The grid bootstrap for continuous time models

• Main Authors: LUI, Yiu Lim, XIAO, Weilin, YU, Jun
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2018
• Subjects: Grid bootstrap; In-fill asymptotics; Continuous time models; Long-span asymptotics.; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2210; https://ink.library.smu.edu.sg/context/soe_research/article/3209/viewcontent/gridbootcont19_.pdf
• Institution: Singapore Management University

This paper considers the grid bootstrap for constructing confidence intervals for the persistence parameter in a class of continuous time models driven by a Levy process. Its asymptotic validity is established by assuming the sampling interval (h) shrinks to zero. Its improvement over the in-fill asymptotic theory is achieved by expanding the coefficient-based statistic around its in fill asymptotic distribution which is non-pivotal and depends on the initial condition. Monte Carlo studies show that the gird bootstrap method performs better than the in-fill asymptotic theory and much better than the long-span theory. Empirical applications to U.S. interest rate data highlight differences between the bootstrap confidence intervals and the confidence intervals obtained from the in- fill and long-span asymptotic distributions.