This paper establishes the consistency and limit distribution of minimum distance (MD) estimators for time series models with deterministic or stochastic trends. We consider models that are linear in the variables, but involve nonlinear restrictions across parameters. Two complications arise. First, the unrestricted and restricted parameter space have to be rotated to separate fast converging components of the MD estimator from slowly converging components. Second, if the model includes stochastic trends it is desirable to use a random matrix to weigh the discrepancy between the unrestricted and restricted parameter estimates. In this case, the objective function of the MD estimator has a stochastic limit. We provide regularity conditions for the non-linear restriction function that are easier to verify than the stochastic equicontinuity conditions that typically arise from direct estimation of the restricted parameters. We derive the optimal weight matrix when the limit distribution of the unrestricted estimator is mixed normal and propose a goodness-of- t test based on over-identifying restrictions. As applications, we investigate cointegration regression models, present-value models, and a permanent-income model based on a linear-quadratic dynamic programming problem.