The Grid Bootstrap for Continuous Time Models

Yiu Lim Lui, Weilin Xiao, Jun Yu   Published : May, 2021   JEL Code: C11, C12   URL to this Article: https://doi.org/10.1080/07350015.2021.1930014

Abstract

This paper proposes the new grid bootstrap to construct confidence intervals (CI) for the persistence parameter in a class of continuous-time models. It is different from the standard grid bootstrap of Hansen (1999) in dealing with the initial condition. The asymptotic validity of the CI is discussed under the in-fill scheme. The modified grid bootstrap leads to uniform inferences on the persistence parameter. Its improvement over in-fill asymptotics is achieved by expanding the coefficient-based statistic around its in-fill asymptotic distribution that is non-pivotal and depends on the initial condition. Monte Carlo studies show that the modified grid bootstrap performs better than Hansen’s grid bootstrap. Empirical applications to U.S. interest rates and volatilities suggest significant differences between the two bootstrap procedures when the initial condition is large.

Keywords

Grid bootstrap; In-fill asymptotics; Continuous-time models; Probabilistic expansion; Distributional expansion; Uniform inference