ar X iv : m at h / 07 01 10 7 v 1 [ m at h . ST ] 3 J an 2 00 7 Aggregation of Nonparametric Estimators for Volatility Matrix ∗

An aggregated method of nonparametric estimators based on time-domain and statedomain estimators is proposed and studied. To attenuate the curse of dimensionality, we propose a factor modeling strategy. We first investigate the asymptotic behavior of nonparametric estimators of the volatility matrix in the time domain and in the state domain. Asymptotic normality is separately established for nonparametric estimators in the time domain and state domain. These two estimators are asymptotically independent. Hence, they can be combined, through a dynamic weighting scheme, to improve the efficiency of volatility matrix estimation. The optimal dynamic weights are derived, and it is shown that the aggregated estimator uniformly dominates volatility matrix estimators using time-domain or state-domain smoothing alone. A simulation study, based on an essentially affine model for the term structure, is conducted, and it demonstrates convincingly that the newly proposed procedure outperforms both timeand state-domain estimators. Empirical studies further endorse the advantages of our aggregated method.