No problem. I had a chance to look at your example in more detail. The following function works with your example model:
function myfilter(x::AbstractVector, λ)
n = length(x)
xnew = zeros(typeof(λ), n)
xnew[1] = x[1]
for i in 2:n
xnew[i] = x[i] + λ * xnew[i-1]
end
xnew
end