Abstract This paper is devoted to testing for bubbles under time-varying non-stationary volatility. Because the limiting distribution of the seminal Phillips, Wu, and Yu (2011) test depends on the variance function and usually requires a bootstrap implementation under heteroskedasticity, we construct the test based on a deformation of the time domain. The proposed test is asymptotically pivotal under the null hypothesis and its limiting distribution coincides with that of the standard test under homoskedasticity, so that the test does not require computationally extensive methods for inference. Appealing finite sample properties are demonstrated through Monte-Carlo simulations. An empirical application demonstrates that the upsurge behavior of cryptocurrency time series in the middle of the sample is partially explained by the volatility change.

中文翻译：

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非平稳波动下气泡的时间变换检验

摘要 本文致力于测试时变非平稳波动下的泡沫。因为开创性的 Phillips、Wu 和 Yu (2011) 检验的极限分布取决于方差函数，并且通常需要在异方差下进行引导实现，所以我们基于时域的变形来构建检验。所提出的检验在原假设下是渐近关键的，并且其极限分布与同方差下的标准检验的分布一致，因此该检验不需要计算广泛的推理方法。通过蒙特卡洛模拟证明了吸引人的有限样本特性。