Types of Causal Analytics
There are a variety of algorithms that are useful to analyze cause and effect.  Here are a few with their strengths and weaknesses.
 

1. Linearity
2. Similar Means
3. Similar Variances

Unfortunately, these assumptions are frequently violated.  In some cases, R cannot be calculated at all, or becomes unstable, or is so small relative to true cause and effect that it no longer has much worth.  For example, highly non-linear operations with tight feedback loops.  Similar means violations can be assisted by data scaling and normalization, however the data is no longer the same and variance and linearity violations may still exist.

Timing must be deduced by applying the calculations repeatedly through sliding time windows.

Gives excellent indications of timing.

Indicates positive or negative response between variables.

Indicates positive or negative response between variables.

Does not give timing unless you use particular model types or use the calculation repeatedly through a sliding time windows.

 
Many people exclusively use statistical correlation.  However, it only works well with linear systems.  For example, we recently applied time-shifted statistical correlation analysis to oil wells which have tight causal loops and a highly non-linear response between a highly variable production flow measurement and a smooth well casing pressure, in an attempt to determine proper time shifts between changing the well's pressure vs. production.  Statistical correlation broke down under these conditions, yielding very low correlations implying the relation was of little value (actual practice informs us otherwise).

To overcome the weaknesses of methods while drawing on their strength, we feel it is important to use a hybrid approach to get a better measure of causality.  We fuse these technologies together using a confidence weighting.
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