Section: New Results

Rational Approximation for fitting Non-Negative EPT densities

Participants : Martine Olivi, Fabien Seyfert.

This work has been done in collaboration with Bernard Hanzon and Conor Sexton from Univ. Cork.

The problem is to fit a probability density function on a large set of financial data. The model class is the set of non-negative EPT (Exponential-Polynomials-Trigonometric) functions which provides a useful framework for probabilistic calculation as illustrated in the link http://www.2-ept.com/2-ept-literature.html . Moreover, an EPT function can alternatively be interpreted as the impulse response of a continuous time stable system whose Laplace transform is a rational transfer function. This interpretation allows us to approach this problem using approximation tools developed by the team. The very context brings up a classical, as yet essentially unsolved difficulty in rational approximation, namely preservation of positivity. This is known to be a hard issue. Our work, initiated in 2011, resulted this year in an improved approach for checking non-negativity of an EPT function. These results have been presented at the 16th IFAC Conference on System Identification [23] . The proposed method was demonstrated on the positive daily Dow Jones Industrial Average (DJIA) log returns over 80 years.