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 innova-
tions. 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.

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• Serial independence tests for innovations of conditional mean and variance models