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.

中文翻译：

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用于检测异方差时间序列中多个持久性偏移的 Bootstrap 程序

本文提出了新的引导程序，用于检测由非平稳波动率驱动的时间序列中的多个持久性变化。假定的波动率过程可以适应离散中断、平滑过渡变化以及趋势波动率。我们开发了原假设的 Wild bootstrap sup-Wald 检验，即该过程是平稳的 [I(0)] 或在整个样本中具有单位根 [I(1)]。我们还提出了一个顺序程序来基于对特定于政权的引导 p 值的排序来估计持久性中断的数量。所提倡的程序的渐近有效性是在零稳定性和各种持久性变化替代方案下建立的。Monte Carlo 模拟支持使用非递归方案生成 I(0) 引导样本和部分递归方案生成 I(1) 引导样本，尤其是当数据生成过程包含 I(1) 段时。与现有测试的比较说明了我们的方法在大小和功率方面提供的有限样本改进。包括对经合组织通货膨胀率的应用。