Skip to Main content Skip to Navigation
Journal articles

Testing for residual correlation of any order in the autoregressive process

Abstract : We are interested in the implications of a linearly autocorrelated driven noise on the asymptotic behavior of the usual least squares estimator in a stable autoregressive process. We show that the least squares estimator is not consistent and we suggest a sharp analysis of its almost sure limiting value as well as its asymptotic normality. We also establish the almost sure convergence and the asymptotic normality of the estimated serial correlation parameter of the driven noise. Then, we derive a statistical procedure enabling to test for correlation of any order in the residuals of an autoregressive modelling, giving clearly better results than the commonly used portmanteau tests of Ljung-Box and Box-Pierce, and appearing to outperform the Breusch-Godfrey procedure on small-sized samples.
Document type :
Journal articles
Complete list of metadata
Contributor : Frédéric Proïa Connect in order to contact the contributor
Submitted on : Tuesday, March 14, 2017 - 6:08:32 AM
Last modification on : Wednesday, November 3, 2021 - 6:05:20 AM

Links full text




Frédéric Proïa. Testing for residual correlation of any order in the autoregressive process. Communications in Statistics - Theory and Methods, Taylor & Francis, 2018, 47 (3), pp.628-654. ⟨10.1080/03610926.2017.1310240⟩. ⟨hal-01488892⟩



Record views