How to analyze time-varying current signal?
Do the indications vary rapidly and/or strongly? If not, you could manually record the values in a spreadsheet every 10 seconds or so — or even ignore the changes altogether, if they are small. If none of these apply, then unless your meter has a built-in computer interface, your best bet is probably to point a webcam at the screen and record a few minutes of video for future analysis. Of course, the question remains whether the figures you see correspond to reality in any meaningful way, and that's difficult to answer unless you know why they change in the first place, and for that you will need a 'scope.