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  \textbf{\Large{\textsc{STANFORD UNIVERSITY}}}\\[5pt]
  \textbf{\Large{\textsc{DEPARTMENT OF STATISTICS}}}\\[5pt]
  \Large{\textsc{DEPARTMENTAL SEMINAR}}
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  4:15 p.m., Tuesday, January 29, 2008\\
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  Sequoia Hall, Room 200\\
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  \textsl{Yingying Fan} \\
  Statistics Department\\
  Harvard University
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  \subsection*{Integration of Time- and State-Domain Methods for Volatility Matrix Estimation}
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\noindent

Time- and state-domain methods are two common approaches for nonparametric volatility
estimation. While the former predominantly uses data from recent history, the latter
mainly relies on historical information. The question of combining these two pieces of
valuable information is an interesting challenge in statistics. We surmount this problem
by dynamically integrating information from both the time and the state domains.
The estimators from these two domains are optimally combined via a data driven
weighting strategy, which provides a more efficient estimator of volatility. Asymptotic
normality is separately established for the time-domain, the state-domain, and the integrated
estimators. By comparing their efficiencies, it is demonstrated that the newly
proposed integrated estimator uniformly dominates the other two estimators. Extensive
simulations and empirical studies further demonstrate convincingly that our integration
procedure outperforms some popular ones such as the RiskMetrics, etc.
Multivariate volatility estimation is far more important in econometrics. To attenuate
the curse of dimensionality, a factor modeling strategy is proposed. To attack the
mathematical complexity, the probabilistic tool, local time, is invoked to establish the
asymptotic normality in the state domain. Similar asymptotic results to those in scalar
volatility estimation are established. A simulation study, based on an essentially affine
model for the term structure, is conducted, and our new procedure outperforms both timeand
state-domain estimators. Empirical studies also favor our integrated estimator.


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