A better approach to this would probably be treating the data as panel data and either doing monthwise hierarchical Bayesian regressions, and testing if the coefficients pooled over time are significantly non-zero, or else using a sort of distributed lag model or instrumental variables model on the monthwise simple regressions. In these cases, it’s better to roll up lagged features of the exogenous time series to serve as constructed covariates in the lag model, than to rely on differencing and time series tests which are like a landmine of interpretation issues.
Checking causality in models like this is very tricky, so a lot of care has to be taken, and you should expect work to proceed slowly and require a lot of posterior checks.
(I am fully aware that I can google it but in my opinion it's usually better to ask someone who is already familiar with the topic because he/she may know good learning materials.)
- < http://www.stat.columbia.edu/~gelman/arm/ >
If you happen to use Python, pymc3 is a great place to look for hierarchical and Bayesian timeseries models with full examples.
This is actually methodologically incorrect. You test Granger non-causality by taking a VAR system and you do not difference the data for stationarity! You use the cointegration order to determine how many extra lags of the exogenous variable to use beyond the order p that defines the lags tested against the null hypothesis (what the authors mention is tested by AIC, BIC, and observing autocorrelation of residuals).
> “The ADF test, differencing and the Granger causality test were performed on data aggregated to monthly frequency”
Hmm. It looks like differencing was done based on the ADF test... this is not valid for Granger causality.
Remember, with the frequentist statistical tests, there are so many fraught issues like this.
In the end, a test like this only talks about the following:
“Under the assumed hypothesis of no causality, how extreme do the observed test statistics appear to be?”
— where the test statistics are in part based on estimated model parameters that are highly sensitive to methodological errors, like differencing prior to computing the coefficient-is-non-zero tests in this Granger VAR model.
In the end it makes me skeptical of interpreting any of the results from the OP.
A good explaination is here: [0].
[0]: < http://davegiles.blogspot.com/2011/04/testing-for-granger-ca... >