Dynamic integration of time- and state-domain methods for volatility estimation

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.