Volatility occupation times
Jia Li, Viktor Todorov, George Tauchen
The Annals of Statistics · 2013 · Volume 41 · Issue 4
Abstract
We propose nonparametric estimators of the occupation measure and the occupation density of the diffusion coefficient (stochastic volatility) of a discretely observed Itô semimartingale on a fixed interval when the mesh of the observation grid shrinks to zero asymptotically. In a first step we estimate the volatility locally over blocks of shrinking length, and then in a second step we use these estimates to construct a sample analogue of the volatility occupation time and a kernel-based estimator of its density. We prove the consistency of our estimators and further derive bounds for their rates of convergence. We use these results to estimate nonparametrically the quantiles associated with the volatility occupation measure.
Keywords
60H10, 60J75, 62F12, 62M05, high-frequency data, local approximation, nonparametric estimation, occupation time, quantiles, spot variance, stochastic volatility
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