Limit Theorems for Power Variations of Pure-Jump Processes with Application to Activity Estimation

By V. Todorov, George Tauchen. 2011

47 citations recorded by the source corpus.

This paper derives the asymptotic behavior of realized power variation of pure-jump It^o semimartingales as the sampling frequency within a fixed interval increases to infinity. We prove convergence in probability and an associated central limit theorem for the realized power variation as a function of its power. We apply the limit theorems to propose an e±cient adaptive estimator for the activity of discretely-sampled It^o semimartingale over a fixed interval.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/78c6aa11fc30e585013b790f37fe70e147b4605c

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Citations in the corpus

Efficient estimation of integrated volatility in presence of infinite variation jumps (2014, methodology): “Similar assumptions about the jumps have been also made when estimating the Blumenthal-Getoor index of jump activity in [1] and [16] among others.”
The Realized Laplace Transform of Volatility (2011, unknown): “And this is the case under fairly general conditions: √ ∆n-consistent estimates for β̂ (when β′ < β/2) can be constructed by using a ratio of power variations over two scales for appropriately chosen power, see Todorov and Tauchen (2009a) and equation (35) in the next section.”
Testing for pure-jump processes for high-frequency data (2015, background): “Interestingly, Todorov and Tauchen (2011) invented a test based on the point estimator of the JAI cleverly constructed as the smallest power for which the realized power variation (without thresholding) does not explode.”