Title: Towards a computationally-tractable maximum entropy principle for non-stationary financial time series
Authors: Patrick Gagliardini - University of Lugano (Switzerland)
Illia Horenko - Universita della Svizzera italiana (Germany)
Anna Marchenko - Universita della Svizzera italiana (Switzerland) [presenting]
Abstract: Statistical analysis of financial time-series of equity returns is hindered by various unobserved/latent factors, resulting in non-stationarity of the overall problem. Parametric methods approach the problem by restricting it to a certain (stationary) distribution class through various assumptions, which often result in misspecification when the problem does not belong to this predefined class. Non-parametric methods are more general, but lead to ill-posed problems and computationally-expensive numerical schemes. We present a non-parametric methodology addressing these issues in a computationally-tractable way by using key concepts like the maximum entropy principle for non-parametric density estimation and a Lasso regularization technique for numerical identification of redundant parameters. In the context of volatility modeling, the presented approach identifies optimal number of regimes with different levels of volatility and their non-parametric switching behaviour. Using historical return data for an equity index we demonstrate that despite viewing the data as conditionally-independent, our methodology leads to identification of robust models being superior to the standard conditional heteroschedasticity models when compared with respect to the Akaike and Bayesian Information Criteria.