AUTOMATED OPTIMAL FORECASTING OF UNIVARIATE MONITORING PROCESSES : Employing a novel optimal forecast methodology to define four classes of forecast approaches and testing them on real-life monitoring processes

Sammanfattning: This work aims to explore practical one-step-ahead forecasting of structurally changing data, an unstable behaviour, that real-life data connected to human activity often exhibit. This setting can be characterized as monitoring process. Various forecast models, methods and approaches can range from being simple and computationally "cheap" to very sophisticated and computationally "expensive". Moreover, different forecast methods handle different data-patterns and structural changes differently: for some particular data types or data intervals some particular forecast methods are better than the others, something that is usually not known beforehand. This raises a question: "Can one design a forecast procedure, that effectively and optimally switches between various forecast methods, adapting the forecast methods usage to the changes in the incoming data flow?" The thesis answers this question by introducing optimality concept, that allows optimal switching between simultaneously executed forecast methods, thus "tailoring" forecast methods to the changes in the data. It is also shown, how another forecast approach: combinational forecasting, where forecast methods are combined using weighted average, can be utilized by optimality principle and can therefore benefit from it. Thus, four classes of forecast results can be considered and compared: basic forecast methods, basic optimality, combinational forecasting, and combinational optimality. The thesis shows, that the usage of optimality gives results, where most of the time optimality is no worse or better than the best of forecast methods, that optimality is based on. Optimality reduces also scattering from multitude of various forecast suggestions to a single number or only a few numbers (in a controllable fashion). Optimality gives additionally lower bound for optimal forecasting: the hypothetically best achievable forecast result. The main conclusion is that optimality approach makes more or less obsolete other traditional ways of treating the monitoring processes: trying to find the single best forecast method for some structurally changing data. This search still can be sought, of course, but it is best done within optimality approach as its innate component. All this makes the proposed optimality approach for forecasting purposes a valid "representative" of a more broad ensemble approach (which likewise motivated development of now popular Ensemble Learning concept as a valid part of Machine Learning framework).