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Detecting atypical observations in financial data: the forward search for elliptical copulas. (English) Zbl 1284.62194

Summary: In the last few years, copulas have been widely applied in many field of studies. Concentrating our attention on financial applications, we pursue the goal to detect multivariate atypical observations by extending to elliptical copulas the forward search originally introduced in linear and nonlinear regression by A. Atkinson and M. Riani [Robust diagnostic regression analysis. New York: Springer (2000; Zbl 0964.62063)]. Considering that, in the forward search, observations are ranked according to their closeness to the fitted data, we need to define a measure through which to initialize, progress and monitor the search. We achieve this goal building up the forward search for elliptical copulas relying on the squared Mahalanobis distance. Stressing the need to find theoretical boundaries for the inference on outliers, we introduce a procedure for computing envelopes as in [M. Riani and A. C. Atkinson, “Fast calibrations of the forward search for testing multiple outliers in regression”, Adv. Data Anal. Classif., ADAC 1, No. 2, 123–141 (2007; doi:10.1007/s11634-007-0007-y)]. Once defined our framework, we apply the forward search to a simulated environment where contaminations are exogenously introduced then, we carry out the analysis on \(n\) equity log-return real time series.

MSC:

62F35 Robustness and adaptive procedures (parametric inference)
62-07 Data analysis (statistics) (MSC2010)

Citations:

Zbl 0964.62063
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References:

[1] Atkinson AC, Riani M (2000) Robust diagnostic regression analysis. Springer-Verlag, New York · Zbl 0964.62063
[2] Durrleman V, Nikeghbali A, Roncalli T (2000) Which copula is the right one? Groupe de Recherche Operationnelle, Credit Lyonnais, France
[3] Embrechts P, Lindskog F, McNeil A (2001) Modelling dependence with copulas and applications to risk management. Department of Mathematics, ETH Zurich
[4] Lindskog F (2000) Modelling dependence with copulas. RiskLab Report, ETH Zurich
[5] Lindskog F, McNeil A, Schmock U (2001) A note on Kendall’s tau for elliptical distributions. ETH preprint
[6] Malevergne Y, Sornette D (2003) Testing the Gaussian copula hypothesis for financial assets dependence. Quant Finance 3: 231–250
[7] Mashal R, Zeevi A (2002) Beyond correlation: extreme co-movements between financial assets. Working paper, Columbia Graduate School of Business
[8] Nelsen RB (1999) An introduction to copulas. Springer, New York · Zbl 0909.62052
[9] Riani M (2004) Extensions of the forward search to time series. Stud Nonlinear Dyn Econom 8(2): 1–23 · Zbl 1081.91592
[10] Riani M, Atkinson AC (2007) Fast calibrations of the forward search for testing multiple outliers in regression. Adv Data Anal Classif 1: 123–141 · Zbl 1301.62069
[11] Riani M, Atkinson AC, Cerioli A (2009) Finding an unknown number of multivariate outliers. J R Stat Soc Ser B 71: 201–221 · Zbl 1248.62091
[12] Rousseeuw PJ (1984) Least median of squares regression. J Am Stat Assoc 79: 871–880 · Zbl 0547.62046
[13] Rousseeuw PJ, Molenberghs G (1993) Transformation of non positive semidefinite correlation matrices. Commun Stat Theory Methods 22: 965–984 · Zbl 0800.62345
[14] Sklar A (1959) Fonctions de repartition a n dimensions et leur marges. Publications de l’Institut de Statistique de l’Universite’ de Paris 8: 229–231 · Zbl 0100.14202
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