Testing for Multiple Bubbles 1: Historical Episodes of Exuberance and Collapse in the S&P 500

Published in International Economic Review, https://doi.org/10.1111/iere.12132</p

Steady-state distributions for models of bubbles: their existence and econometric implications

The purpose of this paper is to examine the properties of bubbles in the light of steady state results for threshold auto-regressive (TAR) models recently derived by Knight and Satchell (2011). We assert that this will have implications for econometrics. We study the conditions under which we can obtain a steady state distribution of asset prices using our simple model of bubbles based on our particular definition of a bubble. We derive general results and further extend the analysis by considering the steady state distribution in three cases of a (I) a normally distributed error process, (II) a non normally (exponentially) distributed steady-state process and (III) a switching random walk with a fairly general i.i.d error process We then examine the issues related to unit root testing for the presence of bubbles using standard econometric procedures. We illustrate as an example, the market for art, which shows distinctly bubble-like characteristics. Our results shed light on the ubiquitous finding of no bubbles in the econometric literature

Signalling the Dotcom bubble: a multiple changes in persistence approach

This study investigates multiple changes in persistence in the dividend-price and price-earnings ratio of the NASDAQ composite index. Recent time series methods that are capable of signalling and dating asset price bubbles are employed, in particular the method developed by Leybourne et al. (2007). The method allows for breaks between periods in which the data are integrated of order zero I(0) and integrated of order one I(1). The results confirm the existence of the so-called Dotcom bubble with its start and end dates. Furthermore, an unexpected negative bubble was also identified, extending from the beginning of the 1970s to the beginning of the 1990s, suggesting that the NASDAQ stock prices were below their fundamental values as indicated by their dividend yields, finding not previously reported in the literature. As the tools used by regulators take considerable time to take effect, methods capable of picking up warnings signals of the start of a bubble could be very useful. We conjecture that the methodology can also be applied to study recent phenomena in real estate, commodity and foreign exchange markets

Multiple changes in persistence vs. explosive behaviour: the Dotcom bubble

Based on a method developed by Leybourne, Kim and Taylor (2007) for detecting multiple changes in persistence, we test for changes in persistence in the dividend-price ratio of the NASDAQ stocks. The results confirm the existence of the so-called Dotcom bubble around the last turn of the century and its start and end dates. Furthermore, we compare the results with a test for detecting and date-stamping explosive unit-root behaviour developed by Phillips, Wu and Yu's (2011) also applied to the NASDAQ price and dividend indices. We find that Leybourne, Kim and Taylor's test is capable of detecting the Dotcom bubble as much as Phillips, Wu and Yu's test is, but there are significant differences between the bubble start and end dates suggested by both methods and between these and the dates reported by the financial media. We also find an unexpected negative bubble extending from the beginning of the 1970s to the beginning of the 1990s where the NASDAQ stock prices were below their fundamental values as indicated by their dividend yields, which has not been reported in the literature so far