Could a company do prior period adjustment for unrealized investment gain/loss back for 3 years? For example, no one booked journal entries for unrealized gain or loss for the years 2010, 2011 and 2012. When closing the book for 2013, could we go back to see how much unrealized gain/loss not recorded for the 3 or 4 years? Assume no new purchase or sale happened for those 4 years.

If it's material, then yes. Otherwise, just let it go.

You should calculate the change that is associated with the current period and the change that is associated with earlier years, that which is associated with the current year is included above the line in the P&L, that which was earlier is included as a prior period adjustment, below the line in the P&L. Obviously materiality should always be your guide, but no matter how small the adjustment, changes in the value of assets should be recorded and reported