Stationary Gaussian Markov processes as limits of stationary autoregressive time series

Philip A. Ernst, Lawrence D. Brown, Larry Shepp and Robert L. Wolpert

Journal of Multivariate Analysis, 2017, vol. 155, issue C, 180-186

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.

Keywords: Continuous autoregressive processes; Stationary Gaussian Markov processes; Stochastic differential equations (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.jmva.2016.12.008

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