Time-Transformed Test for the Explosive Bubbles under Non-stationary Volatility

TL;DR

This paper introduces a new time-domain deformation test for detecting explosive bubbles in financial time series with non-stationary volatility, avoiding bootstrap methods and showing promising finite-sample performance.

Contribution

It proposes a novel test that is asymptotically pivotal under non-stationary volatility, simplifying inference compared to existing methods.

Findings

Test performs well in finite samples via simulations.

Application reveals cryptocurrency bubble behavior linked to volatility shifts.

Test is robust to heteroskedasticity without extensive computation.

Abstract

This paper is devoted to testing for the explosive bubble under time-varying non-stationary volatility. Because the limiting distribution of the seminal Phillips et al. (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.