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Journal of Financial Econometrics Advance Access originally published online on April 25, 2007
Journal of Financial Econometrics 2007 5(3):321-357; doi:10.1093/jjfinec/nbm008
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Copyright © The Author 2007. Published by Oxford University Press.

Aggregation of Nonparametric Estimators for Volatility Matrix

Jianqing Fan
     Princeton University

Yingying Fan
     Princeton University

Jinchi Lv
     Princeton University

Address correspondence to Yingying Fan, Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544, USA, or e-mail: yingying{at}princeton.edu


  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

Financial support from the NSF under grant DMS-0532370 is gratefully acknowledged. We are grateful to Lars Hansen, Robert Kimmel, and conference participants of Financial Mathematics Workshop at SAMSI; the 2006 Xiamen Financial Engineering and Risk Management Workshop; the 69th IMS Annual Meeting for helpful comments.

Jinchi Lv's name has been corrected.

Received April 13, 2006; revised November 15, 2006; accepted March 16, 2007


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