Rouwenhorst

Discretizes a stable AR(1) with process with zero mean. Usage:

include("rouwenhorst.jl")

npts = 10
rho = 0.9
sig = 0.01
gridpts, transition = rouwenhorst(npts, rho, sig)

where rho is the autocorrelation, npts is the number of points in the resulting discretized process, and sig is the error standard deviation.

Returns a vector gridpts with the support and the Markov matrix transition.

Bonus: equiprobable discretization

The function eqprob_discretize (see finitesupport.jl) might come in handy when you need a discrete approximation of a variable with continuous support. A picture worth a thousand words:

How to generate that:

include("finitesupport.jl")

using Distributions
using Plots


some_dist = Pareto(1.2, 0.1)

# Apply the magical `eqprob_discretize`, returning a vector-like object
discrete_version = eqprob_discretize(some_dist, 30);


# Now let's compare the CDFs
domain_cmp = range(0.1, maximum(discrete_version), length=100)


plot(x -> cdf(some_dist, x), domain_cmp, lw=2, legend=:bottomright,
     label="'True'", color=:gray60, title="Pareto distribution")

plot!(discrete_version, cumsum(pmf(discrete_version)),
      label="Discretized", color = :midnightblue, seriestype = :steppost)