This paper is concerned with parametric estimation, model specification and autocorrelation diagnosis for stationary moving averages driven by a Wiener process. By incorporating the analysis of the spectral densities of the discretely observed trajectory, empirical likelihood methods based on moment conditions are developed to the dependent sequences in this paper for estimation and test. Theoretical properties of the empirical likelihood estimator for parameters are provided. Empirical likelihood ratio tests for model specification of the moving averages are proposed by means of the bootstrap strategy. Simulation and empirical case studies are carried out to confirm the effectiveness of the proposed estimation and test.