This article proposes a test to determine if two price series that each contain an explosive autoregressive regime consistent with the presence of a bubble are related in the sense that a linear combination of them is integrated of order zero. We refer to such a phenomenon as ‘co-explosive behaviour’, and propose a test based on a stationarity testing framework. The test allows the explosive episode in one series to lead (or lag) that in the other by a number of time periods. We establish the asymptotic properties of the test statistic and propose a wild bootstrap procedure for obtaining critical values that are robust to heteroskedasticity. Simulations show that the proposed test has good finite sample size and power performance. An empirical application to detect whether co-explosive behaviour exists among a set of precious and non-ferrous metals is presented.

中文翻译：

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金融时间序列中的共爆行为测试

本文提出了一个测试，以确定两个价格序列是否相关，每个价格序列都包含与泡沫存在一致的爆炸性自回归机制，因为它们的线性组合是零阶积分。我们将这种现象称为“共爆行为”，并提出了一种基于平稳性测试框架的测试。该测试允许一个系列中的爆炸性事件领先（或滞后）另一个系列中的多个时间段。我们建立了检验统计量的渐近特性，并提出了一个狂野的引导程序来获得对异方差具有鲁棒性的临界值。仿真表明，所提出的测试具有良好的有限样本量和功效性能。