The Grid Bootstrap for Continuous Time Models

Abstract

This article 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 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 the U.S. interest rates and volatilities suggest significant differences between the two bootstrap procedures when the initial condition is large.

KEYWORDS:

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

Acknowledgments

We thank to Peter Phillips for helpful discussions and comments.

Additional information

Funding

Xiao gratefully acknowledges the financial support of the National Natural Science Foundation of China (No. 71871202). Yu acknowledges the financial support from Singapore Ministry of Education Tier 2 grant under grant MOE2018-T2-2-169.