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

Author
Arratia, A.; Cabaña, A.; Cabaña, E. M.
Type of activity
Journal article
Journal
Journal of statistical planning and inference
Date of publication
2018-12-01
Volume
197
First page
156
Last page
167
DOI
https://doi.org/10.1016/j.jspi.2018.01.004 Open in new window
Repository
http://hdl.handle.net/2117/121525 Open in new window
URL
https://www.sciencedirect.com/science/article/pii/S0378375818300065?via%3Dihub Open in new window
Abstract
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}. © 2018. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommon...
Citation
Arratia, A., Cabaña, A., Cabaña, E. M. Embedding in law of discrete time ARMA processes in continuous time stationary processes. "Journal of statistical planning and inference", 1 Desembre 2018, vol. 197, p. 156-167.
Keywords
CARMA, Continuous-time ARMA, Discrete-time ARMA, Embedding, Levy process
Group of research
LARCA - Laboratory of Relational Algorithmics, Complexity and Learnability

Participants