Sample Path Generation of Lévy-Driven Continuous-Time Autoregressive Moving Average Processes

Reiichiro Kawai ()
Additional contact information
Reiichiro Kawai: University of Sydney

Methodology and Computing in Applied Probability, 2017, vol. 19, issue 1, 175-211

Abstract: Abstract We address the issue of sample path simulation of Lévy-driven continuous-time autoregressive moving average (CARMA) processes. Approximate discrete-time simulation schemes are constructed along with quantifiable error analysis for stable, second-order and non-negative CARMA processes, based upon the so-called series representation of infinitely divisible laws and associated Lévy processes. We prove that under suitable conditions, the simulation scheme can be improved in terms of second-order structure, finite dimensional laws as well as sample path properties. The simulation procedure is often quite simple and allows one to conduct super-sampling without running the algorithm once again. The computational complexity of the proposed scheme is not affected much by the sampling scheme, such as sampling frequency and irregular spacing. Numerical results are presented throughout to illustrate the effectiveness of the proposed simulation scheme.

Keywords: CARMA process; Gamma process; Lévy process; Simulation; Sample path properties; Stable process; Stationary process; 65C30; 62M10; 60G10; 60G51 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s11009-015-9472-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:19:y:2017:i:1:d:10.1007_s11009-015-9472-5

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-015-9472-5

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().