If fasting or restricting food really does relieve depression and anxiety It could be your dietary habits are somehow causing you stress.

1. You could have a food sensitivity. If you react to something common like corn, then fasting or eating very little reduces your exposure and thus your reactions.
2. You could have hyperinsulinism. Eating raises your blood sugar, insulin brinca It too far down, and to rqise It again your body releases adrenaline which makes anxiety and eventually depression.
3. You could be producing endorphins by fasting. If you feel a trancy calm, thats endorphons. Its not a good thing to do.