The book examines fundamental theoretical and methodological issues in studying the development of statistical structure within the measurement-forecasting-effects triad. It demonstrates the necessity of using a unified methodological approach to the study of structural changes and irregularities, based on Euclidean distance and the possibility of decomposing the overall structural change into factor influences. A method for forecasting the development of an n-dimensional statistical structure is proposed. A solution to the problem of determining the effect of structural changes is sought outside the “rules” and “principles” of index factor analysis.