On estimation states of hidden markov models in condition of unknown transition matrix

TL;DR

This paper presents non-parametric methods for estimating the states of a hidden Markov model with an unknown transition matrix, using observations from an AR(p) process, and compares them with optimal methods through simulations.

Contribution

It introduces novel nonlinear filtering algorithms for hidden Markov models with unknown transition matrices, applicable to AR(p) driven systems.

Findings

Proposed algorithms perform well compared to optimal methods with known transition matrices.

Simulation results demonstrate the effectiveness of the non-parametric estimation methods.

The methods are suitable for systems where transition probabilities are unknown or difficult to estimate.

Abstract

In this paper, we develop methods of nonlinear filtering and prediction of an unobservable Markov chain with a finite set of states. This Markov chain controls coefficients of AR(p) model. Using observations generated by AR(p) model we have to estimate the state of Markov chain in the case of an unknown probability transition matrix. Comparison of proposed non-parametric algorithms with the optimal methods in the case of the known transition matrix is carried out by simulating.