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

Bellini, Tiziano

Adv. Data Anal. Classif., ADAC 4, No. 4, 287-299 (2010).

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)

Keywords:

copulas; forward search; squared Mahalanobis distance

Citations:

Zbl 0964.62063

References:

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