TY - JOUR
T1 - Dynamic integration of time- And state-domain methods for volatility estimation
AU - Fan, Jianqing
AU - Fan, Yingying
AU - Jiang, Jiancheng
N1 - Funding Information:
Jianqing Fan is Frederick L. Moore 18 Professor of Finance (E-mail: jqfan@ princeton.edu), Yingying Fan is Ph.D. Candidate (E-mail: yingying@princeton. edu), and Jiancheng Jiang is Associate Research Scholar (E-mail: jjiang@ princeton.edu), Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544. Jiancheng Jiang is also Assistant Professor, Department of Mathematics and Statistics, University of North Carolina, Charlotte, NC 28223 (E-mail: [email protected]). This work was supported in part by the Research Grants Council of the Hong Kong SAR (project CUHK 400903/03P), the National Science Foundation (grants DMS-03-55179 and DMS-05-32370), and Chinese National Science Foundation (grant 10471006). The authors thank reviewers for constructive comments and Dr. Juan Gu for assistance.
PY - 2007/6
Y1 - 2007/6
N2 - Time- and state-domain methods are two common approaches to nonparametric prediction. Whereas the former uses data predominantly from recent history, the latter relies mainly on historical information. 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 state domains. The estimators from these two domains are optimally combined based on 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 the efficiency of the estimators, we demonstrate that the proposed integrated estimator uniformly dominates the other two estimators. The proposed dynamic integration approach is also applicable to other estimation problems in time series. Extensive simulations are conducted to demonstrate that the newly proposed procedure outperforms some popular ones, such as the RiskMetrics and historical simulation approaches, among others. In addition, empirical studies convincingly endorse our integration method.
AB - Time- and state-domain methods are two common approaches to nonparametric prediction. Whereas the former uses data predominantly from recent history, the latter relies mainly on historical information. 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 state domains. The estimators from these two domains are optimally combined based on 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 the efficiency of the estimators, we demonstrate that the proposed integrated estimator uniformly dominates the other two estimators. The proposed dynamic integration approach is also applicable to other estimation problems in time series. Extensive simulations are conducted to demonstrate that the newly proposed procedure outperforms some popular ones, such as the RiskMetrics and historical simulation approaches, among others. In addition, empirical studies convincingly endorse our integration method.
KW - Bayes
KW - Dynamical integration
KW - Smoothing
KW - State domain
KW - Time domain
KW - Volatility
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U2 - 10.1198/016214507000000176
DO - 10.1198/016214507000000176
M3 - Article
AN - SCOPUS:34250695929
SN - 0162-1459
VL - 102
SP - 618
EP - 631
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 478
ER -