| Markov chain is widely used in financial economy,Internet,language recognition,microbial gene and other fields.In this paper,we mainly study the parameter estimation method and its application of the high-order Markov chain model.For the parameters on the high-order Markov chain model of a single data sequence,we propose an estimation method based on nonlinear least squares.Compared with the traditional estimation method,this method converts the original constrained optimization problem into an unconstrained nonlinear regression problem by constructing an auxiliary function,which simplifies the estimation process and improves the accuracy of prediction,at the same time,it solves the problem of statistical inference which cannot be involved in traditional methods.In addition,in this paper,we also extend this estimation method to higher-order multivariate Markov chain models,and demonstrate the effectiveness of the proposed estimation method in numerical examples.When a data sequence is added to the original high-order multivariate Markov chain model,an incremental high-order multivariate Markov chain model is introduced in this paper,which is used to establish the relationship between the new model after added the datasequence and the original model,in order to avoid repeatedly evaluating the estimated parameters.For the incremental high-order multivariate Markov chain model,we discuss two types of estimation methods,i.e.,the constrained linear programming method and nonlinear least squares method.The numerical results based on a simple example and sales demand forecasting example illustrate that the incremental high-order multivariate Markov chain model not only maintains the prediction performance of the traditional high-order multivariate Markov chain model,but also has great advantages in terms of saving computing resources.When a large of classification data sequences are involved in the problem,the advantages of the incremental model will be more obvious. |
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