Embedding in law of discrete time ARMA processes in continuous time stationary processes

Argimiro Arratia, Alejandra Cabaña, Enrique M. Cabaña

Research output: Contribution to journalArticleResearch

Abstract

© 2018 Elsevier B.V. Given any stationary time series {Xn:n∈Z} satisfying an ARMA(p,q) model for arbitrary p and q with infinitely divisible innovations, we construct a continuous time stationary process {xt:t∈R} such that the distribution of {xn:n∈Z}, the process sampled at discrete time, coincides with the distribution of {Xn}. In particular the autocovariance function of {xt} interpolates that of {Xn}.
Original languageEnglish
Pages (from-to)156-167
JournalJournal of Statistical Planning and Inference
Volume197
DOIs
Publication statusPublished - 1 Dec 2018

Keywords

  • CARMA
  • Continuous-time ARMA
  • Discrete-time ARMA
  • Embedding
  • Lévy process

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