A goodness-of-fit test for VARMA(p, q) models Articles uri icon

publication date

  • December 2018

start page

  • 126

end page

  • 140


  • 197

International Standard Serial Number (ISSN)

  • 0378-3758

Electronic International Standard Serial Number (EISSN)

  • 1873-1171


  • A goodness-of-fit approach for multivariate VARMA(p, q) models is presented. The idea is to consider a stochastic process based on a modified residual correlation matrix sequence, that is shown to converge to the Brownian bridge. Standard criteria based on this new random function, as for instance the Kolmogorov-Smirnov and Cramer-von Mises statistics, will have then a pivotal null asymptotic distribution. The properties of these two methods are investigated by simulation. As compared with the traditional methods in this area, their size does not depend critically on the choice of any lag parameter value, and they have better power properties. (C) 2018 Elsevier B.V. All rights reserved.


  • adjusted residual traces; brownian bridge; residual correlation matrices