Wavelet analysis of a continuous-time Gaussian Process observed at random times and its application to the estimation of the spectral density

Jean-Marc Bardet (1, 2) , Pierre, Raphael Bertrand (3)

1 CES - Centre d'économie de la Sorbonne
2 SAMOS - Statistique Appliquée et MOdélisation Stochastique
3 PAS

In numerous applications (Finance, Internet Traffic, Biology,...) data are observed at random times. From a wavelet analysis, one derives a nonparametric estimator of the spectral density of a Gaussian process with stationary increments (also stationary Gaussian process) observed at random times.

Mots clés: Fractional Brownian motion; Wavelet analysis; Nonparametric estimation; Spectral density; Gaussian processes observed at random times

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

Jean-Marc Bardet, Pierre, Raphael Bertrand. Wavelet analysis of a continuous-time Gaussian Process observed at random times and its application to the estimation of the spectral density. 2008. ⟨hal-00276735v2⟩