Correlation is a bivariate feature analysis technique.
Typically, that is done after univariate features analysis. But before any feature engineering.
Most machine learning is iterative so correlation can be revisited at any stage.
That would be a part of feature selection. There are many methods to find out if there are relationships between the dependent variable and independent variables. To name a few: plots, measures of correlation, measures of mutual information.
First let me answer your specific question:
If you want to decide which feature of two highly correlated, high impact features I would look at the following additional attributes of your features:
How is the data quality or amount of data? Is one better or higher than the other? Choose this one.
Is it in any way harmful to remove one of the features? If yes,...
Both are using the Pearson algorithm to calculate correlations:
However, the floating values operations are slightly different and this slight difference becomes taller when you make several operations like Pearson.
You can try by calculating the Pearson algorithm manually for both cases.
I am not exactly sure what you want to achieve, but here goes my solution
So acf generally tells you the autocorrelation between all lags compared with original trend
so for example, for Dataset 1
The concept of cross-correlation is used in signal processing to find delay in signal and also in image processing to match-images(known as template matching)
The general approach is to go on shifting the signal by 1 and compute correlation and find where the maximum values, here's a solution using matplotlib, if someone wants a ready to use implementation