Long-term nonstationary oscillations (NSOs) are commonly observed in climatological data series such as global surface temperature anomalies (GSTA) and low-frequency climate oscillation indices. In this work, we present a stochastic model that captures NSOs within a given variable. The model employs a data-adaptive decomposition method named empirical mode decomposition (EMD). Irregular oscillatory processes in a given variable can be extracted into a finite number of intrinsic mode functions with the EMD approach. A unique data-adaptive algorithm is proposed in the present paper in order to study the future evolution of the NSO components extracted from EMD. To evaluate the model performance, the model is tested with the synthetic data set from Rössler attractor and with GSTA data. The results of the attractor show that the proposed approach provides a good characterization of the NSOs. For GSTA data, the last 30 observations are truncated and compared to the generated data. Then the model is used to predict the evolution of GSTA data over the next 50 years. The results of the case study confirm the power of the EMD approach and the proposed NSO resampling (NSOR) method as well as their potential for the study of climate variables.