This study considers simultaneous inference of economic time series models for potential policy implications. The process of interest is an unknown function of either time or an observable random vector in macro-finance. To overcome the well-known slow convergence issue with the traditional asymptotic-based approach, we utilize a Gaussian approximation for our time-dependent processes. Relevant theories and finite-sample simulations justify our approach. The empirical applications include the U.S. Phillips curve in macroeconomics and the forward premium puzzle in international finance.