A Finite Form of De Finetti's Theorem for Stationary Markov Exchangeability

De Finetti's theorem for stationary Markov exchangeability states that a sequence having a stationary and Markov exchangeable distribution is a mixture of Markov chains. A finite version of this theorem is given by considering a finite sequence X₁,…, Xₙ which is stationary and Markov exchangeable. It is shown that any portion of k consecutive elements, say X₁,⋯, Xₖ for $k < n$, is nearly a mixture of Markov chains (the distance measured in the variation norm).