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

TL;DR

This paper develops a statistical test to determine the maximum rank of the volatility matrix in high-frequency noisy financial data, utilizing matrix perturbation and pre-averaging techniques to achieve asymptotic normality.

Contribution

It introduces a novel testing procedure for the maximal rank of the volatility process in continuous diffusions with noise, combining matrix perturbation and pre-averaging methods.

Findings

Test statistic has asymptotic mixed normal distribution.

The procedure is consistent for high-frequency noisy data.

Applicable in financial models with microstructure noise.

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.