Autocorrelation-based factor analysis and nonlinear shrinkage estimation of large integrated covariance matrix

Hu, Qilin (2016) Autocorrelation-based factor analysis and nonlinear shrinkage estimation of large integrated covariance matrix. PhD thesis, London School of Economics and Political Science.

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Abstract

The first part of my thesis deals with the factor modeling for high-dimensional time series based on a dimension-reduction viewpoint. we allow the dimension of time series N to be as large as, or even larger than the sample size of the time series. The estimation of the factor loading matrix and subsequently the factors are done via an eigenanalysis on a non-negative definite matrix constructed from autocorrelation matrix. The method is dubbed as AFA. We give explicit comparison of the convergence rates between AFA with PCA. We show that AFA possesses the advantage over PCA when dealing with small dimension time series for both one step and two step estimations, while at large dimension, the performance is still comparable. The second part of my thesis considers large integrated covariance matrix estimation. While the use of intra-day price data increases the sample size substantially for asset allocation, the usual realized covariance matrix still suffers from bias contributed from the extreme eigenvalues when the number of assets is large. We introduce a novel nonlinear shrinkage estimator for the integrated volatility matrix which shrinks the extreme eigenvalues of a realized covariance matrix back to acceptable level, and enjoys a certain asymptotic efficiency at the same time, all at a high dimensional setting where the number of assets can have the same order as the number of data points. Compared to a time-variation adjusted realized covariance estimator and the usual realized covariance matrix, our estimator demonstrates favorable performance in both simulations and a real data analysis in portfolio allocation. This include a novel maximum exposure bound and an actual risk bound when our estimator is used in constructing the minimum variance portfolio.

Item Type:	Thesis (PhD)
Additional Information:	© 2016 Qilin Hu
Library of Congress subject classification:	H Social Sciences > HA Statistics
Sets:	Departments > Statistics
Supervisor:	Lam, Clifford
URI:	http://etheses.lse.ac.uk/id/eprint/3551

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