Infinite variation tempered stable Ornstein-Uhlenbeck processes with discrete observations

Reiichiro Kawai, Hiroki Masuda

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We investigate transition law between consecutive observations of Ornstein-Uhlenbeck processes of infinite variation with tempered stable stationary distribution. Thanks to the Markov autoregressive structure, the transition law can be written in the exact sense as a convolution of three random components; a compound Poisson distribution and two independent tempered stable distributions, one with stability index in (0, 1) and the other with index in (1, 2). We discuss simulation techniques for those three random elements. With the exact transition law and proposed simulation techniques, sample paths simulation proves significantly more efficient, relative to the known approximative technique based on infinite shot noise series representation of tempered stable Lévy processes.

Original languageEnglish
Pages (from-to)125-139
Number of pages15
JournalCommunications in Statistics: Simulation and Computation
Volume41
Issue number1
DOIs
Publication statusPublished - Jan 1 2012

Fingerprint

Discrete Observations
Poisson distribution
Shot noise
Ornstein-Uhlenbeck Process
Stable Process
Convolution
Stable Distribution
Compound Poisson Distribution
Stability Index
Tempered Distribution
Shot Noise
Random Element
Simulation
Series Representation
Sample Path
Stationary Distribution
Consecutive

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation

Cite this

Infinite variation tempered stable Ornstein-Uhlenbeck processes with discrete observations. / Kawai, Reiichiro; Masuda, Hiroki.

In: Communications in Statistics: Simulation and Computation, Vol. 41, No. 1, 01.01.2012, p. 125-139.

Research output: Contribution to journalArticle

@article{df4f728dd9c642edb21408bfb8ccd35e,
title = "Infinite variation tempered stable Ornstein-Uhlenbeck processes with discrete observations",
abstract = "We investigate transition law between consecutive observations of Ornstein-Uhlenbeck processes of infinite variation with tempered stable stationary distribution. Thanks to the Markov autoregressive structure, the transition law can be written in the exact sense as a convolution of three random components; a compound Poisson distribution and two independent tempered stable distributions, one with stability index in (0, 1) and the other with index in (1, 2). We discuss simulation techniques for those three random elements. With the exact transition law and proposed simulation techniques, sample paths simulation proves significantly more efficient, relative to the known approximative technique based on infinite shot noise series representation of tempered stable L{\'e}vy processes.",
author = "Reiichiro Kawai and Hiroki Masuda",
year = "2012",
month = "1",
day = "1",
doi = "10.1080/03610918.2011.582561",
language = "English",
volume = "41",
pages = "125--139",
journal = "Communications in Statistics Part B: Simulation and Computation",
issn = "0361-0918",
publisher = "Taylor and Francis Ltd.",
number = "1",

}

TY - JOUR

T1 - Infinite variation tempered stable Ornstein-Uhlenbeck processes with discrete observations

AU - Kawai, Reiichiro

AU - Masuda, Hiroki

PY - 2012/1/1

Y1 - 2012/1/1

N2 - We investigate transition law between consecutive observations of Ornstein-Uhlenbeck processes of infinite variation with tempered stable stationary distribution. Thanks to the Markov autoregressive structure, the transition law can be written in the exact sense as a convolution of three random components; a compound Poisson distribution and two independent tempered stable distributions, one with stability index in (0, 1) and the other with index in (1, 2). We discuss simulation techniques for those three random elements. With the exact transition law and proposed simulation techniques, sample paths simulation proves significantly more efficient, relative to the known approximative technique based on infinite shot noise series representation of tempered stable Lévy processes.

AB - We investigate transition law between consecutive observations of Ornstein-Uhlenbeck processes of infinite variation with tempered stable stationary distribution. Thanks to the Markov autoregressive structure, the transition law can be written in the exact sense as a convolution of three random components; a compound Poisson distribution and two independent tempered stable distributions, one with stability index in (0, 1) and the other with index in (1, 2). We discuss simulation techniques for those three random elements. With the exact transition law and proposed simulation techniques, sample paths simulation proves significantly more efficient, relative to the known approximative technique based on infinite shot noise series representation of tempered stable Lévy processes.

UR - http://www.scopus.com/inward/record.url?scp=84856540213&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856540213&partnerID=8YFLogxK

U2 - 10.1080/03610918.2011.582561

DO - 10.1080/03610918.2011.582561

M3 - Article

AN - SCOPUS:84856540213

VL - 41

SP - 125

EP - 139

JO - Communications in Statistics Part B: Simulation and Computation

JF - Communications in Statistics Part B: Simulation and Computation

SN - 0361-0918

IS - 1

ER -