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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability