A test for the rank of the volatility process: the random perturbation approach

TL;DR

This paper introduces a novel statistical test to determine the maximal rank of the volatility process in continuous-time stochastic models, using a random perturbation approach to facilitate rank testing.

Contribution

It develops a new rank testing methodology for volatility matrices in Ito semimartingales based on random perturbations, with comprehensive limit theory and applications.

Findings

The test accurately identifies the rank of the volatility process.

The methodology is validated through simulations and theoretical analysis.

A homoscedasticity test for the rank process is also proposed.

Abstract

In this paper we present a test for the maximal rank of the matrix-valued volatility process in the continuous Ito semimartingale framework. Our idea is based upon a random perturbation of the original high frequency observations of an Ito semimartingale, which opens the way for rank testing. We develop the complete limit theory for the test statistic and apply it to various null and alternative hypotheses. Finally, we demonstrate a homoscedasticity test for the rank process.