A goodness of fit test for copulas based on Rosenblatt's transformation

Dobrić, Jadran; Schmid, Friedrich

doi:10.1016/j.csda.2006.08.012

Cited by 121 publications

(92 citation statements)

References 16 publications

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“…Lately, several contributions have been made to test this hypothesis, e.g. Genest and Rivest (1993), Shih (1998), Breymann et al (2003), Malevergne and Sornette (2003), Scaillet (2005), , Fermanian (2005), Panchenko (2005), Berg and Bakken (2005), Genest et al (2006a), Dobrić and Schmid (2007), Quessy et al (2007), , among others. However, general guidelines and recommendations are sparse.…”

Section: Introductionmentioning

confidence: 99%

Copula goodness-of-fit testing: an overview and power comparison

Berg¹

2009

The European Journal of Finance

230

178

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Abstract. Several copula goodness-of-fit approaches are examined, three of which are proposed in this paper. Results are presented from an extensive Monte Carlo study, where we examine the effect of dimension, sample size and strength of dependence on the nominal level and power of the different approaches. While no approach is always the best, some stand out and conclusions and recommendations are made. A novel study of p-value variation due to permuation order, for approaches based on Rosenblatt's transformation is also carried out. Results show significant variation due to permutation order for some of the approaches based on this transform. However, when approaching rejection regions, the additional variation is negligible.

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Section: Introductionmentioning

confidence: 99%

Copula goodness-of-fit testing: an overview and power comparison

Berg¹

2009

The European Journal of Finance

230

178

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“…For our proposed approach (T d−1 , N d−1 , AD) it is not clear whether the bootstrap procedure is valid from a theoretical point of view; see, e.g., [8] and [14]. However, empirical results, presented in Sect.…”

Section: The Parametric Bootstrapmentioning

confidence: 94%

“…, n}, so that the distribution of the latter is known and sufficiently simple to test under the null hypothesis. For Rosenblatt ' Remark 1 As, e.g., [8] describe, there are two problems with the approach described above. First, the pseudo-observations U i , i ∈ {1, .…”

Section: Goodness-of-fit Tests For Copulasmentioning

confidence: 99%

“…Although our proposed goodness-of-fit test can be applied in the case d = 100, it is not easy to use the bootstrap described above in such high dimensions. We therefore, for d = 100, investigate only the error probability of the first kind similar to the case A addressed in [8]. For this, we generate N = 1,000 100-dimensional samples of size n = 150 with parameter chosen such that Kendall's tau equals τ = 0.25 and compute for each generated data set the p-value of the test AD) as before, however, this time with the known copula parameter.…”

Section: An Approximate P-value For (Tmentioning

confidence: 99%

“…For reasons why Archimedean copulas are used in practice, see [9] or [19]. Goodness-of-fit techniques for copulas only more recently gained interest, see, e.g., [5,6,8,[11][12][13][14], and references therein. Although usually presented in a ddimensional setting, only some of the publications actually try to apply goodnessof-fit tests in more than two dimensions, including [5,26] up to dimension d = 5 and [4] up to dimension d = 8.…”

Section: Introductionmentioning

confidence: 99%

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Goodness-of-fit Tests for Archimedean Copulas in High Dimensions

Hering

Hofert

2015

Innovations in Quantitative Risk Management

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A goodness-of-fit transformation for Archimedean copulas is presented from which a test can be derived. In a large-scale simulation study it is shown that the test performs well according to the error probability of the first kind and the power under several alternatives, especially in high dimensions where this test is (still) easy to apply. The test is compared to commonly applied tests for Archimedean copulas. However, these are usually numerically demanding (according to precision and runtime), especially when the dimension is large. The transformation underlying the newly proposed test was originally used for sampling random variates from Archimedean copulas. Its correctness is proven under weaker assumptions. It may be interpreted as an analogon to Rosenblatt's transformation which is linked to the conditional distribution method for sampling random variates. Furthermore, the suggested goodness-of-fit test complements a commonly used goodness-of-fit test based on the Kendall distribution function in the sense that it utilizes all other components of the transformation except the Kendall distribution function. Finally, a graphical test based on the proposed transformation is presented.

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Bibliography

2015

Fundamental Aspects of Operational Risk and Insurance Analytics

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A goodness of fit test for copulas based on Rosenblatt's transformation

Cited by 121 publications

References 16 publications

Copula goodness-of-fit testing: an overview and power comparison

Copula goodness-of-fit testing: an overview and power comparison

Goodness-of-fit Tests for Archimedean Copulas in High Dimensions

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