Tests of serial independence for continuous multivariate time series based on a Möbius decomposition of the independence empirical copula process

Abstract

Serial copula, Test of serial independence, Empirical process, Möbius decomposition, Cramér–von Mises statistic, Bootstrap, Permutation,

Non-parametric weighted tests for independence based on empirical copula process

“…It is worth noting that many copulas can significantly deviate from independence in multiple parts of the distribution at the same time, making the problem of weight selection more complex. The weight choice problem is also unavoidable since even the use of "unweighted" statistics as in Kojadinovic and Holmes (2009), Kojadinovic and Yan (2009) or Genest and Remillard (2004) represents a choice of w(u) = 1, for any u ∈ [0, 1] d , which is not conceptually different from any other w(u). A versatile approach to weight selection could involve a two-step procedure by which the function w(u) is estimated from the data.…”

“…The asymptotic efficiency of a Cramér-von Mises test based on (4) is investigated in Genest et al (2007). More recently, Kojadinovic and Holmes (2009) generalize the results of Deheuvels (1980) to the case of random vectors and derive asymptotic behaviour of corresponding Cramér-von Mises statistics for vectorial independence, with an extension of the test of Kojadinovic and Holmes (2009) to vector time series provided in Kojadinovic and Yan (2009). An important application where a test for independence is used to probe for goodness of fit of Archimedian copulas can be found in Quessy (2010).…”

Modeling Multivariate Distributions with Continuous Margins Using thecopulaRPackage

“…The previous approach has been extended by Kojadinovic and Yan (2010b) to the situation where one wants to test against serial dependence in continuous multivariate time series. The corresponding function is called multSerialIndepTest.…”

An Archimedean Copula Family with Hyperbolic Cotangent Generator

“…7. To avoid decision about univariate distributions, the observations were transformed to unit interval by their corresponding empirical distribution functions, see Fig.…”