Tests for an end-of-sample bubble in financial time series

In this paper, we examine the issue of detecting explosive behavior in economic and financial time series when an explosive episode is both ongoing at the end of the sample and of finite length. We propose a testing strategy based on a subsampling method in which a suitable test statistic is calculated on a finite number of end-of-sample observations, with a critical value obtained using subsample test statistics calculated on the remaining observations. This approach also has the practical advantage that, by virtue of how the critical values are obtained, it can deliver tests which are robust to, among other things, conditional heteroskedasticity and serial correlation in the driving shocks. We also explore modifications of the raw statistics to account for unconditional heteroskedasticity using studentization and a White-type correction. We evaluate the finite sample size and power properties of our proposed procedures and find that they offer promising levels of power, suggesting the possibility for earlier detection of end-of-sample bubble episodes compared to existing procedures.