By the end of the day my ECPM is almost halved.
Does anyone see their ECPM start high in the morning and slowly go down?
Yes, same happens to me. Don’t know why.
That could be the way the ad server of your ad network operates - late reporting of impressions in the end of the day cause your eCPM to decrease. Late installs are reported in the following day, so eCPM in the beginning of the following day is high.
It’s just a thought… As far as I know, appnext server doesn’t work like that (unless you tell me otherwise).
Of course it depends upon the network and how their reports works. And actually I think this is kind of a “rule” for any network who updates their stats every hour. And yes, this is valid for Appnext as well 
The reason is simple(at least for me): I’m located in Eastern Europe(GMT+2), the highest eCPM I get is from USA and when I wake up in the morning I see a great eCPM of $4-7 for the last night(average from all countries that were “active” that night, specially for USA the eCPM is even higher) for the previous night(when actually the USA users are more active), and of course during the day the eCPM will drop because the other countries(from Europe and Asia) are not so ad-friendly as USA is.
So in my opinion it’s pure normal to see the drop in eCPM during the day(if you’re outside of USA at least), but of course there should be logic limits to the eCPM vs Country, for Tier 1 countries the eCPM should not drop near $1.5-2.
What you say makes perfect sense. Should have come up with that answer myself 