TY - JOUR
T1 - Least squares estimators for discretely observed stochastic processes driven by small Lévy noises
AU - Long, Hongwei
AU - Shimizu, Yasutaka
AU - Sun, Wei
N1 - Funding Information:
The authors are grateful to anonymous referees for suggesting to add sections for semi-martingale noise and simulations (Sections 4 and 5 ). This research was supported by JSPS KAKENHI Grant Number 24740061 , Japan Science and Technology Agency, CREST (the 2nd author), and NSERC Grant Number 311945-2008 (the 3rd author).
PY - 2013/4
Y1 - 2013/4
N2 - We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small Lévy noises. We do not impose any moment condition on the driving Lévy process. Under certain regularity conditions on the drift function, we obtain consistency and rate of convergence of the least squares estimator (LSE) of the drift parameter when a small dispersion coefficient ε → 0 and n → ∞ simultaneously. The asymptotic distribution of the LSE in our general setting is shown to be the convolution of a normal distribution and a distribution related to the jump part of the Lévy process. Moreover, we briefly remark that our methodology can be easily extended to the more general case of semi-martingale noises.
AB - We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small Lévy noises. We do not impose any moment condition on the driving Lévy process. Under certain regularity conditions on the drift function, we obtain consistency and rate of convergence of the least squares estimator (LSE) of the drift parameter when a small dispersion coefficient ε → 0 and n → ∞ simultaneously. The asymptotic distribution of the LSE in our general setting is shown to be the convolution of a normal distribution and a distribution related to the jump part of the Lévy process. Moreover, we briefly remark that our methodology can be easily extended to the more general case of semi-martingale noises.
KW - Asymptotic distribution of LSE
KW - Consistency of LSE
KW - Discrete observations
KW - Least squares method
KW - Parameter estimation
KW - Small Lévy noises
KW - Stochastic processes
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U2 - 10.1016/j.jmva.2013.01.012
DO - 10.1016/j.jmva.2013.01.012
M3 - Article
AN - SCOPUS:84873937234
SN - 0047-259X
VL - 116
SP - 422
EP - 439
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
ER -