Existence and uniqueness of the stationary distribution for higher-order Markov chain

The period effect for the limit distribution of a higher-order Markov chain is discussed and the correlation between the connectivity of higher-order matrix and stationary distribution is studied.The conditions of the existence and uniqueness for the stationary distribution of the higher-order Markov chain are proved which improve the theory of parameter estimation.Then the stock index data is modeled with the application of higher-order Markov chain.The estimated parameters indicate that there exist correlations between the neighbors of stock price,and the forecast results are compared with the traditional model.