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Efficient Estimation Of Integrated Volatility Functionals Under General Volatility Dynamics, Jia Li, Yunxiao Liu
Efficient Estimation Of Integrated Volatility Functionals Under General Volatility Dynamics, Jia Li, Yunxiao Liu
Research Collection School Of Economics
We provide an asymptotic theory for the estimation of a general class of smooth nonlinear integrated volatility functionals. Such functionals are broadly useful for measuring financial risk and estimating economic models using high-frequency transaction data. The theory is valid under general volatility dynamics, which accommodates both Itô semimartingales (e.g., jump-diffusions) and long-memory processes (e.g., fractional Brownian motions). We establish the semiparametric efficiency bound under a nonstandard nonergodic setting with infill asymptotics, and show that the proposed estimator attains this efficiency bound. These results on efficient estimation are further extended to a setting with irregularly sampled data.