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

Argimiro Arratia; Alejandra Cabaña; Enrique M. Cabaña

doi:10.1016/j.jspi.2018.01.004

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

Argimiro Arratia, Alejandra Cabaña, Enrique M. Cabaña

Research output: Contribution to journal › Article › Research

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 language	English
Pages (from-to)	156-167
Journal	Journal of Statistical Planning and Inference
Volume	197
DOIs	https://doi.org/10.1016/j.jspi.2018.01.004
Publication status	Published - 1 Dec 2018

Keywords

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

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10.1016/j.jspi.2018.01.004

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title = "Embedding in law of discrete time ARMA processes in continuous time stationary processes",

abstract = "{\textcopyright} 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}.",

keywords = "CARMA, Continuous-time ARMA, Discrete-time ARMA, Embedding, L{\'e}vy process",

author = "Argimiro Arratia and Alejandra Caba{\~n}a and Caba{\~n}a, {Enrique M.}",

year = "2018",

month = dec,

day = "1",

doi = "10.1016/j.jspi.2018.01.004",

language = "English",

volume = "197",

pages = "156--167",

journal = "Journal of Statistical Planning and Inference",

issn = "0378-3758",

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TY - JOUR

T1 - Embedding in law of discrete time ARMA processes in continuous time stationary processes

AU - Arratia, Argimiro

AU - Cabaña, Alejandra

AU - Cabaña, Enrique M.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - © 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}.

AB - © 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}.

KW - CARMA

KW - Continuous-time ARMA

KW - Discrete-time ARMA

KW - Embedding

KW - Lévy process

U2 - 10.1016/j.jspi.2018.01.004

DO - 10.1016/j.jspi.2018.01.004

M3 - Article

VL - 197

SP - 156

EP - 167

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

ER -