Using covariates to improve the efficacy of univariate bubble detection methods

We explore how information additional to a specific price series can be used improve the power of popular univariate autoregressive-based methods for detecting and dating speculative bubble episodes. Following Phillips et al. (2011, 2015) we base our approach on sequences sub-sample regression-based augmented Dickey–Fuller [ADF] statistics. Our point departure from these extant procedures is allow in testing procedures. To do so follow Hansen (1995) augment ADF regressions with covariate regressors. The limiting null distributions resulting statistics depend long-run squared correlation between covariates regression error. show that this dependence accounted by using residual bootstrap re-sampling method. Simulation evidence shows including relevant significantly efficacy both detection tests associated date-stamping procedure, relative standard An empirical application proposed methodology monthly S&P 500 data considered, variety candidate covariates. Using covariates, onset dotcom Black Monday are identified earlier than when methods.