Testing the maximal rank of the volatility process for continuous diffusions observed with noise
File(s)
Published version
Author(s)
Fissler, T
Podolskij, M
Type
Journal Article
Abstract
In this paper, we present a test for the maximal rank of the volatility process in continuous diffusion models observed with noise. Such models are typically applied in mathematical finance, where latent price processes are corrupted by microstructure noise at ultra high frequencies. Using high frequency observations, we construct a test statistic for the maximal rank of the time varying stochastic volatility process. Our methodology is based upon a combination of a matrix perturbation approach and pre-averaging. We will show the asymptotic mixed normality of the test statistic and obtain a consistent testing procedure. We complement the paper with a simulation and an empirical study showing the performances on finite samples.
Date Issued
2017-05-23
Date Acceptance
2016-03-04
Citation
Bernoulli, 2017, 23 (4B), pp.3021-3066
ISSN
1350-7265
Publisher
Bernoulli Society for Mathematical Statistics and Probability
Start Page
3021
End Page
3066
Journal / Book Title
Bernoulli
Volume
23
Issue
4B
Copyright Statement
© 2017 ISI/BS
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000403032000003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
continuous Ito semimartingales
high frequency data
microstructure noise
rank testing
stable convergence
MICROSTRUCTURE NOISE
JUMPS
Publication Status
Accepted