Selection of NARX models estimated using weighted least squares method via GIC-based method and l1-norm regularization methods

Pan Qin, Ryuei Nishii, Zi Jiang Yang

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We investigate the model selection problem for nonlinear autoregressive with exogenous variables models estimated using the weighted least squares (WLS) method. Because WLS changes the statistical property of data under study and violates the assumptions imposed on the well-developed model evaluation and selection methods (e.g. Akaike's information criterion, Schwarz's Bayesian information criterion, and the error reduction ratio based methods), therefore, new approaches should be investigated. In this research, an information criterion based method and two l1-norm regularization methods are taken into consideration: (a) in the former method, for models estimated using WLS, we first derive an information criterion in terms of the generalized information criterion (GIC, proposed by Konishi and Kitagawa in Biometrica 83(4):875-890, 1996), which is a theoretical framework for the analysis and extension of information criteria via a statistical functional approach. Then we develop a robust selection procedure by combining the GIC-based forward stepwisemethod with Subsampling; (b) in the latter two methods, we employ the l1-norm regularization methods, including Lasso and adaptive Lasso, to select models estimated with WLS. Finally, a numerical example is given to test and compare the performance of the three methods.

Original languageEnglish
Pages (from-to)1831-1846
Number of pages16
JournalNonlinear Dynamics
Volume70
Issue number3
DOIs
Publication statusPublished - Nov 1 2012

Fingerprint

L1-norm
Weighted Least Squares
Regularization Method
Least Square Method
Information Criterion
Model Selection
Adaptive Lasso
Model
Model Evaluation
Error Reduction
Bayesian Information Criterion
Subsampling
Lasso
Akaike Information Criterion
Selection Procedures
Violate
Statistical property
Numerical Examples

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

Selection of NARX models estimated using weighted least squares method via GIC-based method and l1-norm regularization methods. / Qin, Pan; Nishii, Ryuei; Yang, Zi Jiang.

In: Nonlinear Dynamics, Vol. 70, No. 3, 01.11.2012, p. 1831-1846.

Research output: Contribution to journalArticle

@article{790b6d5bc88e4fffb82c41849ef84aad,
title = "Selection of NARX models estimated using weighted least squares method via GIC-based method and l1-norm regularization methods",
abstract = "We investigate the model selection problem for nonlinear autoregressive with exogenous variables models estimated using the weighted least squares (WLS) method. Because WLS changes the statistical property of data under study and violates the assumptions imposed on the well-developed model evaluation and selection methods (e.g. Akaike's information criterion, Schwarz's Bayesian information criterion, and the error reduction ratio based methods), therefore, new approaches should be investigated. In this research, an information criterion based method and two l1-norm regularization methods are taken into consideration: (a) in the former method, for models estimated using WLS, we first derive an information criterion in terms of the generalized information criterion (GIC, proposed by Konishi and Kitagawa in Biometrica 83(4):875-890, 1996), which is a theoretical framework for the analysis and extension of information criteria via a statistical functional approach. Then we develop a robust selection procedure by combining the GIC-based forward stepwisemethod with Subsampling; (b) in the latter two methods, we employ the l1-norm regularization methods, including Lasso and adaptive Lasso, to select models estimated with WLS. Finally, a numerical example is given to test and compare the performance of the three methods.",
author = "Pan Qin and Ryuei Nishii and Yang, {Zi Jiang}",
year = "2012",
month = "11",
day = "1",
doi = "10.1007/s11071-012-0576-y",
language = "English",
volume = "70",
pages = "1831--1846",
journal = "Nonlinear Dynamics",
issn = "0924-090X",
publisher = "Springer Netherlands",
number = "3",

}

TY - JOUR

T1 - Selection of NARX models estimated using weighted least squares method via GIC-based method and l1-norm regularization methods

AU - Qin, Pan

AU - Nishii, Ryuei

AU - Yang, Zi Jiang

PY - 2012/11/1

Y1 - 2012/11/1

N2 - We investigate the model selection problem for nonlinear autoregressive with exogenous variables models estimated using the weighted least squares (WLS) method. Because WLS changes the statistical property of data under study and violates the assumptions imposed on the well-developed model evaluation and selection methods (e.g. Akaike's information criterion, Schwarz's Bayesian information criterion, and the error reduction ratio based methods), therefore, new approaches should be investigated. In this research, an information criterion based method and two l1-norm regularization methods are taken into consideration: (a) in the former method, for models estimated using WLS, we first derive an information criterion in terms of the generalized information criterion (GIC, proposed by Konishi and Kitagawa in Biometrica 83(4):875-890, 1996), which is a theoretical framework for the analysis and extension of information criteria via a statistical functional approach. Then we develop a robust selection procedure by combining the GIC-based forward stepwisemethod with Subsampling; (b) in the latter two methods, we employ the l1-norm regularization methods, including Lasso and adaptive Lasso, to select models estimated with WLS. Finally, a numerical example is given to test and compare the performance of the three methods.

AB - We investigate the model selection problem for nonlinear autoregressive with exogenous variables models estimated using the weighted least squares (WLS) method. Because WLS changes the statistical property of data under study and violates the assumptions imposed on the well-developed model evaluation and selection methods (e.g. Akaike's information criterion, Schwarz's Bayesian information criterion, and the error reduction ratio based methods), therefore, new approaches should be investigated. In this research, an information criterion based method and two l1-norm regularization methods are taken into consideration: (a) in the former method, for models estimated using WLS, we first derive an information criterion in terms of the generalized information criterion (GIC, proposed by Konishi and Kitagawa in Biometrica 83(4):875-890, 1996), which is a theoretical framework for the analysis and extension of information criteria via a statistical functional approach. Then we develop a robust selection procedure by combining the GIC-based forward stepwisemethod with Subsampling; (b) in the latter two methods, we employ the l1-norm regularization methods, including Lasso and adaptive Lasso, to select models estimated with WLS. Finally, a numerical example is given to test and compare the performance of the three methods.

UR - http://www.scopus.com/inward/record.url?scp=84870882061&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870882061&partnerID=8YFLogxK

U2 - 10.1007/s11071-012-0576-y

DO - 10.1007/s11071-012-0576-y

M3 - Article

AN - SCOPUS:84870882061

VL - 70

SP - 1831

EP - 1846

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 3

ER -