, Volume 27, Issue 1, pp 3–26 | Cite as

Serial independence tests for innovations of conditional mean and variance models

  • Kilani Ghoudi
  • Bruno Rémillard
Original Paper


In this paper, one studies the asymptotic behavior of empirical processes based on consecutive residuals of univariate conditional mean and variance models. These processes are then used to develop tests of serial independence of the innovations. Even if the limiting distributions of the empirical processes depend on unknown parameters, it is shown that a Monte Carlo method based on the so-called multipliers can be applied to estimate the P values of the proposed test statistics. A simulation study is carried out to demonstrate the effectiveness of the proposed tests and the behavior of the statistics is also studied under contiguous alternatives.


Independence tests Serial independence Randomness GARCH models Residuals Squared residuals Empirical processes Empirical copula Multipliers Bootstrap 

Mathematics Subject Classification

Primary 60F05 Secondary 62G09 62G30 

Supplementary material

11749_2016_521_MOESM1_ESM.pdf (290 kb)
Supplementary material 1 (pdf 289 KB)


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2016

Authors and Affiliations

  1. 1.Department of StatisticsUnited Arab Emirates UniversityAl AinUnited Arab Emirates
  2. 2.CRM, GERAD, Department of Decision SciencesHEC MontréalMontrealCanada

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