It is shown that parametric bootstrap can be used for computing P-values of goodness-of-fit tests of multivariate time series parametric models. These models include Markovian models, GARCH models with non-Gaussian innovations, regime-switching models, as well as semiparametric models involving copulas of multivariate time series. The methodology is intuitive, easy to implement, and provides an interesting alternative to Khmaladze's transform or other projection methods.