Those are both slower than the for loop by quite a bit, and the second one is much slower than the first.
julia> @btime initial_trend_for_loop(series, 12)
24.727 ns (1 allocation: 16 bytes)
-0.7847222222222222
julia> @btime initial_trend_tkf1(series, 12)
96.970 ns (5 allocations: 416 bytes)
-0.7847222222222222
julia> @btime initial_trend_tkf2(series, 12)
778.307 ns (13 allocations: 480 bytes)
-0.7847222222222222