Using covariates to improve the efficacy of univariate bubble detection methods
研究了如何利用额外信息（协变量）改进基于自回归的泡沫检测方法，通过残差自助法处理统计量分布，模拟和实证表明能更早识别股市泡沫。
We explore how information additional to a specific price series can be used to improve the power of popular univariate autoregressive-based methods for detecting and dating speculative price bubble episodes. Following Phillips et al. (2011, 2015) we base our approach on sequences of sub-sample regression-based augmented Dickey–Fuller [ADF] statistics. Our point of departure from these extant procedures is to allow for additional information in the testing and dating procedures. To do so we follow the approach of Hansen (1995) and augment the sub-sample ADF regressions with covariate regressors. The limiting null distributions of the resulting statistics depend on the long-run squared correlation between the covariates and the regression error. We show that this dependence can be accounted for by using a residual bootstrap re-sampling method. Simulation evidence shows that including relevant covariates can significantly improve the efficacy of both the resulting bubble detection tests and the associated date-stamping procedure, relative to using standard sub-sample ADF statistics. An empirical application of the proposed methodology to monthly S&P 500 data is considered, using a variety of candidate covariates. Using these covariates, the onset of the dotcom bubble and the bubble associated with Black Monday are both identified significantly earlier than when using standard methods.