this study aims to test the existence of near unit roots and local persistence in several important variables of economic models (product market, ccapm and black-scholes' formula). it is argued that the rejection of the unit root hypothesis will not necessarily imply in accepting a stationary and ergodic behavior for the time series. in order to do that, the near unit root model developed by phillips, moon and xiao (2001) was selected and an estimation strategy was used. such strategy is described as follows: a) the df-gls test, suggested by elliott, rothenberg and stock (1996); b) optimal selection of lags used by ng and perron (2001); c) the non parametric correction for terms of perturbation non i.i.d., from the kernel smoothing. the empirical results show, for some series, a characterization of the dgp from the local persistence.