Year long clock accuracy

Most quartz clocks and watches have an accuracy or stability of plus or minus 15 seconds a month. (About 1 part in 200000). In order to maintain the correct time to the second or tenth of a second, the watch needs to be synchronized every day or so.

I want a clock that needs to be synchronized less than once a year: the goal is to set your clock with the time ball (the way it's supposed to be done!) at midnight on New Year's and have the clock still be accurate enough to do the countdown one year later. 1 in a billion. Not quite atomic clock accuracy? Can it be done with quartz?

You also want the clock not to lose power over the year.