There is no number-calculating method given officially by Riot Games, and none of the other MMR-speculating websites use our numbers. Every calculation is based on assumptions.
Each and every MMR-providing websites has a different inner-algorithm used to speculate the numbers; and does not share its methods with the other.
We try our best to express summoners' abilities with numbers by reflecting on their past ratings, and to do so by updating our algorithms more than twenty times per two months.
My MMR has decreased by itself.
The MMR is a merely relative calculation; thus, improvements of competency among other players can lead to a decrease in your number.
This system accords its numbers to the tiers/ranks of recently-played opponents, so when their tiers/ranks change, your MMR can also fluctuate.
MMR does not change.
Since MMR values are based on recent game data, you need to click the 'Renew' button in order to see your new MR value.
It says my MMR cannot be found, even though I have played more than 100 ranked games.
MMR indicates your skills and abilities. You will get better as time elapses, but what we want to know is your current skills. Thus, this MMR is based on the recent data, not the past ones. In other words, it does not matter whether you have played 10 matches or 300 matches so far. You must have many recent games to check your MMR.
You will get the most accurate data if you try again after playing 5 to 10 solo-queue ranked games.