Empirical evidence shows that the order of integration of returns and dividend growth is approximately equal to the order of integration of the first-differenced price–dividend ratio, which is about 0.7. Yet the present-value identity implies that the three series should be integrated of the same order. We reconcile this puzzle by showing that the aggregation of antipersistent expected returns and expected dividends gives rise to a price–dividend ratio with properties that mimic long memory in finite samples. In an empirical implementation, we extend and estimate the state-space present-value model by allowing for fractional integration in expected returns and expected dividend growth. This extension improves the model’s forecasting power in-sample and out-of-sample. In addition, expected returns and expected dividend growth modeled as ARFIMA processes are more closely related to future macroeconomic variables, which makes them suitable as leading business cycle indicators.

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Price–dividend ratio,Persistence,Fractional integration,Return predictability,Present-value model

• Economics and Business - Social Sciences