Unilateral 2D Markov-switching autoregressive model

Abstract

For nonlinear two-dimensional spatial data, a 2D Markov-switching unilateral autoregressive model is defined. Strict stationarity is studied and parameter estimation via the variational expectation maximisation (VEM) algorithm is performed. First, a 2D Markov random field (MRF) is constructed for which an imposed causality allows to establish an analogy between this 2D MRF and the Markov chain representation. Based on the proposed 2D MRF, the 2D MS-AR model is defined under some necessary assumptions and useful notations. Finally, parameter estimation of the model is discussed paving the way to broad exploitation perspectives of the proposed 2D MS-AR processes to efficiently model several phenomena exhibiting a structural break in spatial data.