Open Access
November 2012 Model checks for the volatility under microstructure noise
Mathias Vetter, Holger Dette
Bernoulli 18(4): 1421-1447 (November 2012). DOI: 10.3150/11-BEJ384


We consider the problem of testing the parametric form of the volatility for high frequency data. It is demonstrated that in the presence of microstructure noise commonly used tests do not keep the preassigned level and are inconsistent. The concept of preaveraging is used to construct new tests, which do not suffer from these drawbacks. These tests are based on a Kolmogorov–Smirnov or Cramér–von-Mises functional of an integrated stochastic process, for which weak convergence to a (conditional) Gaussian process is established. The finite sample properties of a bootstrap version of the test are illustrated by means of a simulation study.


Download Citation

Mathias Vetter. Holger Dette. "Model checks for the volatility under microstructure noise." Bernoulli 18 (4) 1421 - 1447, November 2012.


Published: November 2012
First available in Project Euclid: 12 November 2012

zbMATH: 1329.62416
MathSciNet: MR2995803
Digital Object Identifier: 10.3150/11-BEJ384

Keywords: Goodness-of-fit test , Heteroscedasticity , microstructure noise , Parametric bootstrap , stable convergence

Rights: Copyright © 2012 Bernoulli Society for Mathematical Statistics and Probability

Vol.18 • No. 4 • November 2012
Back to Top