A Nonlinear Least Squares Solution of a Minimax Estimation Problem for Stationary Time Series
|
digital
Article
|
||||||||||||||||||||||
Article |
Ebook format Pdf readable on these devices:
|
|
|
|
|
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 biographyMarica 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). |
Browse the archive
Online First Articles
Recent issues
STATISTICA & APPLICAZIONI - 2022 - 2
STATISTICA & APPLICAZIONI - 2022 - 1
STATISTICA & APPLICAZIONI - 2021 - 2
STATISTICA & APPLICAZIONI - 2022 - 1
STATISTICA & APPLICAZIONI - 2021 - 2
