TY - JOUR
T1 - Tempered stable Ornstein- Uhlenbeck processes: A practical view
T2 - A practical view
AU - Bianchi, Michele Leonardo
AU - Rachev, Svetlozar
AU - Fabozzi, Frank J.
N1 - Publisher Copyright:
© 2017 Taylor & Francis Group, LLC.
PY - 2017/1/2
Y1 - 2017/1/2
N2 - We study the one-dimensional Ornstein–Uhlenbeck (OU) processes with marginal law given by tempered stable and tempered infinitely divisible distributions. We investigate the transition law between consecutive observations of these processes and evaluate the characteristic function of integrated tempered OU processes with a view toward practical applications. We then analyze how to draw a random sample from this class of processes by considering both the classical inverse transform algorithm and an acceptance–rejection method based on simulating a stable random sample. Using a maximum likelihood estimation method based on the fast Fourier transform, we empirically assess the simulation algorithm performance.
AB - We study the one-dimensional Ornstein–Uhlenbeck (OU) processes with marginal law given by tempered stable and tempered infinitely divisible distributions. We investigate the transition law between consecutive observations of these processes and evaluate the characteristic function of integrated tempered OU processes with a view toward practical applications. We then analyze how to draw a random sample from this class of processes by considering both the classical inverse transform algorithm and an acceptance–rejection method based on simulating a stable random sample. Using a maximum likelihood estimation method based on the fast Fourier transform, we empirically assess the simulation algorithm performance.
KW - Acceptance–rejection sampling
KW - Maximum likelihood estimation
KW - Ornstein–Uhlenbeck processes
KW - Tempered infinitely divisible distributions
KW - Tempered stable distributions
UR - http://www.scopus.com/inward/record.url?scp=84992411360&partnerID=8YFLogxK
U2 - 10.1080/03610918.2014.966834
DO - 10.1080/03610918.2014.966834
M3 - Article
SN - 0361-0918
VL - 46
SP - 423
EP - 445
JO - COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
JF - COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
IS - 1
ER -