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
Recommended Citation
Ernst, P. A., Brown, L. D., Shepp, L., & Wolpert, R. L. (2017). Stationary Gaussian Markov Processes as Limits of Stationary Autoregressive Time Series. Journal of Multivariate Analysis, 155 180-186. http://dx.doi.org/10.1016/j.jmva.2016.12.008
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Date Posted: 25 October 2018
This document has been peer reviewed.