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Editor: Universidad Carlos III de Madrid. Departamento de Estadística

Issued date: 2013-12

Sponsor: Research partially supported by Grant ECO2011-25706 Spain

Serie-No.: UC3M Working papers. Statistics and Econometrics13-21

Keywords: Brownian bridge , Error sample correlation matrix , Goodness-of-fit process , Model selection , VARMAp,q models , Weak convergence

Rights: Atribución-NoComercial-SinDerivadas 3.0 España

Abstract:As an extension of the univariate technique in Ubierna and Velilla 2007, we present a goodness-of-fit process for VARMA p,q models in which the residuals of the fit are considered. We also formulatean explicit form of the asymptotic covariance function, asAs an extension of the univariate technique in Ubierna and Velilla 2007, we present a goodness-of-fit process for VARMA p,q models in which the residuals of the fit are considered. We also formulatean explicit form of the asymptotic covariance function, as well as a suitable representation of the limitprocess. More importantly, we propose a new goodness-of-fit process based on a transformed correlationmatrix sequence. The new goodness-of-fit process is proved to converge weakly to the Brownian bridge.Several simulations, comparisons, and examples are presented. These results illustrate the scope of bothour theoretical findings and contributions. Our method is shown to be sensitive to detect lack of fit.Thus, it can be considered as a useful tool tool for identifying a proper time series model.+-





Autor: Velilla, Santiago; Nguyen, Huong

Fuente: http://e-archivo.uc3m.es


Introducción



Universidad Carlos III de Madrid Repositorio institucional e-Archivo http:--e-archivo.uc3m.es Departamento de Estadística DES - Working Papers.
Statistics and Econometrics.
WS 2013-12 A new goodness-of-fit process for varma (p,q) models: construction and empirical properties Velilla, Santiago http:--hdl.handle.net-10016-18886 Descargado de e-Archivo, repositorio institucional de la Universidad Carlos III de Madrid Working Paper 13-23 Departamento de Estadı́stica Statistics and Econometrics Series 21 Universidad Carlos III de Madrid December 2013 Calle Madrid, 126 28903 Getafe (Spain) Fax (34) 91 624-98-49 A NEW GOODNESS-OF-FIT PROCESS FOR VARMA(p,q) MODELS: CONSTRUCTION AND EMPIRICAL PROPERTIES Santiago Velillaa and Huong Nguyena Abstract As an extension of the univariate technique in Ubierna and Velilla (2007), we present a goodness-offit process for VARMA(p,q) models in which the residuals of the fit are considered.
We also formulate an explicit form of the asymptotic covariance function, as well as a suitable representation of the limit process.
More importantly, we propose a new goodness-of-fit process based on a transformed correlation matrix sequence.
The new goodness-of-fit process is proved to converge weakly to the Brownian bridge. Several simulations, comparisons, and examples are presented.
These results illustrate the scope of both our theoretical findings and contributions.
Our method is shown to be sensitive to detect lack of fit. Thus, it can be considered as a useful tool tool for identifying a proper time series model. Keywords: Brownian bridge, error sample correlation matrix, goodness-of-fit process, model selection, VARMA(p,q) models, weak convergence. a Universidad Carlos III de Madrid, Department of Statistics, Facultad de Ciencias Sociales y Jurı́dicas, Campus de Getafe, Madrid, Spain.
E-mail addresses: santiago.velilla@uc3m.es (Santi- ago Velilla) and huong.nguyen@uc3m.es.
(Huong Nguyen). Research partially supported b...





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