**Title** : Order Determination for Probabilistic Functions of Finite Markov Chains

**Authors** :

Finesso, Lorenzo

**Journal** : M.S. Thesis Number: MS 87-4

December 31, 1987

Let {Y sub t} be a stationary stochastic process with values in the finite set YY. We model {Y sub t} as a probabilistic function of a finite state Markov Chain {X sub t} i.e. X sub t is such that: P[Y sub t | X sup t, Y sup t-1] = P[Y sub t | X sub t] Define the cardinality of the state space of {X sub t} as the order of the model. The problem is to determine the order given the observations {y sub 1, y sub 2, y sub T}. We show that under mild conditions on the probability distribution function P sub Y (.) of {Y sub t} the order is identifiable and can be consistently determined from the data.

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