QuantEcon.jl

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This is already accomplished on the Python side in https://github.com/QuantEcon/QuantEcon.py/pull/658

An ongoing discussion for the Julia side is here:

• https://discourse.quantecon.org/t/estimate-markovchain-from-data-using-ml/239
• https://discourse.quantecon.org/t/estimating-markov-chain-probabilities-in-julia-using-proportions/981

@msilva913 proposes

function estimate_markov(X::Vector, nstates::Int64)
    P = zeros(nstates, nstates)
    n = length(X) - 1
    for t = 1:n
        # add one each count is observed
        P[X[t], X[t+1]] = P[X[t], X[t+1]] + 1
    end
    for i = 1:nstates
        # divide by total number of counts
        P[i, :] .= P[i, :]/sum(P[i, :])
    end
    return P
end

Note that this will lead to division by zero errors for states that are never visited. The Python code handles this by dropping such states.

Is it estimate_mc_discrete (#161)?