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Rational Bubbles and Fractional Alternatives


  • Andersson, Michael K.

    (Dept. of Economic Statistics, Stockholm School of Economics)

  • Nydahl, Stefan

    (Dept. of Economics, Uppsala University)


This paper suggests a new and more flexible framework for studying the existence of rational bubbles in stock prices. The present value model provides the robust no rational bubbles restriction of a stationary price-dividend ratio. The validity of this restriction has previously been investigated, but we extend the test procedure to allow for fractionally integrated alternatives. Thus, the price-dividend ratio may be a stationary process, where the mean-reversion is at a much slower (persistent) rate than that of stationary ARMA specifications. This pesistence may be hard to detect using traditional random walk tests. Indeed, when testing the no rational bubble restriction on US and Swedish data this distinction is important. For Sweden we conclude that the price-dividend ratio is ruled by a fractionally integrated process (no rational bubble), whereas it follows a unit root process for the US (a rational bubble). Using Dickey-Fuller type tests the unit root hypothesis cannot be rejected for any of the markets.

Suggested Citation

  • Andersson, Michael K. & Nydahl, Stefan, 1998. "Rational Bubbles and Fractional Alternatives," SSE/EFI Working Paper Series in Economics and Finance 266, Stockholm School of Economics.
  • Handle: RePEc:hhs:hastef:0266

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    Cited by:

    1. Golinski, Adam & Madeira, Joao & Rambaccussing, Dooruj, 2014. "Fractional Integration of the Price-Dividend Ratio in a Present-Value Model of Stock Prices," SIRE Discussion Papers 2015-79, Scottish Institute for Research in Economics (SIRE).
    2. Chaker Aloui, 2003. "Long-Range Dependence in Daily Volatility on Tunisian Stock Market," Working Papers 0340, Economic Research Forum, revised 12 2003.

    More about this item


    Present value models; Unit roots; Fractional Integration;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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