Statistics Colloquium on Nov 08, 2013

 

Friday, Nov 8, 2013, 04:00 pm

Shrinkage estimation of the dependence structure of high-dimensional time series

Prof. Dr. Rainer von Sachs (Université catholique de Louvain)

Visiting Professor Chair of Stochastics

Abstract:
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 (in the static case) or via the cross-spectral density matrix (in the dynamic case), 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: similarly to ridge regression, this
approach reduces the dispersion among the empirical 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 a gentle introduction into this type of shrinkage methods before we report 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. In this context, shrinkage of the state-by-state covariance matrices combined with an EM algorithm for estimation of
the transition probabilities, allows to clearly stabilize both the estimators and the filters for reconstruction of the hidden state variables.
This talk reviews, among others, collaborative work with H. Böhm, M. Fiecas, J. Franke and Joseph Tadjuidje
Kamgaing.

Time: 04:00 pm
Location: FO 6, Kármán - Auditorium, Eilfschornsteinstraße 15, 52062 Aachen