  Estimation of high-dimensional covariance matrices in latent factor models is
an important topic in many fields and especially in finance. Since the number
of financial assets grows while the estimation window length remains of limited
size, the often used sample estimator yields noisy estimates which are not even
positive definite. Under the assumption of latent factor models, the covariance
matrix is decomposed into a common low-rank component and a full-rank
idiosyncratic component. In this paper we focus on the estimation of the
idiosyncratic component, under the assumption of a grouped structure of the
time series, which may arise due to specific factors such as industries, asset
classes or countries. We propose a generalized methodology for estimation of
the block-diagonal idiosyncratic component by clustering the residual series
and applying shrinkage to the obtained blocks in order to ensure positive
definiteness. We derive two different estimators based on different clustering
methods and test their performance using simulation and historical data. The
proposed methods are shown to provide reliable estimates and outperform other
state-of-the-art estimators based on thresholding methods.
