Information quantity evaluation of multivariate SETAR processes of order one and applications

The Self-Exciting Threshold Autoregressive model (SETAR) is non-linear and considers threshold values to model time series affected by regimes. It is extended through the Multivariate SETAR (MSETAR) model, where the threshold variable can also be a multivariate process. The stationary marginal density (smd) of an MSETAR process of order one corresponds to a Unified Skew-Normal density. In this paper, the smd of an MSETAR of order one process was considered to compute explicit expressions of differential entropy and Kullback–Leibler and Jeffrey’s divergences between two MSETAR(1) processes. In addition, two asymptotic tests based on divergences were built for statistical significance testing of the disparity between MSETAR(1) processes and the threshold coefficient matrix. Information measures considered involved high-dimensional integrals that likewise depended on multivariate cumulative density normal function. To solve these integrals, Genz’s algorithm was considered based on Cholesky decomposition and Monte Carlo approximation. Some numerical experiments and applications to fish condition factor and Chilean economic perception time series illustrate performance.