answer suggests comparing a p value with a significance threshold to assess evidence against the null. Its wording that a large p value means the null is accepted is too strong: such a result means the test does not reject the null at that threshold, not that the null has been proven. The brief descriptions of chi-square and likelihood-ratio tests are also simplified, so the excerpt is an introductory orientation rather than a full guide to assumptions, model setup, or inference.
Key ideas
- Granger causality tests assess whether lagged values of one series add predictive information for another.
- The output lists several test statistics that evaluate restrictions under different reference distributions or formulations.
- A small p value can provide evidence against the null at a chosen significance level.
- A large p value means the test fails to reject the null; it does not establish that the null is true.
Tags
Full text
# statsmodels's granger causality tests return value
# 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
--
```
what is the difference between the 4 tests and how to get a conclusion from the p value.
thank you for your help.
## Answer by Cirev Nat (score 1)
https://quant.stackexchange.com/a/75979
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.