Mathematisches Kolloquium

Freitag, 12.06.2015 14:15 Uhr

Titel: Estimation and statistical inference for covariance matrices of high-dimensional time series

Rainer von Sachs (Université Catholique de Louvain)

In high-dimensional time series analysis, when (effective) sample sizes and dimensionality are of the same order of magnitude, estimating the dependence structure across a panel of time series, via the covariance matrix can pose severe problems: generally the nonparametric matrix estimators are close to being ill-conditioned, and hence numerically very unstable, due to the well-known phenomenon of potentially high linear correlation among the columns of the matrix. One possibility to regularize these estimators is shrinkage towards a well-conditioned target: this approach reduces the dispersion among the eigenvalues of the matrices, leads to better conditioning numbers and even better mean-squared error properties of the resulting estimators.
In this talk we first give an introduction into this type of shrinkage methods including the presentation of an appropriate asymptotic framework where both sample-size and dimensionality of the considered matrices tend to infinity. We also report on recent work on deriving the limiting distribution of the considered covariance estimators via a new result on strong approximations by Brownian motions which allows in particular, but not exclusively, to come up with statistical inference on bilinear forms of the considered covariance estimators.
We conclude with presenting some applications in nonparametric time series analysis. In particular we consider the case of estimating sudden changes in the structure of high-dimensional financial time series: based on a hidden Markov model, we treat regime switching of a vector of asset returns from some large portfolio, switching e.g. from a low volatile market to a state with higher risk.

This talk reviews, among others, collaborative work with M. Fiecas, J. Franke and Joseph Tadjuidje Kamgaing as well as with A. Steland.

Wir laden herzlich alle Interessierten zu diesem Vortrag ein.

Ort:  Raum 008/SeMath, Pontdriesch 14-16, 52062 Aachen