Serial independence tests for innovations of conditional mean and variance models

Kilani Ghoudi; Bruno Rémillard

doi:10.1007/s11749-016-0521-3

Serial independence tests for innovations of conditional mean and variance models

Kilani Ghoudi, Bruno Rémillard

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

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.

Original language	English
Pages (from-to)	3-26
Number of pages	24
Journal	Test
Volume	27
Issue number	1
DOIs	https://doi.org/10.1007/s11749-016-0521-3
Publication status	Published - Mar 1 2018

Keywords

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

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/s11749-016-0521-3

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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.",

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AU - Ghoudi, Kilani

AU - Rémillard, Bruno

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N2 - 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.

AB - 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.

KW - Bootstrap

KW - Empirical copula

KW - Empirical processes

KW - GARCH models

KW - Independence tests

KW - Multipliers

KW - Randomness

KW - Residuals

KW - Serial independence

KW - Squared residuals

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Serial independence tests for innovations of conditional mean and variance models

Abstract

Keywords

ASJC Scopus subject areas

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