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.
Highlights
In a series of influential articles, Phillips, Wu, and Yu (2011; PWY hereafter) and Phillips et al (2014, 2015a, b) have established a sound theoretical foundation of right-V
In the wake of this work, the most prominent testing procedures—the sup augmented Dickey–Fuller (SADF) test and its generalized version—have been applied in a plethora of empirical studies, in which data explosiveness is interpreted as indicating an asset-price bubble
We investigate the capacity of various sup-ADF-style testing procedures for detecting and date-stamping financial bubbles
Summary
In a series of influential articles, Phillips, Wu, and Yu (2011; PWY hereafter) and Phillips et al (2014, 2015a, b) have established a sound theoretical foundation of right-. PWY and PSY motivate their SADF and GSADF testing procedures on the basis of the well-known present-value stock-price model with constant expected returns (Campbell et al 1997). Within this framework, the date-t stock-price Pt is given by the Euler equation. Bubble reveals a major empirical shortcoming in that it always bursts entirely, from one trading unit to the These abrupt bursts entail unrealistic stock-price trajectories, and incompatible volatility dynamics (Rotermann and Wilfling 2014). 3, we consider the bubble specification suggested by Rotermann and Wilfling (2018) This bubble model—a mixture of two lognormal processes—(i) generates realistic trajectories and stock-price volatility paths and (ii) satisfies the rationality condition (3) plus the two Diba–Grossman conditions mentioned above. Adding them as in Eq (2), we obtain the fundamental stock price as
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