Serial independence tests for innovations of conditional mean and variance models
Kilani Ghoudi and
Bruno Rémillard ()
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Kilani Ghoudi: United Arab Emirates University
Bruno Rémillard: HEC Montréal
TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2018, vol. 27, issue 1, No 2, 3-26
Abstract 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.
Keywords: Independence tests; Serial independence; Randomness; GARCH models; Residuals; Squared residuals; Empirical processes; Empirical copula; Multipliers; Bootstrap; Primary 60F05; Secondary 62G09; 62G30 (search for similar items in EconPapers)
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