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 language | English |
|---|---|
| Pages (from-to) | 125-139 |
| Number of pages | 15 |
| Journal | Communications in Statistics: Simulation and Computation |
| Volume | 41 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 1 2012 |
Fingerprint
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 journal › Article
}
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 -