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Limit theorems for the empirical distribution function of scaled increments of itô semimartingales at high frequencies

Publication ,  Journal Article
Todorov, V; Tauchen, G
Published in: Annals of Applied Probability
January 1, 2014

We derive limit theorems for the empirical distribution function of "devolatilized" increments of an Itô semimartingale observed at high frequencies. These "devolatilized" increments are formed by suitably rescaling and truncating the raw increments to remove the effects of stochastic volatility and "large" jumps. We derive the limit of the empirical c.d.f. of the adjusted increments for any Itô semimartingale whose dominant component at high frequencies has activity index of 1<ß ≤ 2, where ß = 2 corresponds to diffusion. We further derive an associated CLT in the jump-diffusion case. We use the developed limit theory to construct a feasible and pivotal test for the class of Itô semimartingales with nonvanishing diffusion coefficient against Itô semimartingales with no diffusion component. © Institute of Mathematical Statistics, 2014.

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Published In

Annals of Applied Probability

DOI

ISSN

1050-5164

Publication Date

January 1, 2014

Volume

24

Issue

5

Start / End Page

1850 / 1888

Related Subject Headings

  • Statistics & Probability
  • 0104 Statistics
  • 0102 Applied Mathematics
 

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Todorov, V., & Tauchen, G. (2014). Limit theorems for the empirical distribution function of scaled increments of itô semimartingales at high frequencies. Annals of Applied Probability, 24(5), 1850–1888. https://doi.org/10.1214/13-AAP965
Todorov, V., and G. Tauchen. “Limit theorems for the empirical distribution function of scaled increments of itô semimartingales at high frequencies.” Annals of Applied Probability 24, no. 5 (January 1, 2014): 1850–88. https://doi.org/10.1214/13-AAP965.
Todorov V, Tauchen G. Limit theorems for the empirical distribution function of scaled increments of itô semimartingales at high frequencies. Annals of Applied Probability. 2014 Jan 1;24(5):1850–88.
Todorov, V., and G. Tauchen. “Limit theorems for the empirical distribution function of scaled increments of itô semimartingales at high frequencies.” Annals of Applied Probability, vol. 24, no. 5, Jan. 2014, pp. 1850–88. Scopus, doi:10.1214/13-AAP965.
Todorov V, Tauchen G. Limit theorems for the empirical distribution function of scaled increments of itô semimartingales at high frequencies. Annals of Applied Probability. 2014 Jan 1;24(5):1850–1888.

Published In

Annals of Applied Probability

DOI

ISSN

1050-5164

Publication Date

January 1, 2014

Volume

24

Issue

5

Start / End Page

1850 / 1888

Related Subject Headings

  • Statistics & Probability
  • 0104 Statistics
  • 0102 Applied Mathematics