Hidden markov linear regression model and its parameter estimation

Abstract

This article first defines a hidden Markov linear regression model for the purpose of further studying the mutual transformation between different states in the linear regression model, and the regression relationship between the dependent variable and the independent variable in each state. And then, K-means clustering analysis methods are used to identify the hidden states of observed data, and the maximum likelihood estimation of the hidden state transition probability matrix elements is obtained by using the maximum likelihood estimation method, and parameter estimation of unknown parameters in linear regression model is also presented by using the least squares method. Finally, the observation vector set is generated according to the defined model, and the empirical simulation demonstrates that the parameter estimation method shown in this work is reliable.