A Mahalanobis Distance-Based Modification of the RENES Method for Environment State Estimation in Generalized RrINAR Models of Higher Order

Abstract

The dynamic of integer-valued autoregressive model in random environment is governed by the realization $\{z_n\}_{n=1}^\infty$ of a Markov chain referred to as the random environment process. At given moment $n\in\mathbb{N}$, the realization $z_n$ defines the environment conditions and determines all model parameters at that moment. In most cases, the K-means clustering technique has been used to estimate $\{z_n\}_{n=1}^\infty$, which is a necessary step in models application. However, the application of the K-means technique is not always the optimal solution, as it disregards certain information and may yield suboptimal results in some scenarios. To enhance clustering performance for data sequences corresponding to generalized random environment integer-valued autoregressive time series of higher order, the so-called RENES clustering method was developed. Despite its advantages, RENES also has some drawbacks and is highly complex to implement. To address these challenges, we propose a modification of the RENES method based on the Mahalanobis distance, designed to simplify the algorithm and improve its practical applicability while preserving clustering accuracy. The effectiveness of this modification was evaluated using the same simulations and real-life data where the RENES method had previously demonstrated its validity, and notable improvements were observed.