A comparative study of several bootstrap-based tests for the volatility in continuous-time diffusion models

Abstract

This article develops three bootstrap-based tests for a parametric form of volatil- ity function in continuous-time diffusion models. The three tests are the generalized likelihood ratio test by Fan et al. (Ann Stat 29(1):153–193, 2001), the nonparamet- ric kernel test (LWZ) by Li and Wang (J Econometrics 87(1):145–165, 1998) and Zheng (J Econ 75(2):263–289, 1996) and the nonparametric test (CHS) by Chen et al. (2017). Monte Carlo simulations are performed to evaluate the sizes and power properties of these bootstrap-based tests in finite samples over a range of bandwidth values. We find that the bootstrap-based tests are not influenced by prior restrictions on the functional form of the drift function and that the bootstrap-based CHS test has better power performance than the bootstrap-based GLR and LWZ tests in detect- ing a parametric form of volatility. An empirical study on weekly treasury bill rate is further conducted to demonstrate these bootstrap-based test procedures.