Marc Hoffmann (Ceremade, Université Paris Dauphine - PSL)

Title : Disentangling endogenous and exogenous correlations of low frequency data using high frequency information

Abstract : Given empirical data of two times series, we address the problem of extracting the part of endogenous and exogenous dynamics that altogether form the empirical correlation of the time series. In this formulation, our question is ill-posed and our purpose hopeless without an additional structure. We assume 1) the simplest model, namely discretely observed correlated Brownian motions, that may serve as a representative model for low frequency prices of correlated financial assets, up to an absolutely continuous change of measure. 2) Moreover, we have access to some additional microscopic information, namely the fluctuation of the prices at high frequencies, via marked point processes models that diffuse to the original time series at a macroscopic scale.

First and second order characteristics are not sufficient to recover the parameters of the model, but adding third order characteristics does the job, at least mathematically. This enables us to overcome the latent structure of our model and quantify the part of endogenous versus exogenous effects that have an explicit trace on the macroscopic correlation (our initial low frequency observable). We numerically test our approach and show some early results on empirical financial data.

A joint ongoing work with E. Bacry, T. Deschatre, J.F. Muzy and R. Ruan

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