Yes, it is possible.

There are three very interesting ways to record information generated by Arduino.

Computer (via Serial RS-232 or Ethernet)

This is the most basic way. You connect the Arduino to a computer (via Serial RS-232) and make a program (simple script) that connects to the Arduino and writes the information to a text file. Suggested languages for this: Processing, Python or Groovy.

SD card

You can store information on the Arduino using an SD card. There are modules, shields and even Arduinos that already comes with an input to an SD card. In addition, the existing libraries for recording and reading are very simple to use.

Notes on Using SD with Arduino

ScadaBR (ModBus)

Another interesting option is to use ScadaBR. ScadaBR is a Java web application (to run on Tomcat). This application can interpret several protocols, one being ModBus (via Serial RS-232 or RS-485 or via Ethernet). Thus, you use a ModBus library on the Arduino, connect your Arduino via Serial on the Computer with ScadaBR and configure the ScadaBR to receive information from the Arduino. The great advantage of this approach is that the ScadaBR can be used for several Arduinos and to log the most different types of information. The sky is the limit.

ScadaBR uses the Derby (Apache) database and the information is stored in it. It is quite simple to get a period of time. It has even graphics ready.

In order to get an idea of the power of the combination of the Arduino + ScadaBR, in the company that worked the maintenance team developed a solution with this combination that allows to reconnect an electrical substation using ScadaBR.

Summary

If your Arduino can run near a computer and the problem you want to solve is timely, go to Computer via Serial. You'll get it right quickly.

If your Arduino should rotate away from a computer and you do not have time to connect it via Ethernet or RS-485, then go to the SD Card option.

If you want a solution to suit various Arduino and other devices that talk ModBus, go to ScadaBR.