Efficient estimation of integrated volatility in presence of infinite variation jumps
By Jean Jacod, V. Todorov. 2014
81 citations recorded by the source corpus.
We propose new nonparametric estimators of the integrated volatility of an It\^{o} semimartingale observed at discrete times on a fixed time interval with mesh of the observation grid shrinking to zero. The proposed estimators achieve the optimal rate and variance of estimating integrated volatility even in the presence of infinite variation jumps when the latter are stochastic integrals with respect to locally "stable" L\'{e}vy processes, that is, processes whose L\'{e}vy measure around zero behaves like that of a stable process. On a first step, we estimate locally volatility from the empirical characteristic function of the increments of the process over blocks of shrinking length and then we sum these estimates to form initial estimators of the integrated volatility. The estimators contain bias when jumps of infinite variation are present, and on a second step we estimate and remove this bias by using integrated volatility estimators formed from the empirical characteristic function of the high-frequency increments for different values of its argument. The second step debiased estimators achieve efficiency and we derive a feasible central limit theorem for them.
Subfields: Demography, Finance
View Paper: https://www.semanticscholar.org/paper/3c202a11d2959c39c1691234828eefe096b98c77
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Citations in the corpus
- Does Anything Beat 5-Minute RV? A Comparison of Realized Measures Across Multiple Asset Classes (2015, unknown): “Simulation results in Patton and Sheppard (2009a), and empirical results in Hansen and Lunde (2005), Patton and Sheppard (2009b) and Patton (2011a) The asset for which we find that RV5min is significantly beaten, the 10-year US Treasury note futures contract (TY), is among the most frequently traded”
- Testing for pure-jump processes for high-frequency data (2015, methodology): “By (6.22) and (6.29) in Jacod and Todorov (2014), we have |ζ ′k(j, l)− ζk(j, l)| (A.15) ≤Ku4n∆1/2n φn + |U2jvn+(2l−k−1)∆n(un)−Uj(un)|, which, together with Lemma A.2 and the property of Ut(un), shows that ∣ ∣ ∣ ∣ EF2jvn ξ1,j(un) ( (1/(kn − 1)) ∑kn−1 l=1 (ζ ′ 0(j, l)− ζ0(j, l)) Uj(un) )∣ ∣ ∣ ∣ ≤…”
- On the number of common factors with high‐frequency data (2017, result): “These choices of parameter values are similar to those in Jacod & Todorov (2014) and Kong et al. (2015).”