High Dimensional Covariance Matrix Estimation Using a Factor Model

Details High Dimensional Covariance Matrix Estimation Using a Factor Model High Dimensional Covariance Matrix Estimation Using a Factor Model

2007-01-04

arxiv.org/abs/math/0701124v1

Mathematics

Statistics Theory

43 pages, 11 PostScript figures

Scientific paper

High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality $p$ tends to $\infty$ as the sample size $n$ increases. Motivated by the Arbitrage Pricing Theory in finance, a multi-factor model is employed to reduce dimensionality and to estimate the covariance matrix. The factors are observable and the number of factors $K$ is allowed to grow with $p$. We investigate impact of $p$ and $K$ on the performance of the model-based covariance matrix estimator. Under mild assumptions, we have established convergence rates and asymptotic normality of the model-based estimator. Its performance is compared with that of the sample covariance matrix. We identify situations under which the factor approach increases performance substantially or marginally. The impacts of covariance matrix estimation on portfolio allocation and risk management are studied. The asymptotic results are supported by a thorough simulation study.

Affiliated with

Also associated with

No associations

Rating

High Dimensional Covariance Matrix Estimation Using a Factor Model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with High Dimensional Covariance Matrix Estimation Using a Factor Model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and High Dimensional Covariance Matrix Estimation Using a Factor Model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-310306