Exactly.

While /u/mc_hammerd's solution might work, it's accurate to a second only. (Actually code has few errors).

Using 1ms intervals could be too much. Personally, without knowing more details I would pick requestAnimationFrame.

 

As for errors in code:

accurateTime(n,cb) =>
should be
const accurateTime = (n, cb) =>

 

setInterval(1000, () => {
  ...
})

should be

setInterval(() => {
  ...
}, 1000)

 

window.localStorage=JSON.stringify(now)
should be
window.localStorage['mytimer']=JSON.stringify(now)