Neurocomputing has been adjusted effectively in time series forecasting activities, yet the vicinity of exceptions that frequently happens in time arrangement information might contaminate the system preparing information. This is because of its capacity to naturally realise any example without earlier suspicions and loss of sweeping statement. In principle, the most widely recognised calculation for preparing the system is the backpropagation (BP) calculation, which inclines toward minimisation of standard slightest squares (OLS) estimator, particularly the mean squared mistake (MSE). Regardless, this calculation is not by any stretch of the imagination strong when the exceptions are available, and it might prompt bogus expectation of future qualities. In this paper, we exhibit another calculation which controls the firefly algorithm of least median squares (FFA-LMedS) estimator for neural system nonlinear autoregressive moving average (ANN-NARMA) model enhancement to provide betterment for the peripheral issue in time arrangement information. Moreover, execution of the solidified model in correlation with another hearty ANN-NARMA models, utilising M-estimators, Iterative LMedS and Particle Swarm Optimisation on LMedS (PSO-LMedS) with root mean squared blunder (RMSE) qualities, is highlighted in this paper. In the interim, the actual monthly information of Malaysian Aggregate, Sand and Roof Materials value was taken from January 1980 to December 2012 (base year 1980=100) with various levels of anomaly issues. It was found that the robustified ANN-NARMA model utilising FFA-LMedS delivered the best results, with the RMSE values having almost no mistakes at all in all the preparation, testing and acceptance sets for every single distinctive variable. Findings of the studies are hoped to assist the regarded powers including the PFI development tasks to overcome cost overwhelms.