Since AAM is a SaaS, and it cannot be installed and managed in your environment wholly. So, data is collected stored and processed on AAM's servers. Also, you can have the data collected by AAM on your web properties to be exported and can have that at your place and can re use that data or use that for reports. You will have to contact AAM support or your AAM consultant to create an export.
If there is any specific question related to data security, then you can contact AAM support and all the details will be provided to you.