A note on estimation of quarticity based on spot volatility
基于瞬时波动率的四次变差估计札记
We study an estimator of twice the integrated quarticity of a continuous Itô semimartingale, constructed from squared returns and local estimates of spot volatility. For a shrinking estimation window, we establish a functional stable central limit theorem for a bias-corrected version of the estimator. The limiting conditional variance is $56\int_0^t c_s^4\dd s$, where $c$ denotes spot variance. The proof identifies a common martingale approximation for the three components…