Another approach for the asymptotic properties of threshold vector ARMA models

Abstract In the present contribution, we propose and exploit a link between vector threshold autoregressive moving average (TVARMA) and time-dependent VARMA (tdVARMA) models. We show that an adequate parametrization permits the TVARMA model to be included in the broad class of tdVARMA structures. It allows us to derive new results on the asymptotic properties of the estimators of TVARMA parameters obtained under weaker conditions than those given in the literature, at least when the threshold variable is exogenous. As a consequence, new tests are proposed. A simulation study gives evidence of the achieved results that are applied to study the behavior of the monthly CPI, US unemployment, and US federal funds effective rate.