Yes - Divide the unearned income (like interest and dividends) by 12 and multiply by the number of months you lived in each state.
Let's say you had $900 in interest income for the year. Dividing by 12 gives you $75/month.
If you moved in the middle of July, you spent 6.5 months in the first state and 5.5 months in the new states.
- Interest allocated to first state: 6.5 x 75 = 487.50
- Interest allocated to second state: 5.5 x 75 = 412.50