On Multi-step MLE-process for Markov Sequences

TL;DR

This paper develops multi-step maximum likelihood estimation procedures for nonlinear autoregressive processes, improving efficiency and reducing the learning interval, with theoretical analysis and numerical illustrations.

Contribution

It introduces two- and three-step MLE-based estimator processes for nonlinear autoregressive models, achieving asymptotic efficiency with shorter learning intervals.

Findings

The two-step procedure yields asymptotically efficient estimators.

The methods are validated through numerical examples.

The approach reduces the data needed for reliable estimation.

Abstract

We consider the problem of the construction of the estimator-process of the unknown finite-dimensional parameter in the case of the observations of nonlinear autoregressive process. The estimation is done in two or three steps. First we estimate the unknown parameter by a learning relatively short part of observations and then we use the one-step MLE idea to construct an-estimator process which is asymptotically equivalent to the MLE. To have the learning interval shorter we introduce the two-step procedure which leads to the asymptotically efficient estimator-process too. The presented results are illustrated with the help of two numerical examples.