Nonparametric estimation problem for a time-periodic signal in a periodic noise

Dominique Dehay (1) , Khalil El Waled (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper we construct a kernel estimator of a periodic signal when the observation follows the model d zeta(t) = f (t)dt + sigma(t)dW(t), where f, sigma : R -> R are continuous periodic and {W-t, t >= 0} is a Brownian motion. We state its consistency as well as the asymptotic normality

Mots clés: Periodic signal; Kernel estimation; Continuous time; Periodic variance; Black-Scholes-Merton model

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

Dominique Dehay, Khalil El Waled. Nonparametric estimation problem for a time-periodic signal in a periodic noise. Statistics and Probability Letters, 2013, 83 (2), pp.608-615. ⟨10.1016/j.spl.2012.11.008⟩. ⟨hal-00811767⟩