Statistics Papers

Document Type

Technical Report

Date of this Version

3-2017

Publication Source

Journal of Multivariate Analysis

Volume

155

Start Page

180

Last Page

186

DOI

10.1016/j.jmva.2016.12.008

Abstract

We consider the class, ℂp, of all zero mean stationary Gaussian processes, {Yt : t ∈ (—∞, ∞)} with p derivatives, for which the vector valued process {(Yt(0) ,...,Yt(p)) : t ≥ 0} is a p + 1-vector Markov process, where Yt(0) = Y(t). We provide a rigorous description and treatment of these stationary Gaussian processes as limits of stationary AR(p) time series.

Copyright/Permission Statement

© 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

continuous autoregressive processes, stationary Gaussian Markov processes, stochastic differential equations

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Date Posted: 25 October 2018

This document has been peer reviewed.