Forecasting random perturbations allows improving the control quality in intelligent transport systems and ensuring the efficient operation of diagnostic systems. Several works are known where extrapolator models based on Chebyshev polynomials orthogonal on equidistant points are presented. These models use a predictive polynomial whose coefficients are computed using the least squares criterion. Additionally, an analysis of forecast errors for random stationary input signals has been conducted. At the same time, in the case of non-stationary input signals, singular perturbations may occur, the influence of which on the extrapolator leads to significant forecast errors. This article presents an example of the occurrence of additive perturbations that arise in automatic train control systems. An analytical expression has been derived, and calculations of forecast error magnitudes in the presence of singular perturbations have been conducted. The analysis of the calculation results allows determining the influence of extrapolator parameters on the forecast error magnitude, highlighting the necessity of detecting singular perturbations, and excluding their influence on the forecast error magnitude. The article discusses an algorithm for detecting singular perturbations and their exclusion during the forecasting process. The conclusion is drawn about the effectiveness of using extrapolators for random perturbations with the exclusion of singular perturbations in intelligent systems for automatic train control in subway transportation.