STABLE PARAMETER ESTIMATION OF AUTOREGRESSIVE MODELS BASED ON GENERALIZED METHOD OF LEAST MODULES
A.V. Panyukov
National Research South Ural State University, Lenin ave., 76, Chelyabinsk, 454080, Russia
Keywords: алгоритм, модель авторегрессии, линейное программирование, параметрическая идентификация, algorithm, autoregressive model, linear programming, parameter identification
Abstract
The prevailing method to determine the factors of the regression equation is the least squares method (LSM), i.e. the parametric method that requires a number of severe restrictions: independence and normality of the distribution of measurement errors, no correlation of exogenous variable. It is known that even minor violations of these assumptions is dramatically reducing the effectiveness of evaluations. It should be noted the fragility of the LSM estimation procedure under large errors that comes to insolvent evaluation. Finding the autoregression equation factors significantly complicated by the bad conditionality of equations system representing the necessary conditions minimum sum of squares of deviations. The least t modules method (LMM) is alternative to LSM to ensure sustainability of under violation of LSM restrictions. Two options for implementing LMM: weighted LMM (WLMM) and generalized LMM (GLMM) are discussed in the report. Interdependence of WLMM and GLMM established in the work allows GLMM estimation brings to the iterative procedure with WLMM evaluations. The latter are calculated by solving the corresponding linear programming tasks.
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