# Mark Podolskij: How many Brownian motions are needed to model a d-dimensional price process?

**Time: **
Wed 2019-04-03 15.15

**Lecturer: **
Mark Podolskij (Aarhus University)

**Location: ** Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University ￼

Abstract: In this talk we will first briefly review the classical volatility estimation methods in financial applications. We will show that the problem of finding the minimal amount of Brownian motion needed to model a d-dimensional price process is equivalent to determining the maximal rank of the volatility matrix. In the next step we will present a test for the maximal rank of the matrix-valued volatility process in the continuous diffusion framework. Our idea is based upon a random perturbation of the original high frequency observations of the diffusion, 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. Our talk is based on the article

J. Jacod and M. Podolskij (2013): A test for the rank of the volatility process: the random perturbation approach.

J. Jacod and M. Podolskij (2013): A test for the rank of the volatility process: the random perturbation approach.

*Annals of Statistics*, 41(5), 2391–2427.