I study the invertibility problem for time-varying dynamic stochastic general equilibrium (DSGE) models. The question of interest is whether the shocks of a time-varying DSGE model can be recovered from an infinite time-varying VAR on the observable variables. Then I focus on DSGE models whose coefficients are driven by a Markov chain, and propose tractable methods to check their invertibility. Finally, I illustrate the validity of such methods via computations and examples. My results relate with the works of Amisano and Tristani (J Econ Dyn Control 34(10):1837–1858, 2010; J Econ Dyn Control 35(12):2167–2185, 2011), Bekiros and Paccagnini (Empir Econ 45(1):635–664, 2013), Hallin (J R Stat Soc Ser B 42:210–212, 1980; in: Anderson (ed) Time series analysis, theory and practice, North-Holland, Amsterdam, 1983; Adv Appl Probab 18:170–210, 1986), Francq and Zakoian (J Econ 102:339–364, 2001), Franchi and Vidotto (Econ Lett 120:100–103, 2013) and Franchi and Paruolo (Comput Econ 46(4):613–626, 2015).