Bootstrap procedures for detecting multiple persistence shifts in heteroskedastic time series

This paper proposes new bootstrap procedures for detecting multiple persistence shifts in a time series driven by nonstationary volatility. The assumed volatility process can accommodate discrete breaks, smooth transition variation as well as trending volatility. We develop wild bootstrap sup-Wald tests of the null hypothesis that the process is either stationary [I(0)] or has a unit root [I(1)] throughout the sample. We also propose a sequential procedure to estimate the number of persistence breaks based on ordering the regime-specific bootstrap p-values. The asymptotic validity of the advocated procedures is established both under the null of stability and a variety of persistence change alternatives. Monte Carlo simulations support the use of a non-recursive scheme for generating the I(0) bootstrap samples and a partially recursive scheme for generating the I(1) bootstrap samples, especially when the data generating process contains an I(1) segment. A comparison with existing tests illustrates the finite sample improvements offered by our methods in terms of both size and power. An application to OECD inflation rates is included.