Storing data is one thing, but how will you get that data to the computer ?
If you have an Arduino Pro Mini with a ATmega328p, that has only 1k of EEPROM memory.
You can add a EEPROM, they are cheap.
You could also add a add-on board with a microSD slot.
An integer in most Arduino boards are two bytes, so a week storage would require 40kbytes.
The ArduIMU V4 has a microSD slot.