Analysis and forecasting of time series is a popular predictive tool for working with large amounts of data reflecting the patterns of processes’ behavior under study in the economic, financial, socio-political and other spheres. However, their potential is not enough to effectively forecasting of the situation development in non-stationary processes, which are a characteristic feature and trend of our time in various society spheres. Such processes are characterized by unpredictability of behavior, for example, in cases of: (i) an abrupt transition from one state to another, due to an event that causes an abrupt (jump) change in the process values; (ii) violation or weak severity of seasonality in the processes during the transition from a stable state to a crisis. In this paper we propose a cognitive modelling-driven approach to time series forecasting for predicting target indicators in non-stationary processes. The approach implementation is aimed at improving the forecast quality of target indicators in such processes by (i) building and correcting competing models based on time series, and (ii) activating dominant models from among the competing ones by taking into account the correcting signals. These signals are formed (in monitoring mode) as a result of the analysis of qualitative information (judgments and opinions of the decision makers and experts) using a fuzzy cognitive map of the situation - a model for representing causal influences between system-forming factors in such processes.