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Author Franke, Jürgen ♦ Kreiss, Jens-Peter ♦ Moser, Martin
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Bootstrap Autoregressive Order Selection ♦ Bootstrap Order Selection ♦ Appropriate Order ♦ Bootstrap Procedure ♦ Infinite Order ♦ Bootstrap Principle ♦ Final Prediction Error ♦ Order Selection ♦ Asymptotic Property ♦ Relevant Expression ♦ So-called Final Prediction Error ♦ Infinite Order Autoregressive Model ♦ Autoregressive Model ♦ Following Type ♦ Stationary Autoregressive Process ♦ Non-stochastic Order
Abstract this paper we deal with the problem of fitting an autoregression of order p to given data coming from a stationary autoregressive process with infinite order. The paper is mainly concerned with the selection of an appropriate order of the autoregressive model. Based on the so-called final prediction error (FPE) a bootstrap order selection can be proposed, because it turns out that one relevant expression occuring in the FPE is ready for the application of the bootstrap principle. Some asymptotic properties of the bootstrap order selection are proved. To carry through the bootstrap procedure an autoregression with increasing but non-stochastic order is fitted to the given data. The paper is concluded by some simulations. Keywords: Autoregression; bootstrap; final prediction error; order selection. 1. Introduction In this paper we deal with observations X 1 ; : : : ; X n which are realizations of an infinite order autoregressive model (AR(1)-model) of the following type X t =
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