Statistical inference across time scales - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Electronic Journal of Statistics Année : 2011

Statistical inference across time scales

Résumé

We consider a compound Poisson process with symmetric Bernoulli jumps, observed at time i Delta for i = 0, 1, ... over [0, T], for different sizes of Delta = Delta(T) relative to T in the limit T -> infinity. We quantify the smooth statistical transition from a microscopic Poissonian regime (when Delta(T) -> 0) to a macroscopic Gaussian regime (when Delta(T) -> infinity). The classical quadratic variation estimator is efficient for estimating the intensity of the Poisson process in both microscopic and macroscopoic scales but surprisingly, it shows a substantial loss of information in the intermediate scale Delta(T) -> Delta(infinity) is an element of (0, infinity). This loss can be explicitly related to Delta(infinity). We provide an estimator that is efficient simultaneously in microscopic, intermediate and macroscopic regimes. We discuss the implications of these findings beyond this idealised framework.

Dates et versions

hal-00692996 , version 1 (01-05-2012)

Identifiants

Citer

Celine Duval, Marc Hoffmann. Statistical inference across time scales. Electronic Journal of Statistics , 2011, 5 (?), pp.2004--2030. ⟨10.1214/11-EJS660⟩. ⟨hal-00692996⟩
34 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More