The forecasting of a signal that locally satisfies linear recurrence relations (LRRs) with slowly changing coefficients is considered. A method that estimates the local LRRs using the subspace-based method, predicts their coefficients and constructs a forecast using the LRR with the predicted coefficients is proposed. This method is implemented for time series that have the form of a noisy sum of sine waves with modulated frequencies. Linear and sinusoidal frequency modulations are considered. The application of the algorithm is demonstrated with numerical examples.