Parameter estimation of linear regression models usually employs least squares (LS) and maximum likelihood (ML) estimators. While maximum likelihood remains one of the best estimators within the classical statistics paradigm to date, it is highly reliant on the assumption about the joint probability distribution of the data for optimal results. In this paper we use the Generalized Method of Moments (GMM) to address the deficiencies of LS/ML in order to estimate the underlying data generating process (DGP). We use GMM as a statistical technique that incorporate observed noise data with the information in population moment conditions to determine estimates of unknown parameters of the underlying model. Periodic impulsive noise (short-term) has been measured, deseasonalized and modeled using GMM. The numerical results show that the model captures the noise process accurately.