Prediction models found a wide application in advanced control systems, intelligent systems of information decision support, play a significant role in any activity concerned with signal processing procedures, involving detecting failures of different technological processes. Methods based on the wavelet analysis are characterized by a unique ability of detailed frequency analysis in the time. The paper presents stability conditions of a prediction model, which are developed on the basis of the multi-scale wavelet transform, as well an example of the prediction model applied in the oil refining process.