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.
Highlights
In the 19th century, when the well-known British biologist and statistician Galton studied the genetic laws of parent height and the height of their children, he established an empirical straight-line equation for the height of an adult child about the average height of the parent, and named it as regression equation
EMPIRICAL SIMULATION In order to test the reliability of the inference method of the hidden Markov multiple linear regression model introduced in this article, this section will give the number of hidden states K, the hidden state transition probability matrix A, and the linear regression model in each hidden state Coefficient βk
This article combines the hidden Markov model and the linear regression model to give the definition of the hidden Markov linear regression model
Summary
In the 19th century, when the well-known British biologist and statistician Galton studied the genetic laws of parent height and the height of their children, he established an empirical straight-line equation for the height of an adult child about the average height of the parent, and named it as regression equation. Based on the existing research results of linear regression model and hidden Markov model, this article further studies the hidden Markov linear regression model with a fixed number of hidden states. When the macro economy is in two different states with inflation and deflation, and the consumer market is in two different states with consumption upgrade and consumption degradation, the regression relationship between the dependent and independent variables in the linear regression model is different, and these two states are often changed. A model capable of correctly expressing the rules of mutual transformation between different states and the regression relationship between the dependent variable and the independent variable in each state, named a hidden Markov multiple linear regression model, is introduced and is committed to the model inference and its parameters estimation research. This is the important contribution and value of this article, since it brings benefits to the application of hidden Markov model
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