Intermittent estimation of stationary time series

Simple item page
dc.creatorMorvai, G.
dc.creatorWeiss, B.
dc.date2007-11-02
dc.date.accessioned2026-07-07T09:45:12Z
dc.date.available2026-07-07T09:45:12Z
dc.descriptionLet $\{X_n\}_{n=0}^{\infty}$ be a stationary real-valued time series with unknown distribution. Our goal is to estimate the conditional expectation of $X_{n+1}$ based on the observations $X_i$, $0\le i\le n$ in a strongly consistent way. Bailey and Ryabko proved that this is not possible even for ergodic binary time series if one estimates at all values of $n$. We propose a very simple algorithm which will make prediction infinitely often at carefully selected stopping times chosen by our rule. We show that under certain conditions our procedure is strongly (pointwise) consistent, and $L_2$ consistent without any condition. An upper bound on the growth of the stopping times is also presented in this paper.
dc.identifierhttps://arxiv.org/abs/0711.0350
dc.identifierhttp://arxiv.org/abs/0711.0350
dc.identifierTest 13 (2004), no. 2, 525--542
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163121
dc.subjectProbability
dc.subjectInformation Theory
dc.titleIntermittent estimation of stationary time series
dc.typetext

Files

Collections

arXiv