Rational Bubbles and Fractional Alternatives

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.