Nonparametric tests for the pathwise properties of semimartingales

Rama Cont (1) , Cecilia Mancini (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 UniFI - Università degli Studi di Firenze = University of Florence = Université de Florence

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 and a finite variation jump component.

Mots clés: semimartingale; high frequency data; threshold estimator; nonparametric statistics; jump process; financial econometrics

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]

Rama Cont, Cecilia Mancini. Nonparametric tests for the pathwise properties of semimartingales. Bernoulli, 2011, 17 (2), pp.781-813. ⟨10.3150/10-BEJ293⟩. ⟨hal-00588490⟩