Efficient Integrated Volatility Estimation in the Presence of Infinite Variation Jumps via Debiased Truncated Realized Variations
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than two decades. One of the most well-known and widely studied problems is the estimation of the quadratic variation of the continuous component of an Itô semimartingale with jumps. Several rate- and variance-efficient estimators have been proposed in the literature when the jump component is of bounded variation. However, to date, very few methods can deal with jumps of unbounded variation. By developing new high-order expansions of the truncated moments of a locally stable Lévy process, we construct a new rate- and variance-efficient volatility estimator for a class of Itô semimartingales whose jumps behave locally like those of a stable Lévy process with Blumenthal-Getoor index $Y\in (1,8/5)$ (hence, of unbounded variation). The proposed method is based on a two-step debiasing procedure for the truncated realized quadratic variation of the process. Our Monte Carlo experiments indicate that the method outperforms other efficient alternatives in the literature in the setting covered by our theoretical framework.
- Pub Date:
- September 2022
- Economics - Econometrics;
- Mathematics - Statistics Theory;
- Quantitative Finance - Statistical Finance
- An earlier version of this manuscript was circulated under the title "Efficient Volatility Estimation for L\'evy Processes with Jumps of Unbounded Variation". The results therein were constrained to L\'evy processes, whereas here we consider a much larger class of It\^o semimartingales. arXiv admin note: text overlap with arXiv:2202.00877