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Bootstrap for order identification in ARMA(P,Q) structures

Independent Journal of Management & Production

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Title Bootstrap for order identification in ARMA(P,Q) structures
 
Creator Chaves Neto, Anselmo
Biembengut Faria, Thais Mariane
 
Subject —
Order Identification; Bootstrap ; Correlograms
 
Description The identification of de order p,q, of ARMA models is a critical step in time-series modelling. In classic Box-Jenkins method of identification the autocorrelation function (ACF) and the partial autocorrelation (PACF) function should be estimated, but the classical expressions used to measure the variability of the respective estimators are obtained on the basis of asymptotic results. In addition, when having sets of few observations, the traditional confidence intervals to test the null hypotheses display low performance. The bootstrap method may be an alternative for identifying the order of ARMA models, since it allows to obtain an approximation of the distribution of the statistics involved in this step. Therefore it is possible to obtain more accurate confidence intervals than those obtained by the classical method of identification. In this paper we propose a bootstrap procedure to identify the order of ARMA models. The algorithm was tested on simulated time series from models of structures AR(1), AR(2), AR(3), MA(1), MA(2), MA(3), ARMA(1,1) and ARMA (2,2). This way we determined the sampling distributions of ACF and PACF, free from the Gaussian assumption. The examples show that the bootstrap has good performance in samples of all sizes and that it is superior to the asymptotic method for small samples.
 
Publisher Instituto Federal de Educação, Ciência e Tecnologia de São Paulo
 
Contributor —
 
Date 2015-03-01
 
Type info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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Format application/pdf
text/html
 
Identifier http://www.ijmp.jor.br/index.php/ijmp/article/view/244
10.14807/ijmp.v6i1.244
 
Source Independent Journal of Management & Production; Vol 6, No 1 (2015): Independent Journal of Management & Production; 169-181
2236-269X
 
Language eng
 
Relation http://www.ijmp.jor.br/index.php/ijmp/article/view/244/216
http://www.ijmp.jor.br/index.php/ijmp/article/view/244/438
http://www.ijmp.jor.br/index.php/ijmp/article/downloadSuppFile/244/79