A Nonlinear Least Squares Solution of a Minimax Estimation Problem for Stationary Time Series - Marica Manisera, Aride Mazzali - Vita e Pensiero - Articolo Statistica & Applicazioni

A Nonlinear Least Squares Solution of a Minimax Estimation Problem for Stationary Time Series

digital A Nonlinear Least Squares Solution of a Minimax Estimation Problem for Stationary Time Series
Article
journal STATISTICA & APPLICAZIONI
issue STATISTICA & APPLICAZIONI - 2006 - 1
title A Nonlinear Least Squares Solution of a Minimax Estimation Problem for Stationary Time Series
Authors
Publisher Vita e Pensiero
format Article | Pdf
language English
online since 06-2016
issn 1824-6672 (print) | 2283-6659 (digital)
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The parameter estimation problem for the ARMA models is considered under a minimax approach: when the objective is to minimize the largest deviations in time series, it is useful to define a generalized version of a minimax estimator, minimizing the sum of the r-th powers of the k < n largest absolute deviations. The solution to that problem can be obtained by a searching procedure based on a grid of values on the admissible parametric space. The aim of this paper is propose a new procedure (called FINLS) to solve that minimax problem when a quadratic loss function is considered. FINLS approximates the searching procedure by a modified NLS method, with a filter matrix W selecting the largest absolute deviations to be included in the computation. Some applications account for the validity of the proposed estimation process. The results of a simulative study empirically show that the asymptotic properties of the NLS estimator could be extended to the proposed estimator. We also propose an asymptotic estimator for the covariance matrix of the FINLS estimated parameters.

Authors biography

Marica Mazzali, Department of Quantitative Methods – University of Brescia – C.da S. Chiara, 50, 25122 Brescia (e-mail: mazzali@eco.unibs.it)
Aride Manisera, Department of Quantitative Methods – University of Brescia – C.da S. Chiara, 50, 25122 Brescia (e-mail: manisera@eco.unibs.it).



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