Bootstrapping Non-Stationary Stochastic Volatility
非平稳随机波动率下的自助法AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要研究随机波动率下的时间序列回归，并明确应用于结构变化检验。
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非平稳随机波动率下的自助法
- 研究问题
- 当时间序列回归的创新波动率由非平稳随机过程驱动时，如何建立自助法有效性并处理条件统计量的随机极限分布？
- 方法与思路
- 作者使用分布意义下的弱收敛研究给定波动率过程的 wild bootstrap，覆盖近积分波动率及近积分 GARCH 等情形。
- 材料陈述的贡献
- 摘要称建立新的有效性条件，并用于位置模型、结构变化与单位根检验；模拟显示所考察的小样本中可控制检验尺寸。
- 阅读关注点
- 应核对条件有效性的含义、随机极限的处理方式，以及误差与未来条件方差不存在相关性这一充分条件的具体作用。
- 阅读边界
- 这是 arXiv 预印本，不能据此确认同行评审或期刊接收；摘要未列出全部有效性条件，小样本尺寸控制仅是模拟报告。
原文摘要
In this paper we investigate how the bootstrap can be applied to time series regressions when the volatility of the innovations is random and non-stationary. The volatility of many economic and financial time series displays persistent changes and possible non-stationarity. However, the theory of the bootstrap for such models has focused on deterministic changes of the unconditional variance and little is known about the performance and the validity of the bootstrap when the volatility is driven by a non-stationary stochastic process. This includes near-integrated volatility processes as well as near-integrated GARCH processes. This paper develops conditions for bootstrap validity in time series regressions with non-stationary, stochastic volatility. We show that in such cases the distribution of bootstrap statistics (conditional on the data) is random in the limit. Consequently, the conventional approaches to proving bootstrap validity, involving weak convergence in probability of the bootstrap statistic, fail to deliver the required results. Instead, we use the concept of `weak convergence in distribution' to develop and establish novel conditions for validity of the wild bootstrap, conditional on the volatility process. We apply our results to several testing problems in the presence of non-stationary stochastic volatility, including testing in a location model, testing for structural change and testing for an autoregressive unit root. Sufficient conditions for bootstrap validity include the absence of statistical leverage effects, i.e., correlation between the error process and its future conditional variance. The results are illustrated using Monte Carlo simulations, which indicate that the wild bootstrap leads to size control even in small samples.