Sup-ADF-style bubble-detection methods under test

Monschang Verena, Wilfling Bernd

Abstract
In this paper we analyze the capacity of supremum augmented Dickey-Fuller (SADF), generalized SADF (GSADF), and of several heteroscedasticity-adjusted sup-ADF-style tests for detecting and date-stamping financial bubbles. Our Monte-Carlo simulations find that the majority of the sup-ADF-style tests exhibit substantial size distortions, when the data-generating process is subject to leverage effects. Moreover, the sup-ADF-style tests often have low empirical power in identifying a (flexible and empirically relevant) rational stock-price bubble, recently proposed in the literature. In a simulation study, we compare the effectiveness of two real-time bubble date-stamping procedures (Procedures 1 and 2), both based on variants of the backward SADF (BSADF) test. While Procedure 1 (predominantly) provides better estimates of the bubbles' origination and termination dates than Procedure 2, the first procedure frequently stamps non-existing bubbles. In an empirical application, we use NASDAQ data covering a time-span of 45 years and find that the bubble date-stamping outcomes of both procedures are sensitive to the data-frequency chosen by the econometrician.

Keywords
Stock markets; present-value model; rational bubble; explosiveness; (G)SADF tests; bubble detection; date-stamping