Multivariate Self-Exciting Threshold Autoregressive Models with eXogenous Input

TL;DR

This paper introduces a new multivariate nonlinear time series model called MSETARX, along with an estimation procedure and stationarity conditions, demonstrating the effectiveness of adaptive and least squares estimation methods through simulations.

Contribution

It defines the MSETARX model, establishes stationarity conditions, and evaluates estimation algorithms, advancing nonlinear multivariate time series modeling.

Findings

Adaptive estimation algorithm is effective.

LSE algorithm performs well in simulations.

Stationarity conditions are explicitly derived.

Abstract

This study defines a multivariate Self--Exciting Threshold Autoregressive with eXogenous input (MSETARX) models and present an estimation procedure for the parameters. The conditions for stationarity of the nonlinear MSETARX models is provided. In particular, the efficiency of an adaptive parameter estimation algorithm and LSE (least squares estimate) algorithm for this class of models is then provided via simulations.