"How to test actio-reactio-relations (no correlation)?"
I have a large data set, containing the prices of different store and the corresponding times when prices changed. What I want to know ist who of all stores ist the one who first changes prices and who are the ones who just react to the price change. To give an example:
Store ProductPrice Time
XY 12,50 11:00
XY 13,50 11:15
XX 9,50 11:00
XX 11,00 11:30
Obviously Store XX is the one who is reacting to the price change of XY (This is simplified, in reality this is more articulate since there are thousands of stores and changes). It is easy to to this for example grafically, but is there a way to to somehow achieve this by the using computational power, because it would be hard to generate and compare hundreds of diagrams (There must also be something like a intensity, to say something about the actio-reactio-intesity)?
My approach was to generate the delta of each Price change to find out who is increases/decreases and then somehow aggregate which stores are changing prices in the same direction at the same time and then look for the amount of same patterns in this behaviour.
I hope someone understands this problem and can help me to find a beginning to start working on.
Thank you :-)