Развитие метода RAS на основе гомотетической парадигмы структурного сходства матриц макроэкономических данных

Вопросы статистики. 2014. № 8. С. 46–67.

Motorin V.

The article presents a new method for updating a macroeconomic data matrix on the framework of an advanced RAS multiplicative pattern and GLS principle. The notions of angular and homothetic measures for matrix similarity are introduced. Unified analytical solution of constrained minimization problem for the homothetic measure as an objective function is derived in matrix notation. Special attention to the sensitivity of the solution to small changes in the target matrix margin totals is paid. A decomposing procedure for updating partitioned matrices with very large dimensions is described. In practice the proposed GLS-based method generates much more compact distributions of multiplicative model factors in comparison with RAS method.

Keywords: метод множителей Лагранжа, RAS method, метод RAS, матрицы макроэкономических данных, мультипликативная модель, гомотетия матриц, меры структурного сходства матриц, обобщенный метод наименьших квадратов, декомпозиционный алгоритм, Lagrange multipliers method, macroeconomic data matrices, RAS multiplicative pattern, matrix homothety, measures of matrix similarity, generalized least squares (GLS), decomposing procedure