Matching correlations Discrete Time Markov Chain

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Suppose we have some $n$ dimensional Discrete Time Markov Chain, which is characterized by an $ntimes n$ matrix $A$ and state space $S=1,dots,n$ we denote $(X_n)_n=1^infty$ for the associated discrete time process. Suppose we have given $m < n$ lag-correlations $ell_1,dots,ell_m$ which we want to match, i.e. we want to have $operatornameCorr(X_n, X_n+k)=ell_k$ for all $k=1,dots,m$. Is there an efficient/intuitive method for doing this?




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    Suppose we have some $n$ dimensional Discrete Time Markov Chain, which is characterized by an $ntimes n$ matrix $A$ and state space $S=1,dots,n$ we denote $(X_n)_n=1^infty$ for the associated discrete time process. Suppose we have given $m < n$ lag-correlations $ell_1,dots,ell_m$ which we want to match, i.e. we want to have $operatornameCorr(X_n, X_n+k)=ell_k$ for all $k=1,dots,m$. Is there an efficient/intuitive method for doing this?




    probability matrices markov-chains correlation




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      Question



      Suppose we have some $n$ dimensional Discrete Time Markov Chain, which is characterized by an $ntimes n$ matrix $A$ and state space $S=1,dots,n$ we denote $(X_n)_n=1^infty$ for the associated discrete time process. Suppose we have given $m < n$ lag-correlations $ell_1,dots,ell_m$ which we want to match, i.e. we want to have $operatornameCorr(X_n, X_n+k)=ell_k$ for all $k=1,dots,m$. Is there an efficient/intuitive method for doing this?




      probability matrices markov-chains correlation




      share|cite|improve this question













      Question



      Suppose we have some $n$ dimensional Discrete Time Markov Chain, which is characterized by an $ntimes n$ matrix $A$ and state space $S=1,dots,n$ we denote $(X_n)_n=1^infty$ for the associated discrete time process. Suppose we have given $m < n$ lag-correlations $ell_1,dots,ell_m$ which we want to match, i.e. we want to have $operatornameCorr(X_n, X_n+k)=ell_k$ for all $k=1,dots,m$. Is there an efficient/intuitive method for doing this?





      probability matrices markov-chains correlation





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