I'am comparing two 14 years time series, one being a diversity index and the other annual temperature. I suspect annual temperature to be a strong driver of annual diversity. Accordingly, I found a significant granger causality index when testing for granger causality between temperature and diversity with a lag of three years. However when running a cross correlation analysis between the two time series I found really low correlation between temperature at time t-3 and diversity at time t. Does anyone ever experience such a situation ? In other work, is it possible to observe causality but no correlation ? Thanks in advance !

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