Note that you can also write this:
v = view(x, 1:length(x)-1)
∑μ = sum(fitted, v)
or this
using LazyArrays: @~ # just to construct Base.Broadcast.Broadcasted
...
v = view(x, 1:length(x)-1)
∑μ = sum(@~ fitted.(v))
Both should avoid the allocations, and the lazy broadcast sum is fast on Julia 1.5. They won’t beat the simple loop, but can be tidier.