Aggregation of Nonparametric Estimators for Volatility Matrix

Posted: 16 Jun 2008

See all articles by Jianqing Fan

Jianqing Fan

Princeton University - Bendheim Center for Finance

Yingying Fan

Princeton University

Jinchi Lv

Princeton University

Date Written: Summer 2007

Abstract

An aggregated method of nonparametric estimators based on time-domain and state-domain 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 time- and state-domain estimators. Empirical studies further endorse the advantages of our aggregated method.

Keywords: aggregation, affine model, diffusion, factor, local time, nonparametric function estimation, volatility matrix

Suggested Citation

Fan, Jianqing and Fan, Yingying and Lv, Jinchi, Aggregation of Nonparametric Estimators for Volatility Matrix (Summer 2007). Journal of Financial Econometrics, Vol. 5, Issue 3, pp. 321-357, 2007. Available at SSRN: https://ssrn.com/abstract=1145520 or http://dx.doi.org/10.1093/jjfinec/nbm008

Jianqing Fan (Contact Author)

Princeton University - Bendheim Center for Finance ( email )

26 Prospect Avenue
Princeton, NJ 08540
United States
609-258-7924 (Phone)
609-258-8551 (Fax)

HOME PAGE: http://orfe.princeton.edu/~jqfan/

Yingying Fan

Princeton University ( email )

22 Chambers Street
Princeton, NJ 08544-0708
United States

Jinchi Lv

Princeton University

22 Chambers Street
Princeton, NJ 08544-0708
United States

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