Dresden 2006 – scientific programme
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AKSOE: Physik sozio-ökonomischer Systeme
AKSOE 10: Poster Session (posters are expected to be displayed the full day 8:30-18:00)
AKSOE 10.18: Poster
Wednesday, March 29, 2006, 16:00–18:00, P2
Random matrix theory, elliptical distributions and correlations in incomplete financial data — •Uwe Jaekel1 and Gabriel Frahm1,2 — 1C&C Research Laboratories, NEC Europe Ltd, Sankt Augustin — 2Lehrstuhl für Statistik und Ökonometrie, Universität zu Köln
Recently (e.g. [1,2]) random matrix theory (RMT) has been applied to financial data with interesting implications for the identification of driving factors in financial markets. We discuss complications resulting from the observed non-normality and tail-dependence of financial data. Both facts together limit the applicability of random matrix theory for sample correlation matrices obtained for market data time series since classical theorems assume either normality or componentwise independence of the time series. We show that for the large class of generalized elliptical distributions – consistent with the so-called stylized facts of empirical finance – a covariance matrix estimator (which turns out to be Tyler’s M-estimator [3]) can be derived that allows the application of standard RMT. Another practical problem in the analysis of financial time series is that parts of the data can be missing due to errors, different trading times, index re-compositions, and for various other reasons. We show how RMT can be applied also to incomplete time series by an observed data maximum likelihood approach.
[1] Laloux, L. et al., RISK Magazine, 12, 69 (March 1999)
[2] Plerou, V. et al., PRL 83, 1471 (1999)
[3] Tyler, D.E., Annals of Statistics 15, 234 (1987)