Detecting Atypical Observations in Financial Data : The Forward Search for Elliptical Copulas

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 Atkinson and Riani (Robust diagnostic regression analysis. Springer, New York, 2000). 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 Riani and Atkinson (Adv Data Anal Classif 1:123-141, 2007). 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