Seminari del Dipartimento di Matematica

Seminario del 2010

Dott.ssa Cecilia Mancini (Dip. Matematica per le decisioni, Univ. Firenze)

Nonparametric tests for pathwise properties of semimartingales

probabilità

We propose two nonparametric tests for investigating the pathwise properties of a signal modeled as the sum of a Lévy process and a Brownian semimartingale. Using a nonparametric threshold estimator for the continuous component of the quadratic variation, we design a test for the presence of a continuous martingale component in the process and a test for establishing whether the jumps have finite or infinite variation, based on observations on a discrete time grid. We evaluate the performance of our tests using simulations of various stochastic models and use the tests to investigate the fine structure of the DM/USD exchange rate fluctuations and SPX futures prices. In both cases, our tests reveal the presence of a non-zero Brownian component, combined with a finite variation jump component. This is a joint work with Rama Cont (Univ. di Parigi 6).