TY - JOUR
T1 - Jarque-Bera normality test for the driving Lévy process of a discretely observed univariate SDE
AU - Lee, Sangyeol
AU - Masuda, Hiroki
N1 - Funding Information:
Acknowledgements We are grateful to Professor Marc Hallin and the two anonymous referees for their careful reading and helpful comments that improve the quality of the paper. The authors wish to acknowledge that this work was partly supported by the grants: grant No. R01-2006-000-10545-0 from the Basic Research Program of the Korea Science & Engineering Foundation (S. Lee); and Grant-in-Aid for Young Scientists (B) 20740061 of Japan, and Cooperative Research Program of the Institute of Statistical Mathematics (H. Masuda).
PY - 2010
Y1 - 2010
N2 - In this paper, we study the Jarque-Bera test for a class of univariate parametric stochastic differential equations (SDE) dXt = b(Xt, α)dt + dZt, constructed based on the sample observed at discrete time points tin = ihn, i = 1, 2,..., n, where Z is a nondegenerate Lévy process with finite moments and h is a sequence of positive real numbers with nhn → ∞ and nhn2 → 0 as n → ∞. It is shown that under proper conditions, the Jarque-Bera test statistic based on the Euler residuals can be used to test for the normality of the unobserved Z and the proposed test is consistent against the presence of any nontrivial jump components. Our result indicates that the Jarque-Bera test is easy to implement and asymptotically distribution-free with no fine-tuning parameters. Simulation results to validate the test are given for illustration.
AB - In this paper, we study the Jarque-Bera test for a class of univariate parametric stochastic differential equations (SDE) dXt = b(Xt, α)dt + dZt, constructed based on the sample observed at discrete time points tin = ihn, i = 1, 2,..., n, where Z is a nondegenerate Lévy process with finite moments and h is a sequence of positive real numbers with nhn → ∞ and nhn2 → 0 as n → ∞. It is shown that under proper conditions, the Jarque-Bera test statistic based on the Euler residuals can be used to test for the normality of the unobserved Z and the proposed test is consistent against the presence of any nontrivial jump components. Our result indicates that the Jarque-Bera test is easy to implement and asymptotically distribution-free with no fine-tuning parameters. Simulation results to validate the test are given for illustration.
UR - http://www.scopus.com/inward/record.url?scp=77953718394&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77953718394&partnerID=8YFLogxK
U2 - 10.1007/s11203-010-9043-x
DO - 10.1007/s11203-010-9043-x
M3 - Article
AN - SCOPUS:77953718394
VL - 13
SP - 147
EP - 161
JO - Statistical Inference for Stochastic Processes
JF - Statistical Inference for Stochastic Processes
SN - 1387-0874
IS - 2
ER -