Correlation analysis timeline

Question

I am interest in finding statistically significant correlations of two variables. The variables do not correlate with the normal cor() R function.

My setting is based on oil production where secondary methods are used to produce oil. For example, if you inject water today, it would have an impact after days or even months. Looking at the correlation of the oil production and water injection, there is none due to the lag of the impact.

I would like to know which methods I could use to understand the delay of impact and more importantly the impact itself.

Another example is on the tree growth analysis, if you track the width of the tree bark and the amount of water used everyday, the efforts of adding water could impact growth after some time.

Answer 1

To stick a long the lines you are currently trying to implement, could you look at the correlation between oil production after t amount of time with the water injection, where t is a vector of time points.

So at time t=0, you may find no correlation. At time t=1, you may find no correlation. At time t=2, you may find no correlation. But then at time t=3 you may find a correlation.

However, over the course of time the changing other factors that may effect your outcome (oil production). To adjust for these you would want to use regression.