The covariance estimation of multivariate nonlinear processes is studied. The heteroscedasticity autocorrelation consistent (HAC) and White (1980) estimators are commonly used in the literature to take into account nonlinearities. Noting that the more general HAC estimation procedures may be sometimes viewed too sophisticated in applications, we propose tests for determining whether the simple White estimation could be used or if HAC estimation is necessary to ensure a correct statistical analysis of time series. The theoretical results are illustrated by mean of Monte Carlo experiments. (C) 2015 Elsevier B.V. All rights reserved.