From Two to One Index Isomorphism in Optimization Program for Quarterly Disaggregation of Annual Times Series
Raïmi Aboudou Essessinou *
National Institute of Statistics and Economy Analysis (INSAE) / Institute of Mathematics and Physics, University of Abomey-Calavi (UAC), Benin.
Guy Degla
Institute of Mathematics and Physics, University of Abomey-Calavi (UAC), Benin.
Babacar Mbaye Ndiaye
Laboratory of Mathematics of Decision and Numerical Analysis, University of Cheikh Anta Diop, Dakar, Senegal.
*Author to whom correspondence should be addressed.
Abstract
The quarterly disaggregation of an annual economic aggregate, by a mathematical method with a cyclical indicator, gives rise to a problem of minimization to make the quarterly economic aggregate smooth. This involves two indexes for the quarter and the year, which sometimes can make the resolution algorithm less efficient if the problem is large. In this paper we propose a method of indexing quarterly variables based on an isomorphic transformation of a two-index program into a one-index program, in order to minimize the cost of the algorithm of resolution. This method of continuous indexing of variables, applied to national accounts, shows that the algorithm with a single index is more efficient than the algorithm with two indexes when solving the optimization program of the quarterly disaggregation.
Keywords: Isomorphism, indexing variables, optimization, algorithms performance, quarterly disaggregation.