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SUMMARY:Nonlinear shrinkage of Eigenvalues in Integrated Covolatility Matr
 ix for Portfolio Allocation in High Frequency Data - Clifford Lam (LSE)
DTSTART:20160122T160000Z
DTEND:20160122T170000Z
UID:TALK63639@talks.cam.ac.uk
CONTACT:Quentin Berthet
DESCRIPTION:In portfolio allocation of a large pool of assets\, the use of
  high frequency data allows the corresponding high-dimensional integrated 
 covolatility matrix estimator to be more adaptive to local volatility feat
 ures\, while sample size is significantly increased. To ameliorate the bia
 s contributed from the extreme eigenvalues of the sample covolatility matr
 ix when the dimension p of the matrix is large relative to the average dai
 ly sample size n\, and the contamination by microstructure noise\, various
  researchers attempted regularization with specific assumptions on the tru
 e matrix itself\, like sparsity or factor structure\, which can be restric
 tive at times. With non-synchronous trading and contamination of microstru
 cture noise\, we propose a nonparametrically eigenvalue-regularized integr
 ated covolatility matrix estimator  which does not assume specific structu
 res for the underlying matrix. We show that our estimator is almost surely
  positive definite\, with extreme eigenvalues shrunk nonlinearly under the
  high dimensional framework where the ratio  p/n goes to c>0. We also prov
 e that almost surely\, the optimal weight vector constructed has maximum w
 eight magnitude of order p^{-1/2}\, which is supported by our data analysi
 s. The practical performance of our estimator is illustrated by comparing 
 to the usual two-scale realized covariance matrix as well as some other no
 nparametric alternatives using different simulation settings and a real da
 ta set.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge.
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