Testing the maximal rank of the volatility process for continuous diffusions observed with noise.

Tobias Fissler, Mark Podolskij

Publication: Scientific journalJournal articlepeer-review

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.
Original languageEnglish
Pages (from-to)3021 - 3066
JournalBernoulli
Volume23
Issue number4B
DOIs
Publication statusPublished - 2017

Cite this