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Testing for a rational bubble under long memory

  • Michael Frömmel
  • Robinson Kruse

We analyse the time series properties of the S&P500 dividend--price ratio in the light of long-memory, structural breaks and rational bubbles. We find an increase in the long-memory parameter in the early 1990s by applying a test recently proposed by Sibbertsen and Kruse [ J. Time Series Anal. , 2009, 30 , 263--285]. An application of the unit root test against long memory of Demetrescu et al. [ Econometr. Theory , 2008, 24 , 176--215] suggests that the pre-break data can be characterized by long memory, while the post-break sample contains a unit root. These results reconcile two empirical findings that are seen as contradictory: on the one hand, they confirm the existence of fractional integration in the S&P500 log-dividend--price ratio and, on the other, they are consistent with the existence of a rational bubble. The result of a changing memory parameter in the dividend--price ratio has an important implication for the literature on return predictability: the shift from a stationary dividend--price ratio to a unit root process in 1991 is likely to have caused the well-documented failure of conventional return prediction models since the 1990s.

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File URL: http://hdl.handle.net/10.1080/14697688.2011.578151
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Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

Volume (Year): 12 (2012)
Issue (Month): 11 (November)
Pages: 1723-1732

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Handle: RePEc:taf:quantf:v:12:y:2012:i:11:p:1723-1732
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