Dundee Discussion Papers in Economics 284: Fractional integration of the price-dividend ratio in a present-value model of stock prices

We re-examine the dynamics of returns and dividend growth within the present-value framework of stock prices. We find that the finite sample order of integration of returns is approximately equal to the order of integration of the first-differenced price-dividend ratio. As such, the traditional return fore- casting regressions based on the price-dividend ratio are invalid. Moreover, the nonstationary long memory behaviour of the price-dividend ratio induces antipersistence in returns. This suggests that expected returns should be mod- elled as an ARF IM A process and we show this improves the forecast ability of the present-value model in-sample and out-of-sample.