Résumé : This technical appendix contains proofs for the asymptotic properties of quasi-maximum likelihood (QML) estimators for vector autoregressive moving average (VARMA) models in the case where the coefficients depend on time instead of being constant. We refer to the main theorems of the paper Asymptotic properties of QML estimators for VARMA models with time-dependent coefficients" (Alj, Azrak, Ley and M elard, 2016).