A Nonparametric Test of Serial Independence for Time Series and Residuals

Ghoudi, Kilani; Kulperger, Reg; Rémillard, Bruno

doi:10.1006/jmva.2000.1967

Cited by 62 publications

(55 citation statements)

References 19 publications

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“…All four problems are well known in mathematical statistics and there is an extensive literature dealing with their nonparametric testing, see for review, for example, [12,14].…”

Section: Description Of Considered Problemsmentioning

confidence: 99%

Universal codes as a basis for time series testing

Ryabko

Astola

2006

Statistical Methodology

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We suggest a new approach to hypothesis testing for ergodic and stationary processes. In contrast to standard methods, the suggested approach gives a possibility to make tests, based on any lossless data compression method even if the distribution law of the codeword lengths is not known. We apply this approach to the following four problems: goodness-of-fit testing (or identity testing), testing for independence, testing of serial independence and homogeneity testing and suggest nonparametric statistical tests for these problems. It is important to note that practically used so-called archivers can be used for suggested testing.

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“…All four problems are well known in mathematical statistics and there is an extensive literature dealing with their nonparametric testing, see for review, for example, [12,14].…”

Section: Description Of Considered Problemsmentioning

confidence: 99%

Universal codes as a basis for time series testing

Ryabko

Astola

2006

Statistical Methodology

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“…Common procedures are based on autocorrelations (Moran 1948;Ljung and Box 1978;Dufour and Roy 1985;Hong 2000), entropy measures (Robinson 1991;Hong and White 2005), rank-based dependence measures (Hallin, Ingenbleek, andPuri 1985, 1987;Hallin and Puri 1992;Ferguson, Genest, and Hallin 2000), empirical distribution functions (Skaug and Tjøstheim 1993;Delgado 1996;Ghoudi, Kulperger, and Rémillard 2001), empirical characteristic functions (Hong 1999;Bilodeau and Lafaye de Micheaux 2005), and empirical copulas (Genest and Rémillard 2004).…”

Section: Introductionmentioning

confidence: 99%

Rank-Based Extensions of the Brock, Dechert, and Scheinkman Test

Genest

Ghoudi

Rémillard

2007

Journal of the American Statistical Association

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This article proposes new tests of randomness for innovations in a large class of time series models. These tests are based on functionals of empirical processes constructed from either the model residuals or their associated ranks. The asymptotic behavior of these processes is determined under the null hypothesis of randomness. The limiting distributions are seen to be independent of estimation errors under appropriate regularity conditions. Several test statistics are derived from these processes; the classical Brock, Dechert, and Scheinkman statistic and a rank-based analog are included as special cases. Because the limiting distributions of the rank-based test statistics are marginfree, their finite-sample p values can be easily calculated by simulation. Monte Carlo experiments show that these statistics are quite powerful against several classes of alternatives.

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“…Inspired by the work, among others, of Deheuvels (1981), Ghoudi et al (2001) investigated tests based on a Möbius decomposition of the Blum et al (1961) statistic considered by Delgado (1996). In order to obtain margin-free test statistics, a version of this decomposition based on the empirical copula was studied by Genest and Rémillard (2004).…”

Section: Introductionmentioning

confidence: 99%

“…Our departure point is the work of Ghoudi et al (2001) and Genest and Rémillard (2004). Inspired by the work, among others, of Deheuvels (1981), Ghoudi et al (2001) investigated tests based on a Möbius decomposition of the Blum et al (1961) statistic considered by Delgado (1996).…”

Section: Introductionmentioning

confidence: 99%