  We propose a two-step algorithm for the construction of a Hidden Markov Model
(HMM) of assigned size, i.e. cardinality of the state space of the underlying
Markov chain, whose $n$-dimensional distribution is closest in divergence to a
given distribution. The algorithm is based on the factorization of a pseudo
Hankel matrix, defined in terms of the given distribution, into the product of
a tall and a wide nonnegative matrix. The implementation is based on the
nonnegative matrix factorization (NMF) algorithm. To evaluate the performance
of our algorithm we produced some numerical simulations in the context of HMM
order reduction.
