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CATEGORIES:Statistics
SUMMARY:Nonlinear shrinkage of Eigenvalues in Integrated C
ovolatility Matrix for Portfolio Allocation in Hig
h Frequency Data - Clifford Lam (LSE)
DTSTART;TZID=Europe/London:20160122T160000
DTEND;TZID=Europe/London:20160122T170000
UID:TALK63639AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/63639
DESCRIPTION:In portfolio allocation of a large pool of assets\
, the use of high frequency data allows the corres
ponding high-dimensional integrated covolatility m
atrix estimator to be more adaptive to local volat
ility features\, while sample size is significantl
y increased. To ameliorate the bias contributed fr
om the extreme eigenvalues of the sample covolatil
ity matrix when the dimension p of the matrix is l
arge relative to the average daily sample size n\,
and the contamination by microstructure noise\, v
arious researchers attempted regularization with s
pecific assumptions on the true matrix itself\, li
ke sparsity or factor structure\, which can be res
trictive at times. With non-synchronous trading an
d contamination of microstructure noise\, we propo
se a nonparametrically eigenvalue-regularized inte
grated covolatility matrix estimator which does n
ot assume specific structures for the underlying m
atrix. We show that our estimator is almost surely
positive definite\, with extreme eigenvalues shru
nk nonlinearly under the high dimensional framewor
k where the ratio p/n goes to c>0. We also prove
that almost surely\, the optimal weight vector con
structed has maximum weight magnitude of order p^{
-1/2}\, which is supported by our data analysis. T
he practical performance of our estimator is illus
trated by comparing to the usual two-scale realize
d covariance matrix as well as some other nonparam
etric alternatives using different simulation sett
ings and a real data set.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge.
CONTACT:Quentin Berthet
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