It is well-known that pretesting the presence of the jump component in an underlying price process is crucial for modeling this process. In this paper, we propose a consistent test for jump intensity of the conditional Poisson process in a stochastic volatility jump diffusion model. Theoretically, we derive the infill and long-span asymptotic properties of realized power variation under some suitable conditions, and verify the asymptotic size and power of the proposed test. Furthermore, the finite-sample performance of our proposed test is illustrated through simulation analysis, and an application to real price series provides empirical evidence of significant jump intensities.

The varying coefficient model assumes that the regression function depends linearly on some regressors, and that the regression coefficients are smooth functions of other predictor variables. It provides an appreciable flexibility in capturing the underlying dynamics in data and avoids the so-called "curse of dimensionality" in analyzing complex and multivariate nonlinear structures. Existing estimation methods usually assume that the errors for the model are independent; however, they may not be satisfied in practice. In this study, we investigated the estimation for the varying coefficient model with correlated errors via B-spline. The B-spline approach, as a global smoothing method, is computationally efficient. Under suitable conditions, the convergence rates of the proposed estimators were obtained. Furthermore, two simulation examples were employed to demonstrate the performance of the proposed approach and the necessity of considering correlated errors.